Showing papers on "Similarity solution published in 2019"

Heat transfer and nanofluid flow over a porous plate with radiation and slip boundary conditions

Abstract: Presence of different terms with various values can alter the thermal behavior of the nanofluids flow over porous surfaces. The aim of this research is to study the influence of nanoparticles volume fraction, nanoparticles type, suction or injection, the heat generation or absorption, the Eckert number, thermal and velocity slip parameters, and radiation on the velocity and temperature fields on the flow and heat transfer over a porous flat plate. Four different types of nanoparticles including metal nanoparticles (Cu), metal oxide nanoparticles (Al2O3) and carbon-based nanomaterials (MWCNTs and SWCNTs) which were dispersed in the water (as based fluid) are studied. The governing equations are converted into the ordinary differential equations using similarity solution and solved numerically by the RKF45 algorithm. The results of the simulations showed a contradiction with the results of other researchers who expressed that using nanoparticles with higher thermal conductivity and volume fraction led to increasing heat transfer rate in nanofluids; this study proves that, in some cases, boosting the volume fraction of nanoparticles has a potential to decrease the heat transfer rate due to significant changes in values of some parameters including radiation, heat generation, and viscous dissipation.

Similarity solution of air and nanofluid impingement cooling of a cylindrical porous heat sink

Abstract: In the present paper, a numerical study on flow and heat transfer of air/nanofluid impinging jet flow through a cylindrical porous heat sink has been done The cooling fluid flows uniformly through the porous foam over the hot disk Conservation equations of mass, momentum and energy in form of partial differential equation, by using similarity variables, converted to nonlinear ordinary differential equations and finally these equations have been solved numerically Also, results are validated through comparison with those of a commercial CFD code with an acceptable agreement In this study, effects of dimensionless parameters in the form of geometrical, porous media characteristics and cooling fluid properties on the velocity profile, temperature profile and average Nusselt number have been scrutinized Results indicate that addition of nanoparticles, thermal conductivity ratio increment and aspect ratio reduction will enhance the heat sink thermal performance

Evolution of supernovae-driven superbubbles with conduction and cooling

Abstract: We use spherically symmetric hydrodynamic simulations to study the dynamical evolution and internal structure of superbubbles (SBs) driven by clustered supernovae (SNe), focusing on the effects of thermal conduction and cooling in the interface between the hot bubble interior and cooled shell. Our simulations employ an effective diffusivity to account for turbulent mixing from nonlinear instabilities that are not captured in 1D. The conductive heat flux into the shell is balanced by a combination of cooling in the interface and evaporation of shell gas into the bubble interior. This evaporation increases the density, and decreases the temperature, of the SB interior by more than an order of magnitude relative to simulations without conduction. However, most of the energy conducted into the interface is immediately lost to cooling, reducing the evaporative mass flux required to balance conduction. As a result, the evaporation rate is typically a factor of $\sim$3-30 lower than predicted by the classical similarity solution of Weaver et al. (1977), which neglects cooling. Blast waves from the first $\sim$30 SNe remain supersonic in the SB interior because reduced evaporation from the interface lowers the mass they sweep up in the hot interior. Updating the Weaver solution to include cooling, we construct a new analytic model to predict the cooling rate, evaporation rate, and temporal evolution of SBs. The cooling rate, and hence the hot gas mass, momentum, and energy delivered by SBs, is set by the ambient ISM density and the efficiency of nonlinear mixing at the bubble/shell interface.

Brownian movement and thermophoretic aspects in third-grade nanofluid over oscillatory moving sheet

Abstract: An enhancement in energy by using nanoparticles is a topic of broad interest in the present century due to its industrial and engineering importance. Therefore, this investigation is based on the thermophoretic and Brownian movement aspects in third-grade nanofluid flow under an applied magnetic field. The role of Joule dissipation is considered in the energy expression. The flow generation is due to the time-dependent periodic motion of the sheet. The partial differential system is converted into expressions of ordinary ones via appropriate variables. The local similarity solution for a coupled system of nonlinear ordinary differential expressions is developed by a homotopy analysis method. A theoretical based graphical analysis is comprehensively discussed for the flow parameters. The numerical data of local Nusselt and Sherwood numbers are expressed in tabular form. It is observed that the presence of non-Newtonian parameters result in an enhancement of the momentum boundary layer. Both thermophoresis and Brownian parameters play an efficient role to enhance the nanoparticles' temperature. This study also reveals that the factor of skin friction oscillates and increases periodically by increasing the non-Newtonian parameters.

Mixed convection and stability analysis of stagnation-point boundary layer flow and heat transfer of hybrid nanofluids over a vertical plate

Abstract: This study aims to study the mixed convection flow and heat transfer of Al2O3-Cu/water hybrid nanofluid over a vertical plate. Governing equations for conservation of mass, momentum and energy for the hybrid nanofluid over a vertical flat plate are introduced.,The similarity transformation approach is used to transform the set of partial differential equations into a set of non-dimensional ordinary differential equations. Finite-deference with collocation method is used to integrate the governing equations for the velocity and temperature profiles.,The results show that dual solutions exist for the case of opposing flow over the plate. Linear stability analysis was performed to identify a stable solution. The stability analysis shows that the lower branch of the solution is always unstable, while the upper branch of the solution is always stable. The results of boundary layer analysis are reported for the various volume fractions of composite nanoparticles and mixed convection parameter. The outcomes show that the composition of nanoparticles can notably influence the boundary layer flow and heat transfer profiles. It is also found that the trend of the variation of surface skin friction and heat transfer for each of the dual solution branches can be different. The critical values of the mixed convection parameter, λ, where the dual solution branches joint together, are also under the influence of the composition of hybrid nanoparticles. For instance, assuming a total volume fraction of 5 per cent for the mixture of Al2O3 and Cu nanoparticles, the critical value of mixing parameter of λ changes from −3.1940 to −3.2561 by changing the composition of nanofluids from Al2O3 (5 per cent) + Cu (0%) to Al2O3 (2.5%) + Cu (2.5 per cent).,The mixed convection stability analysis and heat transfer study of hybrid nanofluids for a stagnation-point boundary layer flow are addressed for the first time. The introduced hybrid nanofluid model and similarity solution are new and of interest in both mathematical and physical points of view.

Transport of neutral solutes in a viscoelastic solvent through a porous microchannel

Abstract: We study the effect of viscoelasticity on the transportation of neutral solutes through a porous microchannel. The underlying transport phenomenon, modelled using the simplified Phan-Thien-Tanner constitutive equation, is actuated by the combined influence of pressure gradient and electroosmosis. Here, we obtain the closed form solution for the velocity distribution inside the flow domain and calculate the concentration profiles of the neutral solutes within the mass transport boundary layer by invoking the similarity solution approach. To establish the efficacy of viscoelastic solvents in the transportation of neutral solutes, which may find relevance in transdermal drug delivery applications, here we show the variations in the local solute concentration, the length averaged solute concentration at the wall, and the Sherwood number with the viscoelastic parameter. The present study infers that the shear-thinning nature of the viscoelastic fluid enhances the convective mass transfer as well as the permeation rate in the porous membranes. A complex interplay between the fluid rheology and the porous structure of the walls influenced by the electrochemistry at the interfacial scale modulates the mass transfer boundary layer of neutral solutes, implicating an effective method of mass transport in transdermal drug delivery applications.

Finite Element Method Solution of Boundary Layer Flow of Powell-Eyring Nanofluid over a Nonlinear Stretching Surface

Abstract: The nonlinear convective flow of Eyring-Powell nanofluid using Catteneo-Christov model with heat generation or absorption term and chemical reaction rate over nonlinear stretching surface is analyzed. The simultaneous nonlinear partial differential equations governing the boundary layer flow are transformed to the corresponding nonlinear ordinary differential equations using similarity solution and then solved using Galerkin finite element method (GFEM). The impacts of pertinent governing parameters like Brownian diffusion, thermophoresis, mixed convection, heat generation or absorption, chemical reaction rate, Deborah numbers, Prandtl number, magnetic field parameter, Lewis number, nonlinear stretching sheet, and Eyring-Powell fluid parameters on velocity field, temperature, and nanoparticle concentration are given in both figures and tabular form. The result shows that the rise in chemical reaction rate will improve mass transfer rate and reduce heat transfer rate and local buoyancy parameter has quit opposite effect. The attributes of local skin friction coefficient, Nusselt number, and Sheer wood number are investigated and validated with existing literatures.

Numerical modeling of Glauert type exponentially decaying wall jet flows of nanofluids using Tiwari and Das’ nanofluid model

Abstract: Purpose The purpose of this study is to present a simple analytic solution to wall jet flow of nanofluids. The concept of exponentially decaying wall jet flows proposed by Glauert (1956) is considered. Design/methodology/approach A proper similarity variables are used to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then solved analytically. Findings Dual solutions are found and a stability analysis has been done. These solutions show that the first solution is physically realizable, whereas the second solution is not practicable. Originality/value The present results are original and new for the study of fluid flow and heat transfer over a static permeable wall, as they successfully extend the problem considered by Glauert (1956) to the case of nanofluids.

Numerical assessment of Bödewadt flow and heat transfer over a permeable disk with variable fluid properties

Abstract: Impact of variable fluid properties on heat transfer in Bodewadt flow with wall suction is the main focus of present article. Recent studies have predicted that energy equation in Bodewadt flow can have physically compatible solution only when disk is porous. We utilize the usual von-Karman variables to transform the governing equations of fluid motion and heat transfer (with variable properties) into self-similar differential equations. The final problem comprises of a parameter θ e that measures the degree of dependence of fluid viscosity on temperature. A numerical approach is pursued to determine velocity components, wall stresses, temperature and heat transfer rate from the disk. Wall suction velocity is found to have a pivotal role on the solutions. The main outcome of the study is that fluid velocity and temperature around the disk are considerably altered by varying the parameter θ e . The deviations of present results from those obtained with constant fluid properties are deliberated. Present results are in perfect agreement with the available literature in a limiting sense.

A nanofluid MHD flow with heat and mass transfers over a sheet by nonlinear boundary conditions: Heat and mass transfers enhancement

Abstract: In this paper, we have numerically examined the steady boundary layer of a viscous incompressible nanofluid and its heat and mass transfers above a horizontal flat sheet. The boundary conditions considered were a nonlinear magnetic field, a nonlinear velocity and convection. Such nonlinearity in hydrodynamic and heat transfer boundary conditions and also in the magnetic field has not been addressed with the great details in the literature. In this investigation, both the Brownian motion and thermophoretic diffusion have been considered. A similarity solution is achieved and the resulting ordinary differential equations (nonlinear) are worked numerically out. Upon validation, the following hydrodynamic and heat and mass transfers parameters were found: the reduced Sherwood and Nusselt numbers, the reduced skin friction coefficient, and the temperature and nanoparticle volume fraction profiles. All these parameters are found affected by the Lewis, Biot and Prandtl numbers, the stretching, thermophoretic diffusion, Brownian motion and magnetic parameters. The detailed trends observed in this paper are carefully analyzed to provide useful design suggestions.

Investigation of entropy generation in nanofluid’s axisymmetric stagnation flow over a cylinder with constant wall temperature and uniform surface suction-blowing

Abstract: Dimensionless temperature, Nusselt number and entropy generation in stagnation flow of incompressible nanofluid over an infinite cylinder accompanying uniform suction and blow in steady state have been investigated in this study. Free stream has been steady as well with the initial stream rate of k ¯ . Dimensional analysis and similarity solution of Navier-stokes and energy equations have been presented. These equations are simplified implementing appropriate transformations introduced in this research. The similarity equations are solved where the cylinder’s wall is under constant Temperature. All these solutions are acceptable for Reynolds numbers Re = k ¯ a 2 / 2 υ f of 0.1–1000, various dimensionless surface diffusion S = U o / k ¯ a and specific volume fractions of nano particles where a is the cylinder radius and υ f is the kinematic viscosity of the base-fluid. The results show that for all Reynolds numbers, diffusion depth of radial and axial components of velocity field and wall shear stress increases as a result of decline in nano particles volume fraction and growth in surface diffusion. Moreover, increase in nano particles volume fraction and surface suction raises heat transfer coefficient and Nusselt number. Also the largest amount of entropy generated is calculated.

Self-similar breakup of polymeric threads as described by the Oldroyd-B model

Abstract: When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and nonlinear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. Deriving a conservation law along the thread, we can calculate the stress inside the thread from a measurement of the thread thickness. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations.

Similarity Solution and Heat Transfer Characteristics for a Class of Nonlinear Convection-Diffusion Equation with Initial Value Conditions

Abstract: A class of nonlinear convection-diffusion equation is studied in this paper. The partial differential equation is converted into nonlinear ordinary differential equation by introducing a similarity transformation. The asymptotic analytical solutions are obtained by using double-parameter transformation perturbation expansion method (DPTPEM). The influences of convection functional coefficient and power law index on the heat transport characteristics are discussed and shown graphically. The comparison with the numerical results is presented and it is found to be in excellent agreement. The method and technique used in this paper have the significance in studying other engineering problems.

Shock formation in two-layer equal-density viscous gravity currents

Abstract: The flow of a viscous gravity current over a lubricating layer of fluid is modelled using lubrication theory. We study the case of an axisymmetric current with constant influx which allows for a similarity solution, which depends on three parameters: a non-dimensional influx rate . The numerically calculated similarity solutions compare well to experimental measurements with respect to the predictions of self-similarity, the radial extent and the self-similar top-surface shapes of the current.

Evolution of similarity lengths in anisotropic magnetohydrodynamic turbulence

Abstract: In an earlier paper (Wan et al., J. Fluid Mech., vol. 697, 2012, pp. 296–315), the authors showed that a similarity solution for anisotropic incompressible three-dimensional magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field ) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor–Karman-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, mean field strength, and cross-helicity, on the nature of similarity decay is discussed.

Self-similar breakup of polymeric threads as described by the Oldroyd-B model

Abstract: When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and non-linear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. A conservation law balancing pressure and elastic energy permits to calculate the thread thickness exactly. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations.

Similarity solutions and the computation formulas of a nonlinear fractional-order generalized heat equation

Abstract: A generalized nonlinear heat equation with the fractional derivative is proposed, whose similarity solutions are derived from a type of special scalar transformation with two parameters. With the h...

Similarity Solution for the Flow Behind an Exponential Shock Wave in a Rotational Axisymmetric Non-ideal Gas Under the Influence of Gravitational Field with Conductive and Radiative Heat Fluxes

Abstract: In the present paper, we investigated the propagation of exponential cylindrical shock wave in the presence of radiative as well as conductive heat fluxes under the influence of gravitational field. The medium is assumed to be non-ideal gas rotating about the axis of symmetry. The ambient medium has variable azimuthal as well as axial components of fluid velocity. It is manifested that the non-idealness parameter of the gas has decaying effect on the shock wave; however, presence of gravitational field has reverse effect on the shock strength.

An Innovative Approach for Study of Thermal Behavior of an Unsteady Nanofluid Squeezing Flow between Two Parallel Plates Utilizing Artificial Neural Network

Abstract: This study reveals the thermal behavior of an unsteady nanofluid streaming between two parallel plates by using artificial neural network (ANN). Initially, a similarity solution is employed to simplify the partial differential equations (PDSs) and convert them into a system of coupled nonlinear ordinary differential equations (ODEs). Subsequently, a numerical analysis is undertaken to verify the predicted results applying forth order Runge Kutta method. ANN is utilized to provide a nonlinear map between the considered input parameters such as solid volume fraction (Φ), Eckert number (Ec) and a moving parameter which represents the movement of the parallel plates (S), and output parameters like Nusselt number (Nu). Considering the accuracy of the current results, it is concluded that ANN method can be a potential reliable approach for function approximation. Results indicate that an optimal network with 16 neurons exists in hidden layer for which the value of RMSE for testing data is found to be 0.001364.

Some Similarity Solutions and Numerical Solutions to the Time-Fractional Burgers System

Abstract: In the paper, we discuss some similarity solutions of the time-fractional Burgers system (TFBS). Firstly, with the help of the Lie-point symmetry and the corresponding invariant variables, we transform the TFBS to a fractional ordinary differential system (FODS) under the case where the time-fractional derivative is the Riemann–Liouville type. The FODS can be approximated by some integer-order ordinary differential equations; here, we present three such integer-order ordinary differential equations (called IODE-1, IODE-2, and IODE-3, respectively). For IODE-1, we obtain its similarity solutions and numerical solutions, which approximate the similarity solutions and the numerical solutions of the TFBS. Secondly, we apply the numerical analysis method to obtain the numerical solutions of IODE-2 and IODE-3.

Rheometry based on free surface velocity

Abstract: This paper explores the possibility of identifying the rheology of a fluid by monitoring how the free surface velocity field is affected by a perturbation in the flow. The dam-break problem is considered which results from the release of a gate initially separating two fluid pools of different depth. The flow velocity is measured by seeding the free surface with buoyant particles and using Particle Tracking Velocimetry. In parallel, a mathematical model based on the lubrication approximation for fluids with a power-law rheology is developed. The model is validated against a similarity solution which is obtained for the spreading of a gravity current under its own weight and neglecting surface tension. Minimizing the difference between the free surface velocity fields obtained numerically and measured experimentally enables the identification of rheological parameters. The methodology is tested on ideal and noisy synthetic data sets and experimental data obtained with aqueous glycerol.

Impinging Howarth stagnation-point flows

Abstract: The flow of one Howarth stagnation-point flow impinging directly on another Howarth stagnation-point flow is studied, and an exact similarity solution to the Navier-Stokes equations is found. The upper layer fluid has density ρ1 and kinematic viscosity ʋ1 while the lower layer fluid has density ρ2 and kinematic viscosity ʋ2 and the two fluids are assumed to be immiscible. This problem has potentially five independent parameters to investigate, but application of the continuity of the normal stresses at the interface imposes restrictions which reduces the problem to one with three independent parameters, namely a ratio σ of strain rates and the fluid parameter ratios ρ = ρ1/ρ2 and ʋ = ʋ1/ʋ2. Numerical results are presented for selected values of ρ and ʋ for a range of σ and show that stable results exist for all values of σ > 0, and for a range of negative σ values. Sample stable velocity profiles are also presented.