# Showing papers in "International Journal of Numerical Methods for Heat & Fluid Flow in 2017"

Journal ArticleDOI
TL;DR: In this article, the entropy generation in natural convection of nanofluid in a wavy cavity using a single-phase model was analyzed using the finite difference method of the second-order accuracy.
Abstract: Purpose The main purpose of this numerical study is to study on entropy generation in natural convection of nanofluid in a wavy cavity using a single-phase nanofluid model. Design/methodology/approach The cavity is heated non-uniformly from the wavy wall and cooled from the right side while it is insulated from the horizontal walls. The physical domain of the problem is transformed into a rectangular geometry in the computational domain using an algebraic coordinate transformation by introducing new independent variables ξ and η. The governing dimensionless partial differential equations with corresponding initially and boundary conditions were numerically solved by the finite difference method of the second-order accuracy. The governing parameters are Rayleigh number (Ra = 1000-100000), Prandtl number (Pr = 6.82), solid volume fraction parameter of nanoparticles (φ = 0.0-0.05), aspect ratio parameter (A = 1), undulation number (κ = 1-3), wavy contraction ratio (b = 0.1-0.3) and dimensionless time (τ = 0-0.27). Findings It is found that the average Bejan number is an increasing function of nanoparticle volume fraction and a decreasing function of the Rayleigh number, undulation number and wavy contraction ratio. Also, an insertion of nanoparticles leads to an attenuation of convective flow and enhancement of heat transfer. Originality The originality of this work is to analyze the entropy generation in natural convection within a wavy nanofluid cavity using single-phase nanofluid model. The results would benefit scientists and engineers to become familiar with the flow behaviour of such nanofluids, and will be a way to predict the properties of this flow for the possibility of using nanofluids in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.

128 citations

Journal ArticleDOI

TL;DR: In this article, the authors proposed a simplified algorithm to solve the problem of conjugate heat transfer in porous medium by reducing the number of partial differential equations from four to three.
Abstract: Purpose The purpose of this paper is to highlight the advantages of a simplified algorithm to solve the problem of heat and mass transfer in porous medium by reducing the number of partial differential equations from four to three. Design/methodology/approach The approach of the present paper is to develop a simplified algorithm to reduce the number of equations involved in conjugate heat transfer in porous medium. Findings Developed algorithm/method has many advantages over conventional method of solution for conjugate heat transfer in porous medium. Research limitations/implications The current work is applicable to conjugate heat transfer problem. Practical implications The developed algorithm is useful in reducing the number of equations to be solved, thus reducing the computational resources required. Originality/value Development of simplified algorithm and comparison with conventional method.

66 citations

Journal ArticleDOI
Kamel Milani Shirvan
TL;DR: In this article, numerical solutions of surface radiation and combined natural convection heat transfer in a solar cavity receiver were presented by means of second-order upwind scheme using the SIMPLE algorithm.
Abstract: Purpose The purpose of this paper is to present the numerical solutions of surface radiation and combined natural convection heat transfer in a solar cavity receiver. The paper aims to discuss sundry issues that take place in the said model. Design/methodology/approach The numerical solutions are developed by means of second-order upwind scheme using the SIMPLE algorithm. Findings The effects of physical factors such as Rayleigh number (104 ≤ Ra ≤ 106), inclination angels of insulated walls (0o ≤ θ ≤ 10o) and the wall surface emissivity (0 ≤ e ≤ 1) on natural convection-surface radiation heat transfer rate are analyzed. Impact of sundry parameters on flow quantities are discussed and displayed via graphs and tables. Stream lines and isothermal lines have also been drawn in the region of cavity. The numerical results reveal that increasing the Rayleigh number, wall surface emissivity and inclination angels of insulated walls in an open cavity enhances the mean total Nusselt number. The variations of the surface radiation and natural convection heat transfer mean Nusselt numbers are very small to the inclination angle of θ, while a significant change is noted for the case of Rayleigh number and emissivity. Originality/value To the best of authors’ knowledge, this model is reported for the first time.

65 citations

Journal ArticleDOI
TL;DR: In this paper, the Soret and Dufour effects on the double-diffusive convective boundary layer flow of a nanofluid past a moving wedge in the presence of suction were investigated.
Abstract: Purpose The purpose of this study is to investigate the Soret and Dufour effects on the double-diffusive convective boundary layer flow of a nanofluid past a moving wedge in the presence of suction. Design/methodology/approach The similarity transformation is applied to convert the governing nonlinear partial differential equations into ordinary differential equations. Then, they are solved numerically by the fourth-order Runge–Kutta–Gill method along with the shooting technique and the Newton–Raphson method. In addition, the ordinary differential equations are also analytically solved by the homotopy analysis method. Findings The results for dimensionless velocity, temperature, solutal concentration and nanoparticle volume fraction profiles, as well as local skin friction coefficient and local Nusselt and local Sherwood numbers are presented through the plots for various combinations of pertinent parameters involved in the study. The heat transfer rate increases on increasing the Soret parameter and it decreases on increasing the Dufour parameter. The mass transfer behaves oppositely to heat transfer. Practical implication In engineering applications, a wedge is used to hold objects in place, such as engine parts in the gate valves. A gate valve is the valve that opens by lifting a wedge-shaped disc to control the timing and quantity of fluid flow into an engine. Originality/value No such investigation is available in literature, and therefore, the results obtained are novel.

62 citations

Journal ArticleDOI
TL;DR: In this paper, the authors explore a three-dimensional rotating flow of water-based nanofluids caused by an infinite rotating disk using the well-known Buongiorno model which accounts for the combined influence of Brownian motion and thermophoresis.
Abstract: Purpose The purpose of the present study is to explore a three-dimensional rotating flow of water-based nanofluids caused by an infinite rotating disk. Design/methodology/approach Mathematical formulation is performed using the well-known Buongiorno model which accounts for the combined influence of Brownian motion and thermophoresis. The recently suggested condition of passively controlled wall nanoparticle volume fraction has been adopted. Findings The results reveal that temperature decreases with an increase in thermophoresis parameter, whereas it is negligibly affected with a variation in the Brownian motion parameter. Axial velocity is negative because of the downward flow in the vertical direction. Originality/value Two- and three-dimensional streamlines are also sketched and discussed. The computations are found to be in very good agreement with the those of existing studies in the literature for pure fluid.

61 citations

Journal ArticleDOI
TL;DR: In this paper, the authors theoretically analyzed the laminar free convection heat transfer of nanofluids in a square cavity, where the sidewalls of the cavity are subject to temperature difference, whereas the bottom and top are insulated.
Abstract: Purpose The purpose of this study is to theoretically analyze the laminar free convection heat transfer of nanofluids in a square cavity The sidewalls of the cavity are subject to temperature difference, whereas the bottom and top are insulated Based on the available experimental results in the literature, two new non-dimensional parameters, namely, the thermal conductivity parameter (Nc) and dynamic viscosity parameter (Nv) are introduced These parameters indicate the augmentation of the thermal conductivity and dynamic viscosity of the nanofluid by dispersing nanoparticles Design/methodology/approach The governing equations are transformed into non-dimensional form using the thermo-physical properties of the base fluid The obtained governing equations are solved numerically using the finite element method The results are reported for the general non-dimensional form of the problem as well as case studies in the form of isotherms, streamlines and the graphs of the average Nusselt number Using the concept of Nc and Nv, some criteria for convective enhancement of nanofluids are proposed As practical cases, the effect of the size of nanoparticles, the shape of nanoparticles, the type of nanoparticles, the type of base fluids and working temperature on the enhancement of heat transfer are analyzed Findings The results show that the increase of the magnitude of the Rayleigh number increases of the efficiency of using nanofluids The type of nanoparticles and the type of the base fluid significantly affects the enhancement of using nanofluids Some practical cases are found, in which utilizing nanoparticles in the base fluid results in deterioration of the heat transfer The working temperature of the nanofluid is very crucial issue The increase of the working temperature of the nanofluid decreases the convective heat transfer, which limits the capability of nanofluids in decreasing the size of the thermal systems Originality/value In the present study, a separation line based on two non-dimensional parameters (ie Nc and Nv) are introduced The separation line demonstrates a boundary between augmentation and deterioration of heat transfer by using nanoparticles Indeed, by utilizing the separation lines, the convective enhancement of using nanofluid with a specified Nc and Nv can be simply estimated

59 citations

Journal ArticleDOI
TL;DR: In this article, the optimal conditions of mixed convection in a ventilated square cavity filled with Cu-water nanofluid using the Taguchi method were investigated for fixed Grashof number 104.
Abstract: Purpose The purpose of this paper is to study the optimal conditions of the mixed convection in a ventilated square cavity filled with Cu-water nanofluid using the Taguchi method. The paper aims to discuss diverse issues affecting the said model. Design/methodology/approach The numerical solutions of nonlinear coupled equations are developed by means of the Taguchi method. The Taguchi method is used as an effective way to optimize the design process engineering tests. Findings The governing equations are discretized using a finite volume method and solved with semi-implicit method for pressure linked equations (SIMPLE) algorithm. The effect of Richardson number (0.01-10), the volume fraction of nanofluid (0-5 per cent), distance of inlet port position from bottom wall of the cavity (0-0.9 H) and distance of outlet port position from top wall of the cavity (0-0.9 H) as effective parameters are analyzed across four levels. This analysis is done for fixed Grashof number 104. The results show that the mean Nusselt number almost decreases by an increase in the Richardson number, volume fraction of nanofluid, position of the inlet port and position of the outlet port. It is found that the cavity with distance of inlet port position from bottom wall of the cavity 0 and distance of outlet port position from upper wall of the cavity 0.9 H at the Richardson number 0.01 and the volume fraction 3 per cent is the optimal design for heat transfer. Originality/value As far as the authors know, this model has been investigated for the first time.

59 citations

Journal ArticleDOI

TL;DR: In this paper, the authors deal with the study of heat and mass transfer on double-diffusive three-dimensional hydromagnetic boundary layer flow of an electrically conducting Casson nanofluid over a stretching surface.
Abstract: Purpose This paper aims to deal with the study of heat and mass transfer on double-diffusive three-dimensional hydromagnetic boundary layer flow of an electrically conducting Casson nanofluid over a stretching surface. The combined effects of nonlinear thermal radiation, magnetic field, buoyancy forces, thermophoresis and Brownian motion are taken into consideration with convective boundary conditions. Design/methodology/approach Similarity transformations are used to reduce the governing partial differential equations into a set of nonlinear ordinary differential equations. The reduced equations were numerically solved using Runge–Kutta–Fehlberg fourth-fifth-order method along with shooting technique. Findings The impact of several existing physical parameters such as Casson parameter, mixed convection parameter, regular buoyancy ratio parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, temperature ratio parameter on velocity, temperature, solutal and nanofluid concentration profiles are analyzed through graphs and tables in detail. It is found that the solutal component increases for Dufour Lewis number, whereas it decreases for nanofluid Lewis number. Moreover, velocity profiles decrease for Casson parameter, while the Nusselt number increases for Biot number, radiation and temperature ratio parameter. Originality/value This paper is a new work related to three-dimensional double-diffusive flow of Casson nanofluid with buoyancy and nonlinear thermal radiation effect.

54 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied free convection of Casson fluid in a square differentially heated cavity taking into account the effects of thermal radiation and viscous dissipation, and found that an increase in Casson parameter leads to the heat transfer enhancement and fluid flow intensification.
Abstract: Purpose The main purpose of this numerical work is to study free convection of Casson fluid in a square differentially heated cavity taking into account the effects of thermal radiation and viscous dissipation. Design/methodology/approach The cavity is heated from the left vertical wall and cooled from the right vertical wall while horizontal walls are insulated. The governing partial differential equations invoking Rosseland approximation for thermal radiation with corresponding boundary conditions have been solved by finite difference method of the second-order accuracy using dimensionless variables stream function, vorticity and temperature. The governing parameters are Rayleigh number (Ra = 105), Prandtl number (Pr = 0.1, 0.7, 7.0), Casson parameter (γ = 0.1-5.0), radiation parameter (Rd = 0-10), Eckert number (Ec = 0-1.0). Findings It is found that an increase in Casson parameter leads to the heat transfer enhancement and fluid flow intensification. While a growth of Eckert number illustrates the heat transfer suppression. Originality/value The originality of this work is to analyze for the first-time natural convective fluid flow and heat transfer of a Casson fluid within a differentially heated square cavity under the effects of thermal radiation and viscous dissipation. The results would benefit scientists and engineers to become familiar with the flow behavior of such non-Newtonian fluids, and the way to predict the properties of this flow for possibility of using this specific fluid in various engineering and industrial processes, such as chyme movement in intestine, blood flows, lubrication processes with grease and heavy oils, glass blowing, electronic chips, food stuff, slurries, etc.

50 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the effect of sinusoidal heating on convective flow and heat transfer in a sinusoidally heated wavy porous cavity in the presence of internal heat generation or absorption.
Abstract: Purpose The purpose of this paper is to study natural convective flow and heat transfer in a sinusoidally heated wavy porous cavity in the presence of internal heat generation or absorption. Design/methodology/approach Sinusoidal heating is applied on the vertical left wall of the cavity, whereas the wavy right wall is cooled at a constant temperature. The top and bottom walls are taken to be adiabatic. The Darcy model is adopted for fluid flow through the porous medium in the cavity. The governing equations and boundary conditions are solved using the finite difference method over a range of amplitudes and number of undulations of the wavy wall, Darcy–Rayleigh numbers and internal heat generation/absorption parameters. Findings The results are presented in the form of streamlines, isotherms and Nusselt numbers for different values of right wall waviness, Darcy–Rayleigh number and internal heat generation parameter. The flow field and temperature distribution in the cavity are affected by the waviness of the right wall. The wavy nature of the cavity also enhances the heat transfer into the system. The heat transfer rate in the cavity decreases with an increase in the internal heat generation/absorption parameter. Research limitations/implications The present investigation is conducted for steady, two-dimensional natural convective flow in a wavy cavity filled with Darcy porous medium. The waviness of the right wall is described by the amplitude and number of undulations with a well-defined mathematical function. An extension of the present study with the effects of cavity inclination and aspect ratio will be the interest for future work. Practical implications The study might be useful for the design of solar collectors, room ventilation systems and electronic cooling systems. Originality/value This work examines the effects of sinusoidal heating on convective heat transfer in a wavy porous cavity in the presence of internal heat generation or absorption. The study might be useful for the design of solar collectors, room ventilation systems and electronic cooling systems.

48 citations

Journal ArticleDOI
TL;DR: In this article, a two-wave model was constructed for higher-order modified KdV equations and the essential conditions for multiple soliton solutions to exist were derived for nonlinearity and dispersion parameters.
Abstract: Purpose The purpose of this paper is concerned with developing two-mode higher-order modified Korteweg-de Vries (KdV) equations. The study shows that multiple soliton solutions exist for essential conditions related to the nonlinearity and dispersion parameters. Design/methodology/approach The proposed technique for constructing a two-wave model, as presented in this work, has been shown to be very efficient. The employed approach formally derives the essential conditions for soliton solutions to exist. Findings The examined two-wave model features interesting results in propagation of waves and fluid flow. Research limitations/implications The paper presents a new and efficient algorithm for constructing and studying two-wave-mode higher-order modified KdV equations. Practical implications A two-wave model was constructed for higher-order modified KdV equations. The essential conditions for multiple soliton solutions to exist were derived. Social implications The work shows the distinct features of the standard equation and the newly developed equation. Originality/value The work is original and this is the first time for two-wave-mode higher-order modified KdV equations to be constructed and studied.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the Newtonian heating and slip effect on mixed convective flow near a stagnation point in a porous medium with thermal radiation in the presence of magnetohydrodynamic (MHD), heat generation/absorption and chemical reaction.
Abstract: Purpose The purpose of this paper is to investigate the Newtonian heating and slip effect on mixed convective flow near a stagnation point in a porous medium with thermal radiation in the presence of magnetohydrodynamic (MHD), heat generation/absorption and chemical reaction. Design/methodology/approach The governing nonlinear coupled equations are converted into ordinary differential equations by similarity transformation. These equations are solved numerically using a Runge–Kutta–Fehlberg method with shooting technique and analytically using the homotopy analysis method (HAM). Findings The effects of different parameters on the fluid flow and heat transfer are investigated. It is found that the velocity and temperature profiles increase on an increase in the Biot number. The velocity and concentration profiles increase on decreasing the chemical reaction parameter. Practical implications This paper is helpful to the engineers and scientists in the field of thermal and manufacturing engineering. Originality/value The two-dimensional boundary layer flow over a vertical plate with slip and convective boundary conditions near the stagnation-point is analysed in the presence of magnetic field, radiation and heat generation/absorption. This paper is helpful to the engineers and scientists in the field of thermal and manufacturing engineering.

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed the 3D turbulent/transitional natural convection with different turbulence/transition models in a trapezoidal enclosure and compared their results with validated results.
Abstract: Purpose Because the local Re numbers, ratio of inertia to viscous forces, are not same at different regions of the enclosures, the present study aims to deal with the influences of using the turbulent/transition models on numerical results of the natural convection and flow field within a trapezoidal enclosure. Design/methodology/approach The three-dimensional (3D) trapezoidal enclosure with different inclined side walls of 75, 90 and 105 degrees are considered, where the side walls are heated and cooled at Ra = 1.5 × 109 for all cases. The turbulent models of the k-e-RNG, k- ω-shear-stress transport (SST) and the newly developed transition/turbulent model of Reθ-γ-transition SST are utilized to analyze the fluid flow and heat transfer characteristics within the enclosure and compared their results with validated results. Findings Comprehensive comparisons have been carried out for all cases in terms of flow and temperature fields, as well as turbulent quantities, such as turbulent kinetic energy and turbulent viscosity ratio. Furthermore, the velocity and thermal boundary layers have been investigated, and the approximate transition regions for laminar, transitional and turbulent regimes have been determined. Finally, the heat transfer coefficient and skin friction coefficient values have been presented and compared in terms of different turbulent models and configurations. The results show that the transition/turbulence model has better prediction for the flow and heat fields than fully turbulent models, especially for local parameters for all abovementioned governing parameters. Originality value The originality of this work is to analyze the 3D turbulent/transitional natural convection with different turbulence/transition models in a trapezoidal enclosure.

Journal ArticleDOI
TL;DR: In this article, the influence of the Brownian motion and thermophoresis on natural convection heat and mass transfer boundary layer flow of nanofluids over a vertical cone with radiation was analyzed.
Abstract: Purpose In recent years, nanofluids are being widely used in many thermal systems because of their higher thermal conductivity and heat transfer rate. The higher thermal conductivity depends on many parameters such as size, shape and volume and the Brownian motion and thermophoresis of added nanoparticles. The purpose of this paper is to analyze the influence of the Brownian motion and thermophoresis on natural convection heat and mass transfer boundary layer flow of nanofluids over a vertical cone with radiation. Design/methodology/approach Using similarity variables, the non-linear partial differential equations, which represent momentum, energy and diffusion, are transformed into ordinary differential equations. The transformed conservation equations are solved numerically subject to the boundary conditions by using versatile, extensively validated, variational finite-element method. Findings The sway of significant parameters such as magnetic field (M), buoyancy ratio parameter (Nr), Brownian motion parameter (Nb), thermophoresis parameter (Nt), thermal radiation (R), Lewis number (Le) and chemical reaction parameter (Cr) on velocity, temperature and concentration evaluation in the boundary layer region is examined in detail. The results are compared with previously published work and are found to be in agreement. The velocity distributions are reduced, while temperature and concentration profiles elevate with a higher (M). With the improving values of (R), the velocity and temperature sketches improve, while concentration distributions are lowered in the boundary layer region. The temperature and concentration profiles are elevated in the boundary layer region for higher values of (Nt). With the increasing values of (Nb), temperature profiles are enhanced, whereas concentration profiles get depreciated in the flow region. Social implications In recent years, it has been found that magneto-nanofluids are significant in many areas of science and technology. It has applications in optical modulators, magnetooptical wavelength filters, tunable optical fiber filters and optical switches. Magnetic nanoparticles are especially useful in biomedicine, sink float separation, cancer therapy, etc. Specific biomedical applications involving nanofluids include hyperthermia, magnetic cell separation, drug delivery and contrast enhancement in magnetic resonance imaging. Originality/value To the best of the authors’ knowledge, no studies have assessed the impact of the two slip effects, namely, Brownian motion and thermophoresis, on the natural convection of electrically conducted heat and mass transfer to the nanofluid boundary layer flow over a vertical cone in the presence of radiation and chemical reaction; therefore, this problem has been addressed in this study. Comparison of the results of this study’s with those of previously published work was found to be in good agreement.

Journal ArticleDOI
TL;DR: In this article, the authors presented a reliable treatment of the Fokas-Lenells equation, an integrable generalization of the nonlinear Schrodinger equation using a special complex envelope traveling-wave solution to carry out the analysis.
Abstract: Purpose The purpose of this paper is to present a reliable treatment of the Fokas–Lenells equation, an integrable generalization of the nonlinear Schrodinger equation The authors use a special complex envelope traveling-wave solution to carry out the analysis The study confirms the accuracy and efficiency of the used method Design/methodology/approach The proposed technique, namely, the trial equation method, as presented in this work has been shown to be very efficient for solving nonlinear equations with spatio-temporal dispersion Findings A class of chirped soliton-like solutions including bright, dark and kink solitons is derived The associated chirp, including linear and nonlinear contributions, is also determined for each of these optical pulses Parametric conditions for the existence of chirped soliton solutions are presented Research limitations/implications The paper presents a new efficient algorithm for handling an integrable generalization of the nonlinear Schrodinger equation Practical/implications The authors present a useful algorithm to handle nonlinear equations with spatial-temporal dispersion The method is an effective method with promising results Social/implications This is a newly examined model A useful method is presented to offer a reliable treatment Originality/value The paper presents a new efficient algorithm for handling an integrable generalization of the nonlinear Schrodinger equation

Journal ArticleDOI
TL;DR: In this article, the authors investigated the entropy generation due to magnetohydrodynamic natural convection flow and heat transfer in a porous enclosure filled with Cu-water nanofluid in the presence of viscous dissipation effect.
Abstract: Purpose This paper aims to investigate the entropy generation due to magnetohydrodynamic natural convection flow and heat transfer in a porous enclosure filled with Cu-water nanofluid in the presence of viscous dissipation effect. The left and right walls of the cavity are thermally insulated. There are heated and cold parts, and these are placed on the bottom and top wall, respectively, whereas the remaining parts are thermally insulated. Design/methodology/approach The finite volume method is used to solve the dimensionless partial differential equations governing the problem. A comparison with previously published woks is presented and is found to be in an excellent agreement. Findings The minimization of entropy generation and local heat transfer according to different values of the governing parameters are presented in details. It is found that the presence of magnetic field has negative effects on the local entropy generation because of heat transfer and the local total entropy generation. Also, the increase in the heated part length leads to a decrease in the local Nusselt number. Originality/value This problem is original, as it has not been considered previously.

Journal ArticleDOI
TL;DR: In this paper, the influence of second law analysis for electrically conducting fluid of a Casson nanofluid over a wedge was examined using a modified Arrhenius function.
Abstract: Purpose This paper aims to peruse the influence of second law analysis for electrically conducting fluid of a Casson nanofluid over a wedge. For activation energy, a modified Arrhenius function is used. Design/methodology/approach The highly non-linear governing equations are developed using similarity transformations and then computed numerically via Keller–Box method. Findings The influences of emerging parameters on velocity, temperature distribution and concentration of nanoparticle are explained and presented via graphs and tables. Also, the behavior of fluid flow is investigated through the coefficient of skin friction, Nusselt and Sherwood numbers. Results reveal that the velocity profile enhances due to increasing Casson parameter and magnetic parameter, whereas the temperature distribution and concentration of nanoparticle decrease with larger vales of Casson parameter. It is inspected that the concentration boundary layer increases due to activation energy and decreases due to reaction rate and temperature differences. Originality/value The authors believe that all the numerical results are original and significant which are used in biomedicine, industrial, electronics and transportation. The results have not been considered elsewhere.

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TL;DR: In this paper, the authors presented the key features of the fuzzy logic approach as a cost-effective technique in simulations of complex systems and then demonstrate the formulation and application of the method.
Abstract: Purpose The purpose of this paper is to first present the key features of the fuzzy logic (FL) approach as a cost-effective technique in simulations of complex systems and then demonstrate the formulation and application of the method. Design/methodology/approach The FL approach is used as an alternative method of data handling, considering the complexity of analytical and numerical procedures and high costs of empirical experiments. The distance from gas distributor, the temperature and the voidage of the bed, flue gas velocity and the load of the boiler are the input parameters, whereas the overall heat transfer coefficient for the membrane walls constitutes the output. Five overlapping sigmoid and constant linguistic terms are used to describe the input and the output data, respectively. The Takagi–Sugeno inference engine and the weighted average defuzzification methods are applied to determine the fuzzy and crisp output value, respectively. Findings The performed FL model allows predicting the bed-to-wall heat transfer coefficient in a large-scale 670 t/h circulating fluidized bed (CFB) boiler. The local heat transfer coefficients evaluated using the developed model are in very good agreement with the data obtained in complementary investigations. Originality/value The performed model constitutes an easy-to-use and functional tool. The new approach can be helpful for further research on the bed-to-wall heat transfer coefficient in the CFB units.

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TL;DR: In this article, the authors provided a solution for natural convection in a partially heated wavy cavity filled with a nanofluid using Buongiorno's model using finite difference method of the second order accuracy.
Abstract: Purpose The main purpose of this numerical work is to provide a solution for natural convection in a partially heated wavy cavity filled with a nanofluid using Buongiorno’s nanofluid model. Design/methodology/approach The domain of interest is a two-dimensional cavity bounded by an isothermal left wavy wall, adiabatic horizontal flat walls and right flat wall with a partial isothermal zone. In order to study the behaviour of the nanofluid, a two-phase Buongiorno’s mathematical model with the effects of the Brownian motion and thermophoresis is used. The governing dimensionless partial differential equations with corresponding boundary conditions were numerically solved by the finite difference method of the second order accuracy using the algebraic transformation of the physical wavy cavity to computational rectangular domain. The study has been conducted at the following values of the governing parameters: Ra = 104–106, Le = 10, Pr = 6.26, Nr = 0.1, Nb = 0.1, Nt = 0.1, A = 1,  = 1–3, b = 0.2, hhs/L = 0....

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TL;DR: In this article, a computational fluid dynamics (CFD)-based study on semicircular rib-roughened equilateral triangular duct is conducted to investigate heat transfer, friction factor and thermohydraulic performance parameter.
Abstract: Purpose The purpose of this computational fluid dynamics (CFD)-based study on semicircular rib-roughened equilateral triangular duct is to investigate heat transfer, friction factor and thermohydraulic performance parameter. The analysis is carried out by simulating problem in ANSYS (Fluent). The Reynolds number in the study varies from 4,000 to 24,000. Nusselt number is calculated for different Reynolds number using various turbulent models available in ANSYS (Fluent) for a smooth duct and compared the results with the Dittus–Boelter correlation. Design/methodology/approach The analysis has been done by solving basic fluid governing equations (continuity, momentum and energy) by using finite volume method (FVM). The semicircular ribs were fabricated on the absorber plate. The constant amount of heat flux is applied on the absorber plate, whereas other two walls are made adiabatic. The semi-implicit method for pressure linked equations (SIMPLE) algorithm is used with pressure–velocity-coupled disretization to estimate the results. The selection of turbulent model has been done on the basis of Nusselt number prediction in the smooth duct. Findings The renormalization-group k − e model predicts the Nusselt number more accurately as compared to standard k − e model, standard k − ω model, shear stress transport (SST) k − ω and realizable k − e model in the Reynolds number ranges from 4,000 to 24,000 with a ± 5.5% deviation from Dittus–Boelter equation for smooth duct. The maximum thermo-hydraulic performance is observed of the order of 1.7 for arrangement which has a relative roughness height of 0.067 and relative roughness pitch of 7.5 at higher Reynolds Number of 24,000. Originality/value Although, many experimental studies are available in the area of rib-roughened ducts, the present study is based on CFD analysis of semicircular rib-roughened equilateral triangular duct and the results are predicted in terms of Nusselt number, friction factor and thermohydraulic performance parameter. Moreover, the predicted result of Nusselt number and friction factor is validated by comparing with Dittus–Boelter correlation and modified Blasius equation, respectively. This advantage made Fluent a powerful tool for analyzing the internal fluid flow through roughened ducts.

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TL;DR: In this paper, the effects of heat source/sink, Soret and Dufour effects on chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium in the presence of cross-diffusion effects are investigated.
Abstract: Purpose The present investigation aims to deal with the study of unsteady, heat-generating/-absorbing and chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium in the presence of cross-diffusion effects. Design/methodology/approach A numerical computation for the governing equations has been performed using implicit finite difference method of Crank–Nicolson type. Findings The influence of various physical parameters on velocity, temperature and concentration distributions is illustrated graphically, and the physical aspects are discussed in detail. Numerical results for average skin-friction, Nusselt number and Sherwood number are tabulated for the pertaining physical parameters. Results indicate that Soret and Dufour effects have notable influence on heat and mass transfer characteristics of the fluid when the temperature and concentration gradients are high. It is also observed that the consideration of heat generation/absorption plays a vital role in predicting the heat transfer characteristics of moving fluids. Research limitations/implications Consider a two-dimensional, unsteady, free convective flow of an incompressible Casson fluid over a vertical cone and a flat plate saturated with non-Darcy porous medium. The fluid properties are assumed to be constant except for density variations in the buoyancy force term. The fluid flow is moderate and the permeability of the medium is assumed to be low, so that the Forchheimer flow model is applicable. Practical implications The flow of Casson fluids (such as drilling muds, clay coatings and other suspensions, certain oils and greases, polymer melts and many emulsions), in the presence of heat transfer, is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs. Social implications In the heat and mass transfer investigations, the Casson fluid model is found to be accurately applicable in many practical situations in the wings of polymer processing industries and biomechanics, etc.; some prominent examples are silicon suspensions, suspensions of bentonite in water and lithographic varnishes used for printing inks. Originality/value The motivation of the present study is to bring out the effects of heat source/sink, Soret and Dufour effects on chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium. The flow of Casson fluids (such as certain oils and greases, polymer melts and many emulsions) in the presence of heat transfer is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs. A numerical computation for the governing equations has been performed using implicit finite difference method of the Crank–Nicolson type.

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TL;DR: In this paper, the authors studied the problem of transient convection heat transfer in a trapezoidal cavity with spatial side-wall temperature variation and found that the heat transfer rate increases in non-uniform heating increments, whereby low wave number values are more affected by the convection.
Abstract: Purpose This paper aims to study analytically and numerically the problem of transient natural convection heat transfer in a trapezoidal cavity with spatial side-wall temperature variation. Design/methodology/approach The governing equations subject to the initial and boundary conditions are solved numerically by the finite difference scheme consisting of the alternating direction implicit method and the tri-diagonal matrix algorithm. The left sloping wall of the cavity is heated to non-uniform temperature, and the right sloping wall is maintained at a constant cold temperature, while the horizontal walls are kept adiabatic. Findings It is shown that the heat transfer rate increases in non-uniform heating increments, whereby low wave number values are more affected by the convection. The best heat transfer enhancement results from larger side wall inclination angle; however, trapezoidal cavities require longer time compared to that of square to reach steady state. Originality/value The study of natural convection heat transfer in a trapezoidal cavity filled with nanofluid and heated by spatial side-wall temperature has not yet been undertaken. Thus, the authors of the present study believe that this work is valuable.

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TL;DR: In this paper, a comparison of various transport-equation turbulence models and a study of the influence of the turbulent Prandtl number appearing in the formulation of turbulent heat flux are proposed.
Abstract: Purpose The aim of this work is to quantify the relative importance of the turbulence modelling for cavitating flows in thermal regime A comparison of various transport-equation turbulence models and a study of the influence of the turbulent Prandtl number appearing in the formulation of the turbulent heat flux are proposed Numerical simulations are performed on a cavitating Venturi flow for which the running fluid is freon R-114 and results are compared with experimental data Design/methodology/approach A compressible, two-phase, one-fluid Navier–Stokes solver has been developed to investigate the behaviour of cavitation models including thermodynamic effects The code is composed by three conservation laws for mixture variables (mass, momentum and total energy) and a supplementary transport equation for the volume fraction of gas The mass transfer between phases is closed assuming its proportionality to the mixture velocity divergence Findings The influence of turbulence model as regard to the cooling effect due to the vaporization is weak Only the k – e Jones–Launder model under-estimates the temperature drop The amplitude of the wall temperature drop near the Venturi throat increases with the augmentation of the turbulent Prandtl number Originality/value The interaction between Reynolds-averaged Navier–Stokes turbulence closure and non-isothermal phase transition is rarely studied It is the first time such a study on the turbulent Prandtl number effect is reported in cavitating flows

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TL;DR: In this article, the authors studied the effects of the Rayleigh number (Ra = 1e+04 -1e+06), heat source position (l/L = 0.05 -0.35) and dimensionless time (0 < tau < 100) on velocity and temperature fields, streamlines, isotherms and average Nusselt number at the heat source surface.
Abstract: Purpose The purpose of this paper is to study natural convective fluid flow and heat transfer inside a cubical cavity having a local heat source of constant temperature. Design/methodology/approach The cubical cavity is cooled from two vertical opposite walls and heated from the local heater mounted on the bottom wall, while the rest walls are adiabatic. The governing equations formulated in dimensionless vector potential functions and vorticity vector have been solved using implicit finite difference method of the second-order accuracy. The effects of the Rayleigh number (Ra = 1e+04 – 1e+06), heat source position (l/L = 0.05 – 0.35) and dimensionless time (0 < tau < 100) on velocity and temperature fields, streamlines, isotherms and average Nusselt number at the heat source surface have been analyzed. Findings It is found that the extreme left position of the heater (l/L = 0.05) illustrates more essential cooling of the cavity where the thermal plume over the heat source is suppressed by low temperature waves from the cold vertical walls. Originality/value The originality of this work is to analyze transient 3D natural convection in a cubical cavity with a heater of triangular shape and compare obtained 3D data with 2D results. It should be noted that for numerical simulation, the authors used vector potential function and vorticity vector that for transient problems allows to reduce the computational time. The results would benefit scientists and engineers to become familiar with the analysis of transient convective heat and mass transfer in 3D domains with local heaters, and the way to predict the properties of convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.

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TL;DR: In this article, exact solutions for the boundary layer flow of some nanofluids over porous stretching/shrinking surfaces with different configurations were worked out, where five types of nanoparticles together with the water as base fluid are under consideration, namely, Ag, Cu, CuO, Al2O3 and TiO2.
Abstract: Purpose This paper aims to working out exact solutions for the boundary layer flow of some nanofluids over porous stretching/shrinking surfaces with different configurations. To serve to this aim, five types of nanoparticles together with the water as base fluid are under consideration, namely, Ag, Cu, CuO, Al2O3 and TiO2. Design/methodology/approach The physical flow is affected by the presence of velocity slip as well as temperature jump conditions. Findings The knowledge on the influences of nanoparticle volume fraction on the practically significant parameters, such as the skin friction and the rate of heat transfer, for the above considered nanofluids, is easy to gain from the extracted explicit formulas. Originality/value Particularly, formulas clearly point that the heat transfer rate is not only dependent on the thermal conductivity of the material but it also highly relies on the heat capacitance as well as the density of the nanofluid under consideration.

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TL;DR: In this article, the authors analyzed numerical results for heat transfer through mixed convection in an incompressible steady lid-driven fluid flow inside a trapezoidal cavity in the presence of a uniform magnetic field.
Abstract: Purpose The purpose of this paper is to analyze numerical results for heat transfer through mixed convection in an incompressible steady lid-driven fluid flow inside a trapezoidal cavity in the presence of a uniform magnetic field. Design/methodology/approach In this study, the authors have considered three different cases, in which left and right walls of the cavity are tilted at different angles of 0, 30 and 45 degrees, respectively. Both left and right side walls of the cavity are taken cold and the upper wall is insulated and assumed moving with constant speed, whereas the bottom wall is considered to be heated uniformly/non-uniformly. To eliminate pressure term, penalty method is applied to governing Navier–Stokes’ equations. The reduced equations are solved by Galerkin weighted residual technique of finite element method. Grid-independent results are obtained and shown in terms of plots for streamlines, isotherms, Nusselt number and average Nusselt number for a wide range of flow parameters, including Rayleigh numbers Ra, Prandtl number Pr and Hartman number Ha. Findings It has been observed that the effects of moving lid become negligible for Ra = 100,000, whereas increasing Rayleigh number results in stronger streamline circulation and convection dominant effects inside the enclosure. Local Nusselt number Nu along the bottom wall is observed to be maximum at edges and it reduces while moving toward the center from edges, and attains minimum value at the center of the bottom wall. Research limitations/implications The problem is modeled for laminar and incompressible flow, induced magnetic field has been considered negligibly small and local thermal equilibrium has been assumed. Originality/value In this investigation, the authors have presented new and original results for mixed convection flow inside a lid-driven trapezoidal cavity under the influence of a magnetic field. Hence, this study would be important for the researchers working in the area of heat transfer in cavity flows involving magnetic effects to become familiar with the flow behavior and properties.

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TL;DR: In this paper, the authors performed a numerical study for heat transfer through natural convection in the presence of a constant magnetic field in an incompressible steady nanofluid flow inside an isosceles triangular cavity.
Abstract: Purpose The purpose of this paper is to perform a numerical study for heat transfer through natural convection in the presence of a constant magnetic field in an incompressible steady nanofluid flow inside an isosceles triangular cavity. Design/methodology/approach For this flow problem, the left wall of the cavity subjected to uniform/nonuniform heat was considered, while right and bottom walls of the cavity were kept cold. The obtained equations were solved by using the Galerkin weighted residual technique. Results are computed for a wide range of parameters including Rayleigh number (Ra) (10^3 < Ra < 10^7), Hartman number (Ha) (0 < Ha < 60), and heat-generation/-absorption coefficient (q) (−10 < q < 10), while, Prandtl number (Pr) was kept fixed at 6.2. These computed results are presented in terms of stream functions, isotherms, Nusselt numbers and average Nusselt numbers through figures. Findings It is observed that, in case of uniform heating of the side wall, the strength of stream lines’ circulations increases with an increase in Ra and decreases with an increase in Ha. Similarly, by increasing heat-absorption coefficient q, an increase in the circulation strength is noted and the circulation cell moves towards the left wall in the presence of a heat sink (q 0). In the case of nonuniformly heated left wall in the presence of a heat source (q > 0), a higher-temperature gradient is observed in the cavity and isotherms are clustered to the left wall in the lower portion and to right wall in the upper portion; these appear to be straight and parallel to the x-axis near the bottom wall. On the other hand, the heat transfer rate along all the walls of the cavity is observed to be higher for smaller values of q. Whereas, Nusselt number along the bottom wall (Nu-B) increases with an increase in the values of x, while, that along the left wall (Nu-L) first increases and then decreases. But Nusselt number along the right wall (Nu-R) is found to be qualitatively opposite to Nu-L with an increase in distance x. Whereas, average Nusselt number increases with an increase in Rayleigh number Ra and heat-generation/-absorption coefficient q. Research limitations/implications The problem is formulated for an incompressible flow; viscous dissipation has been neglected, negligible induced magnetic field has been considered and local thermal equilibrium has been considered. Originality/value Results presented in this paper are original and new for the effects of a uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity. Hence, this study is important for researchers working in the area of heat transfer in cavity flows involving the nanofluid to become familiar with the flow behavior and properties.

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TL;DR: In this paper, the effects of Brownian motion and thermophoresis in a square cavity by considering it pure fluid as well as porous cavity were analyzed by a finite element method.
Abstract: Purpose Nanofluids are widely used in heat transfer phenomena owing to the higher rate of heat removal as compared to their base fluids. Nanoparticle’s motion in nanofluids is analysed by slip mechanisms that consider physical properties, which can be found in literature. It is assumed that among few, only Brownian motion and thermophoresis affect the slip mechanism to produce a relative velocity between the nanoparticles and the base fluid. The purpose of this paper is to study the effects of Brownian motion and thermophoresis in a square cavity by considering it pure fluid as well as porous cavity. Design/methodology/approach A finite element method is used to solve the flow porous equations together with the heat transfer equation and the mass transfer equation numerically. The heat and mass transfer equations were modified to take into consideration the Brownian motion as well as the thermophoresis effect. Findings A negligible amount of Brownian motion and thermophoresis effect has been found by considering 1 to 3 Vol.% of aluminium oxide as nanoparticles suspended in base fluid of water. Practical implications This study has provided an interesting insight into the importance of Brownian motion as well as the thermophoresis effect in heat enhancement. Originality/value The present study is believed to be an interesting and original contribution on nanofluid thermal behaviours.

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TL;DR: In this article, the authors presented a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain, which is based on Pade-approximation and homotopy-pade technique.
Abstract: Purpose The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. This method, which is based on Pade-approximation and homotopy–Pade technique, is applied to a model of magnetohydrodynamic Falkner–Skan flow as well. These examples indicate that the method can be successfully applied to solve nonlinear differential equations arising in science and engineering. Design/methodology/approach Homotopy–Pade method. Findings The main focus of the paper is on the prediction of the multiplicity of the solutions, however we have calculated multiple (dual) solutions of the model problem namely, mixed convection heat transfer in a porous medium. Research limitations/implications The authors conjecture here that the combination of traditional–Pade and Hankel–Pade generates a useful procedure to predict multiple solutions and to calculate prescribed parameter with acceptable accuracy as well. Validation of this conjecture for other further examples is a challenging research opportunity. Social implications Dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. Originality/value In this study, the authors are using two modified methods.

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TL;DR: In contrast to the various complicated numerical or analytical approximate procedures existing in the literature used to approximate the temperature field over a porous fin, this study outlines a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature fields.
Abstract: Purpose The purpose of this study is to target the solution of nonlinear porous fin problem. In contrast to the various complicated numerical or analytical approximate procedures existing in the literature used to approximate the temperature field over a porous fin, this study outlines a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field. Design/methodology/approach This study uses a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field. Findings Explicit closed-form formulae for the fin tip temperature as well as for the heat transfer rate, hence for the fin efficiency, which are functions of the porosity parameter and Biot number, are provided. The thresholds and the convergence regions regarding the physical parameters of the resulting approximations are easy to determine from the residual formula. Originality/value The novelty of the method is that the accuracy of the solution is controllable and can be gained up to any significant digit of desire by increasing the number of terms in the series solution.