Showing papers in "International Journal of Numerical Methods for Heat & Fluid Flow in 2020"

Effects of magnetic field on micro cross jet injection of dispersed nanoparticles in a microchannel

Abstract: Purpose Water/Al 2 O 3 nanofluid with volume fractions of 0, 0.3 and 0.06 was investigated inside a rectangular microchannel. Jet injection of nanofluid was used to enhance the heat transfer under a homogeneous magnetic field with the strengths of Ha = 0, 20 and 40. Both slip velocity and no-slip boundary conditions were used. Design/methodology/approach The laminar flow was studied using Reynolds numbers of 1, 10 and 50. The results showed that in creep motion state, the constricted cross section caused by fluid jet is not observable and the rise of axial velocity level is only because of the presence of additional size of the microchannel. By increasing the strength of the magnetic field and because of the rise of the Lorentz force, the motion of fluid layers on each other becomes limited. Findings Because of the limitation of sudden changes of fluid in jet injection areas, the magnetic force compresses the fluid to the bottom wall, and this behavior limits the vertical velocity gradients. In the absence of a magnetic field and under the influence of the velocity boundary layer, the fluid motion has more variations. In creeping velocities of fluid, the presence or absence of the magnetic field does not have an essential effect on Nusselt number enhancement. Originality/value In lower velocities of fluid, the effect of the jet is not significant, and the thermal boundary layer affects the entire temperature field. In this case, for Hartmann numbers of 40 and 0, changing the Nusselt number on the heated wall is similar.

A short review on analytical methods for a fully fourth-order nonlinear integral boundary value problem with fractal derivatives

Abstract: This paper aims to review some effective methods for fully fourth-order nonlinear integral boundary value problems with fractal derivatives.,Boundary value problems arise everywhere in engineering, hence two-scale thermodynamics and fractal calculus have been introduced. Some analytical methods are reviewed, mainly including the variational iteration method, the Ritz method, the homotopy perturbation method, the variational principle and the Taylor series method. An example is given to show the simple solution process and the high accuracy of the solution.,An elemental and heuristic explanation of fractal calculus is given, and the main solution process and merits of each reviewed method are elucidated. The fractal boundary value problem in a fractal space can be approximately converted into a classical one by the two-scale transform.,This paper can be served as a paradigm for various practical applications.

Second law analysis of magneto-natural convection in a nanofluid filled wavy-hexagonal porous enclosure

Abstract: Natural convection heat transfer analysis can be completed using entropy generation analysis. This study aims to accomplish both the natural convection heat transfer and entropy generation analyses for a hexagonal cavity loaded with Cu-H2O nanoliquid subjected to an oriented magnetic field.,Control volume-based finite element method is applied to solve the non-dimensional forms of governing equations and then, the entropy generation number is computed.,The results portray that both the average Nusselt and entropy generation numbers boost with increasing aspect ratio for each value of the undulation number, while both of them decrease with increasing the undulation number for each amplitude parameter. There is a maximum value for the entropy generation number at a specified value of Hartmann number. Also, there is a minimum value for the entropy generation number at a specified value of angle of the magnetic field. When the volume fraction of nanoparticles grows, the average Nusselt number increases and the entropy generation number declines. The entropy generation number attains to a maximum value at Ha = 14 for each value of aspect ratio. The average Nusselt number ascends 2.9 per cent and entropy generation number decreases 1.3 per cent for Ha = 0 when ϕ increases from 0 to 4 per cent.,A hexagonal enclosure (complex geometry), which has many industrial applications, is chosen in this study. Not only the characteristics of heat transfer are investigated but also entropy generation analysis is performed in this study. The ecological coefficient of performance for enclosures is calculated, too.

Investigation of micropolar hybrid ferrofluid flow over a vertical plate by considering various base fluid and nanoparticle shape factor

Abstract: The purpose of this paper is to investigate micropolar magnetohydrodynamics (MHD) fluid flow passing over a vertical plate. Three different base fluids have been used that include water, ethylene glycol and ethylene glycol/water (50%–50%). Also, a nanoparticle was used in all of the base fluids. The effects of natural convection heat transfer and magnetic field have been taken into account.,The main purpose of solving the governing equations is to scrutinize the effects of the magnetic parameter, the nanoparticle volume fraction, micropolar parameter and nanoparticles shape factor on velocity, temperature and microrotation profiles, the skin friction coefficient and the Nusselt number. These surveys have been considered for three base fluids simultaneously.,The results indicate that for water-based fluids, the temperature profile of lamina-shaped nanoparticles is 38.09% higher than brick-shaped nanoparticles.,This paper provides micropolar MHD fluid flow analysis considering natural convection heat transfer and magnetic field in three different base fluids. The aim of assessments is the diagnosis of some parameter effects, such as magnetic parameter and nanoparticle volume fraction, on velocity, temperature and microrotation profiles and components. Also, the use of mixed base fluids presented as a novelty in this paper.

A general numerical algorithm for nonlinear differential equations by the variational iteration method

Abstract: The purpose of this paper is to suggest a general numerical algorithm for nonlinear problems by the variational iteration method (VIM).,Firstly, the Laplace transform technique is used to reconstruct the variational iteration algorithm-II. Secondly, its convergence is strictly proved. Thirdly, the numerical steps for the algorithm is given. Finally, some examples are given to show the solution process and the effectiveness of the method.,No variational theory is needed to construct the numerical algorithm, and the incorporation of the Laplace method into the VIM makes the solution process much simpler.,A universal iteration formulation is suggested for nonlinear problems. The VIM cleans up the numerical road to differential equations.

MHD flow and heat transfer of hybrid nanofluid over a permeable moving surface in the presence of thermal radiation

Abstract: This paper aims to investigate the flow and heat transfer characteristics of a hybrid nanofluid (Cu-Al2O3/water) in the presence of magnetohydrodynamics and thermal radiation over a permeable moving surface.,By choosing appropriate similarity variables, the partial differential equations are transformed into a system of linear equations which are solved by using the boundary value problem solver (bvp4c) in MATLAB. The implementation of stability analysis verifies the achievable result of the first solution which is considered stable while the second solution is unstable.,The findings revealed that the presence of a magnetic field and suction slows down the fluid motion because of the synchronism of the magnetic and electric field occurred from the formation of the Lorentz force. Also, the enhancement of the thermal radiation parameter escalates the heat transfer rate of the current study.,The present study is addressing the problem of MHD flow and heat transfer analysis of a hybrid nanofluid towards a permeable moving surface, with the consideration of the thermal radiation effect. The authors show that in both cases of assisting and opposing flow, there exist dual solutions within a specific range of the moving parameters. A stability analysis approved that only one of the solutions are physically relevant.

TiO2-Ag/blood hybrid nanofluid flow through an artery with applications of drug delivery and blood circulation in the respiratory system

Abstract: As transferring biological fluid through an artery is nowadays a pivotal subject, the purpose of this paper is to study the mathematical model of hybrid nanofluid flow comprising pure blood as base fluid and TiO2 and Ag as nanoparticles through the porous channel, which can be an applicable model for drug delivery.,Both walls of the channel have different permeability, which enables the fluid to enter and exit, and variable height, which dilates and squeezes at the uniform rate. By taking advantage of the similarity transformation technique, governing equations have been converted into a system of the non-linear ordinary differential equation. This problem is solved numerically by utilizing BVP4C built-in function in MATLAB software to explore the impacts of pertinent parameters.,The plots of velocity and temperature profile, normal pressure distribution and wall shear stress, as well as Nusselt number for involved parameters, are presented and the logic and physical reasons beyond them are highlighted. It has been observed that the asymmetry of the channel, caused by different permeability at walls, affects the nature of flow significantly.,To the best of the authors’ knowledge, no one has ever attempted to study the flow through a deformable porous channel with blood as a base fluid and as hybrid nanoparticles to describe medical phenomena and treatment applications. Indeed, the achievements of this paper are purely original and the numerical results were never published by any researcher.

Numerical simulation of time-fractional partial differential equations arising in fluid flows via reproducing Kernel method

Abstract: The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this paper is to present results on the numerical simulation for time-fractional partial differential equations arising in transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types.,Those resulting mathematical models are solved by using the reproducing kernel method, which provide appropriate solutions in term of infinite series formula. Convergence analysis, error estimations and error bounds under some hypotheses, which provide the theoretical basis of the proposed method are also discussed.,The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the prospects of the gained results and the method are discussed through academic validations.,In this paper and for the first time: the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows. The authors applied the reproducing kernel method systematically for the numerical solutions of time-fractional Tricomi and Keldysh equations subject to Robin functions types.

Simulation of water/FMWCNT nanofluid forced convection in a microchannel filled with porous material under slip velocity and temperature jump boundary conditions

Abstract: Purpose This study aims to numerically study the forced convection effects on a two-dimensional microchannel filled with a porous material containing the water/FMWCNT nanofluid. The upper and lower microchannel walls were fully insulated thermally along 15 per cent of their lengths at each end of the microchannel, with the in-between length being exposed to a constant temperature. The slip velocity boundary condition was applied along the microchannel walls. Design/methodology/approach The Navier–Stokes equations were discretized before being solved numerically via a FORTRAN computer code. The following ranges were considered for the studied parameters: slip factor (B) equal to 0.001, 0.01 and 0.1; Reynolds number (Re) between 10 and 100; solid nanoparticle mass fraction (ϕ) between 0.0012 and 0.0025; Darcy number (Da) between 0.001 and 0.1; and porosity factor (e) between 0.4 and 0.9. Findings Increasing the Da caused a greater increase in the velocity profile than increasing Re, whereas increasing porosity did not affect the velocity profile growth at all. Originality/value This paper is the continuation of the authors’ previous studies. Using the water/FMWCNT nanofluid as the working fluid in microchannels is among the achievements of this study.

Blood flow of MHD non-Newtonian nanofluid with heat transfer and slip effects: Application of bacterial growth in heart valve

Abstract: This paper aims to investigate a mathematical model with numerical simulation for bacterial growth in the heart valve.,For antibacterial activities and antibodies properties, nanoparticles have been used. As antibiotics are commonly thought to be homogeneously dispersed through the blood, therefore, non-Newtonian fluid of Casson micropolar blood flow in the heart valve for two dimensional with variable properties is used. The heat transfer with induced magnetic field translational attraction under the influence of slip is considered for the resemblance of the heart valve prosthesis. The numeral results have been obtained by using the Chebyshev pseudospectral method.,It is proven that vascular resistance decreases for increasing blood velocity. It is noted that when the magnetic field will be induced from the heart valve prosthesis then it may cause a decrease in vascular resistance. The unbounded molecules and antibiotic concentration that are able to penetrate the bacteria are increased by increasing values of vascular resistance. The bacterial growth density cultivates for upswing values of magnetic permeability and magnetic parameters.,To the best of the authors’ knowledge, this is the first study to investigate a mathematical model with numerical simulation for bacterial growth in the heart valve.

A computational analysis of heat transport irreversibility phenomenon in a magnetized porous channel

Abstract: The purpose of this paper is to evaluate the temperature, the Dirichlet conditions have been considered to the parallel horizontal plates. The model of generalized Brinkman-extended Darcy with the Boussinesq approximation is considered and the governing equations are computed by COMSOL multiphysics.,In the current study, the thermodynamic irreversible principle is applied to study the unsteady Poiseuille–Rayleigh–Benard (PRB) mixed convection in a channel (aspect ratio A = 5), with the effect of a uniform transverse magnetic field.,The effects of various flow parameters on the fluid flow, Hartmann number (Ha), Darcy number (Da), Brinkman number (Br) and porosity (e), are presented graphically and discussed. Numerical results for temperature and velocity profiles, entropy generation variations and contour maps of streamlines, are presented as functions of the governing parameter mentioned above. Basing on the generalized Brinkman-extended Darcy formulation, which allows the satisfaction of the no-slip boundary condition on a solid wall, it is found that the flow field and then entropy generation is notably influenced by the considering control parameters. The results demonstrate that the flow tends toward the steady-state with four various regimes, which strongly depends on the Hartman and Darcy numbers variations. Local thermodynamic irreversibilities are more confined near the active top and bottom horizontal walls of the channel when increasing the Da and decreasing the Hartmann number. Entropy generation is also found to be considerably affected by Brinkman number variation.,In the present work, we are presenting our investigations on the influence of a transverse applied external magnetohydrodynamic on entropy generation at the unsteady laminar PRB flow of an incompressible, Newtonian, viscous electrically conducting binary gas mixture fluid in porous channel of two horizontal heated plates. The numerical solutions for the liquid velocity, the temperature distribution and the rates of heat transport and entropy generation are obtained and are plotted graphically.

Hydrodynamic and thermal analysis of water, ethylene glycol and water-ethylene glycol as base fluids dispersed by aluminum oxide nano-sized solid particles

Abstract: The purpose of this paper is to carry out a hydrodynamic and thermal analysis of turbulent forced-convection flows of pure water, pure ethylene glycol and water-ethylene glycol mixture, as base fluids dispersed by Al2O3 nano-sized solid particles, through a constant temperature-surfaced rectangular cross-section channel with detached and attached obstacles, using a computational fluid dynamics (CFD) technique. Effects of various base fluids and different Al2O3 nano-sized solid particle solid volume fractions with Reynolds numbers ranging from 5,000 to 50,000 were analyzed. The contour plots of dynamic pressure, stream-function, velocity-magnitude, axial velocity, transverse velocity, turbulent intensity, turbulent kinetic energy, turbulent viscosity and temperature fields, the axial velocity profiles, the local and average Nusselt numbers, as well as the local and average coefficients of skin friction, were obtained and investigated numerically.,The fluid flow and temperature fields were simulated using the Commercial CFD Software FLUENT. The same package included a preprocessor GAMBIT which was used to create the mesh needed for the solver. The RANS equations, along with the standard k-epsilon turbulence model and the energy equation were used to control the channel flow model. All the equations were discretized by the finite volume method using a two-dimensional formulation, using the semi-implicit method for pressure-linked equations pressure-velocity coupling algorithm. With regard to the flow characteristics, the interpolation QUICK scheme was applied, and a second-order upwind scheme was used for the pressure terms. The under-relaxation was changed between the values 0.3 and 1.0 to control the update of the computed variables at each iteration. Moreover, various grid systems were tested to analyze the effect of the grid size on the numerical solution. Then, the solutions are said to be converging when the normalized residuals are smaller than 10-12 and 10-9 for the energy equation and the other variables, respectively. The equations were iterated by the solver till it reached the needed residuals or when it stabilized at a fixed value.,The result analysis showed that the pure ethylene glycol with Al2O3 nanoparticles showed a significant heat transfer enhancement, in terms of local and average Nusselt numbers, compared with other pure or mixed fluid-based nanofluids, with low-pressure losses in terms of local and average skin friction coefficients.,The present research ended up at interesting results which constitute a valuable contribution to the improvement of the knowledge basis of professional work through research related to turbulent flow forced-convection within channels supplied with obstacles, and especially inside heat exchangers and solar flat plate collectors.

Magneto-thermal-convection stability in an inclined cylindrical annulus filled with a molten metal

Abstract: Metal-cooled reactors generally use molten metals such as sodium, potassium or a combination of sodium and potassium because of their excellent heat transfer properties so that the reactor can operate at much lower pressures and higher temperatures. The purpose of this paper is to investigate the stability of natural convection in an inclined ring filled with molten potassium under the influence of a radial magnetism.,A numerical simulation of electrically conductive fluid natural convection stability is performed on an inclined cylindrical annulus under the influence of a radial magnetism. The upper and lower walls are adiabatic, while the internal and external cylinders are kept at even temperatures. The equations governing this fluid system are solved numerically using finite volume method. The SIMPLER algorithm is used for pressure-speed coupling in the momentum equation.,Numerical results for various effective parameters that solve the problem in the initial oscillatory state are discussed in terms of isobars, isotherms and flow lines in the annulus for a wide range of Hartmann numbers (0 ≤ Ha ≤ 80), inclination angles (0 ≤ γ ≤ 90°) and radii ratios λ ≤ 6. The dependency stability diagrams between complicated situations with the critical value of the Rayleigh number RaCr and the corresponding frequency FrCr are established on the basis of the numeric data of this investigation. The angle of inclination and the radii ratio of the annulus have a significant effect on the stabilization of the magneto-convective flux and show that the best stabilization of the natural oscillatory convection is obtained by the intensity of the strongest magnetic field, the high radii ratio and inclination of the annulus at γ = 30°.,This numerical model is selected for its various applications in technology and industry.,To the best of the authors’ knowledge, the influence of the inclination of the cylindrical annulus (ring), with various radii ratio, on natural oscillatory convection under a radial magnetism has never been investigated.

Dufour and Soret effects on Darcy-Forchheimer flow of second-grade fluid with the variable magnetic field and thermal conductivity

Abstract: This study aims to investigate the effect of two-dimensional Darcy-Forchheimer flow over second-grade fluid with linear stretching. Heat transfer through convective boundary conditions is taken into account.,Nonlinear coupled governing equations are tackled with a homotopy algorithm, while for numerical computation the computer software package BVPh 2.0 is used. The convergence analysis is also presented for the validation of analytical and numerical results.,Valuation for the impact of key parameters such as variable thermal conductivity, Dufour and Soret effects and variable magnetic field in an electrically conducted fluid on the velocity, concentration and temperature profiles are graphically illustrated. It is observed from the results that temperature distribution rises by Dufour number whereas concentration distribution rises by Soret number. The Forchheimer number and porosity parameter raise the skin friction coefficient. The permeable medium has a vital impact and can help in reining the rate of heat transfer.,The permeable medium has a vital impact and can help in reining the rate of heat transfer.,To the best of the authors’ knowledge, this study is reported for the first time.

Impact of nano-particles shapes on Al2O3-water nano-fluid flow due to a stretching cylinder

Abstract: The purpose of this study is to theoretically probe the shape impacts of nano-particle on boundary layer flow of nano-fluid toward a stretching cylinder with heat-transmission effects. The base fluid used for this study is pure water, and aluminum oxide nano-particles are suspended in it. Four different shapes of nano-particle, namely, cylindrical, brick, platelets and blades, are considered to carry out the study.,The problem is modelled mathematically and the nonlinear system of equations is attained by using appropriate transmutations. The solution of transmuted equations is achieved by utilizing a shooting technique with Fourth-Fifth order Runge–Kutta Fehlberg scheme. Numerically attained results are elucidated through graphs and tables which are further compared under limiting cases with existing literature to check the validity of the results.,It is observed that fluid velocity and temperature of cylindrical shaped water nano-fluids are more than the nano-fluid having brick-shaped nano-particles. Moreover, it is seen that the nano-fluids suspended with platelets-shaped nano-particles have higher velocity and temperature than the nano-fluids containing blade-shaped nano-particles. The curvature parameter and nano-particles volume fraction have increasing effects on flow velocity and temperature of nano-fluids containing all types of nano-particle shapes.,Numerous authors have examined the impacts of nano-particle shapes on characteristics of heat transfer and fluid flow. However, to the best of the authors’ knowledge, the shape impacts of nano-particles on boundary layer flow of nano-fluid toward a stretching cylinder with heat-transmission effects have not been discussed. So, to fulfill this gap, the present paper explicates the impacts of various nano-particle shapes on Al2O3–water-based nano-fluid flow past a stretching cylinder with heat-transfer effects.

Hybrid nanofluid flow towards a stagnation point on an exponentially stretching/shrinking vertical sheet with buoyancy effects

Abstract: This paper aims to examine the hybrid nanofluid flow towards a stagnation point on an exponentially stretching/shrinking vertical sheet with buoyancy effects.,Here, the authors consider copper (Cu) and alumina (Al2O3) as hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions.,The authors found that the heat transfer rate is greater for Al2O3-Cu/water hybrid nanofluid if compared to Cu/water nanofluid. Besides, the non-uniqueness of the solutions is observed for certain physical parameters. The authors also notice that the bifurcation of the solutions occurs in the downward buoyant force and the shrinking regions. In addition, the first solution of the skin friction and heat transfer coefficients increase with the added hybrid nanoparticles and the mixed convection parameter. The temporal stability analysis shows that one of the solutions is stable as time evolves.,The present work is dealing with the problem of a mixed convection flow of a hybrid nanofluid towards a stagnation point on an exponentially stretching/shrinking vertical sheet, with the buoyancy effects is taken into consideration. The authors show that two solutions are obtained for a single value of parameter for both stretching and shrinking cases, as well as for both buoyancy aiding and opposing flows. A temporal stability analysis then shows that only one of the solutions is stable and physically reliable as time evolves.

A new fractal model for the soliton motion in a microgravity space

Abstract: On a microgravity condition, a motion of soliton might be subject to a microgravity-induced motion There is no theory so far to study the effect of air density and gravity on the motion property Here, the author considers the air as discrete molecules and a motion of a soliton is modeled based on He’s fractal derivative in a microgravity space The variational principle of the alternative model is constructed by semi-inverse method The variational principle can be used to establish the conservation laws and reveal the structure of the solution Finally, its approximate analytical solution is found by using two-scale method and homotopy perturbation method (HPM),The author establishes a new fractal model based on He’s fractal derivative in a microgravity space and its variational principle is obtained via the semi-inverse method The approximate analytical solution of the fractal model is obtained by using two-scale method and HPM,He’s fractal derivative is a powerful tool to establish a mathematical model in microgravity space The variational principle of the fractal model can be used to establish the conservation laws and reveal the structure of the solution,The author proposes the first fractal model for the soliton motion in a microgravtity space and obtains its variational principle and approximate solution

FEM-CBS algorithm for convective transport of nanofluids in inclined enclosures filled with anisotropic non-Darcy porous media using LTNEM

Abstract: The Galerkin finite element method (FEM) based on the characteristic-based split (CBS) scheme is applied to simulate the nanofluid flow and thermal fields inside an inclined geometry filled by a heat-generating hydrodynamically and thermally anisotropic non-Darcy porous medium using the local thermal non-equilibrium model (LTNEM) Property of the hydrodynamic anisotropy is taken in both the Forchheimer coefficient and permeability and these tools are considered as functions of inclination of the principal axes Also, the thermal conductivity for the porous phase is assumed to be anisotropic,The Galerkin FEM based on the CBS scheme is applied to solve the partial differential equations governing the flow and thermal fields,It is noted that the net rate of the heat transfer between the nanofluid and solid phases are influenced by variations of the anisotropic properties Also, the system is reached to the thermal equilibrium state at H > 100 Further, the maximum nanofluid temperature is reduced by 1227% when the nanoparticles volume fraction is varied from 0% to 4%,This paper aims to study the nanofluid flow and heat transfer characteristics inside an inclined enclosure filled with a heat-generating, hydrodynamically and thermally anisotropic porous medium using the CBS scheme The LTNEM is considered between the nanofluid and porous phases while the local thermal equilibrium model (LTEM) between the base fluid (water) and the nanoparticles (alumina) is taken into account The Galerkin FEM is introduced to discretize the governing system of equations Also, examine influences of the anisotropic properties (permeability, Forchheimer terms and thermal conductivity of the porous medium), inclination angle and nanoparticles volume fraction on the net rate of the heat transfer between the nanofluid and porous phases and on the local thermal non-equilibrium state is one of the concerns of this paper

MHD hybrid nanofluid flow over a permeable stretching/shrinking sheet with thermal radiation effect

Abstract: This study aims to investigate the heat transfer characteristic of the magnetohydrodynamic (MHD) hybrid nanofluid over the linear stretching and shrinking surface in the presence of suction and thermal radiation effects.,Mathematical equations are transformed into pairs of self-similarity equations using similarity transformation. Boundary value problem solver (bvp4c) in MATLAB was adopted to solve the system of reduced similarity equations. In this study, the authors particularly examine the flow and heat transfer properties for different values of suction and thermal radiation parameters using single-phase nanofluid model. A comparison of the present results shows a good agreement with the published results.,It is noticed that the efficiency of heat transfer of hybrid nanofluid (Cu-Al2O3/H2O) is greater than the nanofluid (Cu/H2O). Furthermore, it is also found that dual solutions exist for a specific range of the stretching/shrinking parameter with different values of suction and radiation parameters. The results indicate that the skin friction coefficient and the local Nusselt number increase with suction effect. The values of the skin friction coefficient increases, but the local Nusselt number decreases for the first solution with the increasing of thermal radiation parameter. It is also observed that suction and thermal radiation widen the range of the stretching/shrinking parameter for which the solution exists.,In practice, the investigation on the flow and heat transfer of MHD hybrid nanofluid through a stretching/shrinking sheet with suction and thermal radiation effects is very important and useful. The problems related to hybrid nanofluid has numerous real-life and industrial applications, for example microfluidics, manufacturing, transportation, military and biomedical, etc.,In specific, this study focused on increasing thermal conductivity using a hybrid nanofluid mathematical model. This paper is able to obtain the dual solutions. To the best of author’s knowledge, this study is new and there is no previous published work similar to present study.

3D optimization of baffle arrangement in a multi-phase nanofluid natural convection based on numerical simulation

Abstract: The purpose of this study is investigating the effect of using multi-phase nanofluids, Rayleigh number and baffle arrangement simultaneously on the heat transfer rate and Predict the optimal arrangement type of baffles in the differentiation of Rayleigh number in a 3D enclosure.,Simulations were performed on the base of the L25 Taguchi orthogonal array, and each test was conducted under different height and baffle arrangement. The multi-phase thermal lattice Boltzmann based on the D3Q19 method was used for modeling fluid flow and temperature fields.,Streamlines, isotherms, nanofluid volume fraction distribution and Nusselt number along the wall surface for 104 < Ra < 108 have been demonstrated. Signal-to-noise ratios have been analyzed to predict optimal conditions of maximize and minimize the heat transfer rate. The results show that by choosing the appropriate height and arrangement of the baffles, the average Nusselt number can be changed by more than 57 per cent.,The value of this paper is surveying three-dimensional and two-phase simulation for nanofluid. Also using the Taguchi method for Predicting the optimal arrangement type of baffles in a multi-part enclosure. Finally statistical analysis of the results by using of two maximum and minimum target Function heat transfer rates.

Dufour and Soret effects on Al2O3-water nanofluid flow over a moving thin needle: Tiwari and Das model

Abstract: This paper aims to examine the effect of Dufour and Soret diffusions on Al2O3-water nanofluid flow over a moving thin needle by using the Tiwari and Das model.,The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the skin friction, heat transfer and mass transfer coefficients, as well as the velocity, temperature and concentration profiles for different values of the physical parameters, are analysed and discussed.,The non-uniqueness of the solutions is observed for a certain range of the physical parameters. The authors also notice that the bifurcation of the solutions occurs in which the needle moves toward the origin (λ < 0). It is discovered that the first branch solutions of the skin friction coefficient and the heat transfer coefficients increase, but the mass transfer coefficient decreases in the presence of nanoparticle. Additionally, the simultaneous effect of Dufour and Soret diffusions tends to enhance the heat transfer coefficient; however, dual behaviours are observed for the mass transfer coefficient. Further analysis shows that between the two solutions, only one of them is stable and thus physically reliable in the long run.,The problem of Al2O3-water nanofluid flow over a moving thin needle with Dufour and Soret effects are the important originality of the present study. Besides, the temporal stability of the dual solutions is examined for time.

Experimental and numerical analysis on using CuO-Al2O3/water hybrid nanofluid in a U-type tubular heat exchanger

Abstract: Heat exchangers (HEXs) are extensively used in many applications such as heating and cooling systems To increase the thermal performance of HEXs, nano-sized particles could be added to the base working fluid which can improve the thermophysical properties of the fluid In addition, further improvement in the thermal performance of nanofluids can be obtained by using two or more different nanoparticles which are known as hybrid nanofluids This paper aims to improve the thermal efficiency of U-type tubular HEX (THEX) by using CuO-Al2O3/water hybrid nanofluid,Numerical simulation has been used to model THEX with various configurations Also, CuO-Al2O3/water hybrid nanofluid has been experimented in THEX in two various modes including parallel (PTHEX) and counter flow (CTHEX) regarding to the numerical findings Hybrid nanofluids have been prepared in two particle concentrations and compared with CuO/water nanofluid at the same concentrations and also with water,The numerical simulation results showed that adding fins and also using hybrid nanofluid can increase heat transfer rate in HEX However, adding fins cannot be a good option in U-type THEX with lower diameter because it increases pressure drop notably Experimental results of this work illustrated that using Al2O3-CuO/water hybrid nanofluid in the THEX improved thermal performance significantly Maximum enhancement in overall heat transfer coefficient of THEX by using CuO-Al2O3/water nanofluid in 05% and 1% concentrations achieved as 95% and 12%, respectively,The obtained findings of the study showed the positive effects of using hybrid type nanofluid in comparison with single type nanofluid In this study, numerical and experimental analysis have been conducted to investigate the effect of using hybrid type nanofluid in U-type HEX The obtained results exhibited successful utilization of CuO-Al2O3/water hybrid type nanofluid in HEX Moreover, it was observed that thermal performance analysis of the nanofluids without any experiment can be done by using numerical method

Difference equation vs differential equation on different scales

Abstract: The purpose of this paper is to demonstrate that the numerical method is not everything for nonlinear equations. Some properties cannot be revealed numerically; an example is used to elucidate the fact.,A variational principle is established for the generalized KdV – Burgers equation by the semi-inverse method, and the equation is solved analytically by the exp-function method, and some exact solutions are obtained, including blowup solutions and discontinuous solutions. The solution morphologies are studied by illustrations using different scales.,Solitary solution is the basic property of nonlinear wave equations. This paper finds some new properties of the KdV–Burgers equation, which have not been reported in open literature and cannot be effectively elucidated by numerical methods. When the solitary solution or the blowup solution is observed on a much small scale, their discontinuous property is first found.,The variational principle can explain the blowup and discontinuous properties of a nonlinear wave equation, and the exp-function method is a good candidate to reveal the solution properties.

Numerical investigation of the effect of water/Al2O3 nanofluid on heat transfer in trapezoidal, sinusoidal and stepped microchannels

Abstract: Purpose The purpose of this study is three-dimensional flow and heat transfer investigation of water/Al2O3 nanofluid inside a microchannel with different cross-sections in two-phase mode. Design/methodology/approach The effect of microchannel walls geometry (trapezoidal, sinusoidal and stepped microchannels) on flow characteristics and also changing circular cross section to trapezoidal cross section in laminar flow at Reynolds numbers of 50, 100, 300 and 600 were investigated. In this study, two-phase water/Al2O3 nanofluid is simulated by the mixture model, and the effect of volume fraction of nanoparticles on performance evaluation criterion (PEC) is studied. The accuracy of obtained results was compared with the experimental and numerical results of other similar papers. Findings Results show that in flow at lower Reynolds numbers, sinusoidal walls create a pressure drop in pure water flow which improves heat transfer to obtain PEC 1. Results showed that the stepped microchannel had higher pressure drop, better thermal performance and higher PEC than other microchannels. Originality/value Review of previous studies showed that existing papers have not compared and investigated nanofluid in a two-phase mode in inhomogeneous circular, stepped and sinusoidal cross and trapezoidal cross-sections by considering the effect of changing channel shape, which is the aim of the present paper.

Variable diffusion and conductivity change in 3D rotating Williamson fluid flow along with magnetic field and activation energy

Abstract: The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface.,A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method.,The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior.,This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.

Thermo-hydraulic and entropy generation analysis for magnetohydrodynamic pressure driven flow of nanofluid through an asymmetric wavy channel

Abstract: The purpose of this paper is to analyze the thermal, hydraulic and entropy generation characteristics for the magneto-hydrodynamic (MHD) pressure-driven flow of Al2O3-water nanofluid through an asymmetric wavy channel.,Galerkin finite element method is used to solve the governing transport equations numerically within the computational domain using the appropriate boundary conditions. The temperature and flow fields are computed by varying Reynolds number (Re), Hartmann number (Ha) and nano-particle volume fraction (ϕ) in the following range: 10 ≤ Re ≤ 500, 0 ≤ Ha ≤ 75 and 0 ≤ ϕ ≤ 5%.,The formation of the recirculation zones in the wavy passages, the size of it and the strength of the vortices formed can be modulated by the application of the magnetic field. The overall heat transfer rate increases with Ha for all ϕ both for a lower and higher regime of Re although the enhancement is more for lower values of Re and nanofluids as compared to base fluid and for intermediate values of Re, the effect of a magnetic field is almost insignificant. The magnetic performance factor (PFmagnetic) decreases with Ha although the rate of decrement varies with Re. The increase ϕ also enhances PFmagnetic especially at lower and higher values of Re. The addition of nano-particle enhances the entropy generation at lower values of the Re, while the opposite effect is seen for higher values of Re.,The present study has enormous practical relevance for the design of heat exchanger applied for solar collectors, process plants, textile and aerospace applications.,The combined effects on the heat transfer rate and the associated pressure drop penalty due to the applied magnetic field for the flow of nanofluid through an asymmetric wavy channel have not been reported to date. The effect of the magnetic field on the formation of recirculation zones and hot spot intensity in the asymmetric wavy channel has been examined in detail. The PFmagnetic is investigated first time for the MHD nanofluid flow through a wavy channel.

A variational approach for novel solitary solutions of FitzHugh–Nagumo equation arising in the nonlinear reaction–diffusion equation

Abstract: In the nonlinear model of reaction–diffusion, the Fitzhugh–Nagumo equation plays a very significant role. This paper aims to generate innovative solitary solutions of the Fitzhugh–Nagumo equation through the use of variational formulation.,The partial differential equation of Fitzhugh–Nagumo is modified by the appropriate wave transforms into a dimensionless nonlinear ordinary differential equation, which is solved by a semi-inverse variational method.,This paper uses a variational approach to the Fitzhugh–Nagumo equation developing new solitary solutions. The condition for the continuation of new solitary solutions has been met. In addition, this paper sets out the Fitzhugh–Nagumo equation fractal model and its variational principle. The findings of the solitary solutions have shown that the suggested method is very reliable and efficient. The suggested algorithm is very effective and is almost ideal for use in such problems.,The Fitzhugh–Nagumo equation is an important nonlinear equation for reaction–diffusion and is typically used for modeling nerve impulses transmission. The Fitzhugh–Nagumo equation is reduced to the real Newell–Whitehead equation if β = −1. This study provides researchers with an extremely useful source of information in this area.

MHD Marangoni boundary layer problem for hybrid nanofluids with thermal radiation

Abstract: Purpose The purpose of this paper is to study flow of the Marangoni boundary layer pasta surface embedded in a porous medium saturated by a hybrid nanofluid in the presence of a magnetic field and thermal radiation. Design/methodology/approach The governing model was converted into ordinary differential equations applying proper similarity transformations. Therefore, Laplace transform was used to exactly solve the resulted equations. Hence, the influence of the velocity profile and temperature distribution was investigated under impacts of the involved parameters. Findings In the case of regular fluid, i.e. the solid volume fractions are zeros, the current results are in a very good agreement with those in the literature. It was found that the velocity decreases (increases) on increasing the parameters of copper-nanoparticles volume fraction, magnetic field and suction (permeability and injection). Further, the temperature increases (decreases) with an increase of the copper-nanoparticles volume fraction, magnetic field, injection and radiation (permeability and suction). Originality/value The current results of the Marangoni boundary layer problem for hybrid nanofluids are new, original and extend the previous problems investigated by many authors for the case of regular/nano fluids.

Magneto-hydrodynamics of a solid-liquid two-phase fluid in rotating channel due to peristaltic wavy movement

Abstract: Numerous researchers have probed the peristaltic flows because of their immense usage in industrial engineering, biomedical engineering and biological sciences. However, the investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap in the existing literature, this paper will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of a magnetic field. The purpose of this study is to investigate the two-phase velocity distribution and rotation parameter when magneto-hydrodynamics is applied.,The constituent equations are solved under the condition of low Reynolds number and long wavelength. The exact method is used to attain the subsequent equations and a comprehensive graphical study for fluid phase, particulate phase velocity and flow rates are furnished. The impacts of pertinent parameters, magnetic field and rotation are discussed in detail.,It is witnessed that the velocity profile of particulate phase gets higher values for the same parameters as compared to the fluid phase velocity. Moreover, the axial velocity increases with different values of particle volume fraction, but in case of magnetic field and rotation parameter, it shows the opposite behavior.,The outcomes of study have viable industrial implementations in systems comprising solid-liquid based flows of fluids involving peristaltic movement.,The investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap, the present study will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of magnetic field.

Natural convection of a nanofluid-filled circular enclosure partially saturated with a porous medium using ISPH method

Abstract: The purpose of this study is to simulate the natural convection of a heated square shape embedded in a circular enclosure filled with nanofluid using an incompressible smoothed particle hydrodynamics (ISPH) method.,In the ISPH method, the evaluated pressure was stabilized by using a modified source term in solving the pressure Poisson equation. The divergence of the velocity was corrected, and the dummy particles were used to treat the rigid boundary. Dummy wall particles were initially settled in outer layers of the circular enclosure for preventing particle penetration and reducing the error of truncated kernel. The circular enclosure was partially filled with a porous medium near to the outer region. The single-phase model was used for the nanofluid, and the Brinkman–Forchheimer-extended Darcy model was used for the porous medium. Dummy wall particles were initially settled in outer layers of circular enclosure for preventing particle penetration and reducing error from the truncated kernel on the boundary.,The length of the inner square shape plays an important role in enhancing the heat transfer and reducing the fluid flow inside a circular enclosure. The porous layer represents a resistance force for the fluid flow and heat transfer, and, consequently, the velocity field and temperature distributions are reduced at the outer region of the circular cylinder. Then, the radius of the inner square shape, Darcy parameter and radius of the porous layer were considered the main factors for controlling the fluid flow and heat transfer inside a circular enclosure. The average Nusselt number decreases as the inner square length, radius of the porous layer and solid volume fraction increase.,The stabilized ISPH method is corrected for simulating the natural convection from an inner hot square inside a nanofluid-filled circular enclosure saturated with a partial layer of a porous medium.