Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity,non-uniform heat source and radiation

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.     

Combined effects of non-uniform heat source/sink and thermal radiation on heat transfer over an unsteady stretching permeable surface

The present paper is concerned with the study of flow and heat transfer characteristics in the unsteady laminar boundary layer flow of an incompressible viscous fluid over continuously stretching permeable surface in the presence of a non-uniform heat source/sink and thermal radiation. The unsteadiness in the flow and temperature fields is because of the time-dependent stretching velocity and surface temperature. Similarity transformations are used to convert the governing time-dependent nonlinear boundary layer equations for momentum and thermal energy are reduced to a system of nonlinear ordinary differential equations containing Prandtl number, non-uniform heat source/sink parameter, thermal radiation and unsteadiness parameter with appropriate boundary conditions. These equations are solved numerically by applying shooting method using Runge–Kutta–Fehlberg method. Comparison of numerical results is made with the earlier published results under limiting cases. The effects of the unsteadiness parameter, thermal radiation, suction/injection parameter, non-uniform heat source/sink parameter on flow and heat transfer characteristics as well as on the local Nusselt number are shown graphically.     

The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet

An analysis has been carried out to study the momentum and heat transfer characteristics in an incompressible electrically conducting non-Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly non-linear coupled ordinary differential equations by similarity transformations. The effect of variable fluid viscosity, Magnetic parameter, Prandtl number, variable thermal conductivity, heat source/sink parameter and thermal radiation parameter are analyzed for velocity, temperature fields, and wall temperature gradient. The resultant coupled highly non-linear ordinary differential equations are solved numerically by employing a shooting technique with fourth order Runge–Kutta integration scheme. The fluid viscosity and thermal conductivity, respectively, assumed to vary as an inverse and linear function of temperature. The analysis reveals that the wall temperature profile decreases significantly due to increase in magnetic field parameter. Further, it is noticed that the skin friction of the sheet decreases due to increase in the Magnetic parameter of the flow characteristics.     

Effects of thermal radiation and magnetic field on unsteady mixed convection flow and heat transfer over an exponentially stretching surface with suction in the presence of internal heat generation/absorption

In this paper, the problem of unsteady laminar two-dimensional boundary layer flow and heat transfer of an incompressible viscous fluid in the presence of thermal radiation, internal heat generation or absorption, and magnetic field over an exponentially stretching surface subjected to suction with an exponential temperature distribution is discussed numerically. The governing boundary layer equations are reduced to a system of ordinary differential equations. New numerical method using Mathematica has been used to solve such system after obtaining the missed initial conditions. Comparison of obtained numerical results is made with previously published results in some special cases, and found to be in a good agreement.     

Effects of radiation and variable viscosity on unsteady MHD flow of a rotating fluid from stretching surface in porous medium

This work is focused on the study of unsteady magnetohydrodynamics boundary-layer flow and heat transfer for a viscous laminar incompressible electrically conducting and rotating fluid due to a stretching surface embedded in a saturated porous medium with a temperature-dependent viscosity in the presence of a magnetic field and thermal radiation effects. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. With appropriate transformations, the unsteady MHD boundary layer equations are reduced to local nonsimilarity equations. Numerical solutions of these equations are obtained by using the Runge–Kutta integration scheme as well as the local nonsimilarity method with second order truncation. Comparisons with previously published work have been conducted and the results are found to be in excellent agreement. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity in primary and secondary flows as well as the local skin-friction coefficients and the local Nusselt number are illustrated graphically to show interesting features of Darcy number, viscosity-variation, magnetic field, rotation of the fluid, and conduction radiation parameters.     

MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet

This article presents a numerical solution for the magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a semi-infinite non-isothermal stretching sheet with internal heat generation/absorption. The flow is caused by linear stretching of a sheet from an impermeable wall. Thermal conductivity is assumed to vary linearly with temperature. The governing partial differential equations of momentum and energy are converted into ordinary differential equations by using a classical similarity transformation along with appropriate boundary conditions. The intricate coupled non-linear boundary value problem has been solved by Keller box method. It is important to note that the momentum and thermal boundary layer thickness decrease with increase in the power-law index in presence/absence of variable thermal conductivity.     

Lie group analysis of natural convection heat and mass transfer in an inclined surface with chemical reaction

In this paper we examine the convective flow, heat and mass transfer of an incompressible viscous fluid past a semi-infinite inclined surface with first-order homogeneous chemical reaction by Lie group analysis. The governing partial differential equations are reduced to a system of ordinary differential equations using scaling symmetries. Numerical solutions of the resulting ordinary differential equations are obtained using the fourth-order Runge–Kutta method. From the numerical results, it is observed that the thickness of the momentum boundary layer increases with increasing the chemical reaction parameter and the Schmidt number. The thicknesses of the thermal and concentration boundary layers are decreased with increasing the chemical reaction parameter and the Schmidt number.     

Stagnation point flow of dusty Casson fluid with thermal radiation and buoyancy effects

The aim of the study is to examine the stagnation point flow of a dusty Casson fluid over a stretching sheet with thermal radiation and buoyancy effects. The governing boundary layer equations are represented by a system of partial differential equation. After applying suitable similarity transformations, the resulting boundary layer equations are solved numerically using the Runge Kutta Fehlberg fourth-fifth order method (RKF-45 method). The behaviors of velocity, temperature and concentration profiles of fluid and dusty particles with respect to change in fluid particle interaction parameter, Casson paramter, Grashof number, radiation parameter, Prandtl number, number density, thermal equilibrium time, relaxation time, specific heat of fluid and dusty particles, ratio of diffusion coefficients, Schmidt number and Eckert number are analysed graphically and discussed. Our computed results interpret that velocity distribution decays for higher estimation of Casson parameter while temperature distribution shows increasing behavior for larger radiation parameter.     

UNSTEADY NATURAL CONVECTIVE BOUNDARY LAYER FLOW AND HEAT TRANSFER OF FRACTIONAL SECOND-GRADE NANOFLUIDS WITH DIFFERENT PARTICLE SHAPES

The present study is concerned with unsteady natural convective boundary layer flow and heat transfer of fractional second-grade nanofuids for different particle shapes. Nonlinear boundary layer governing equations are formulated with time fractional derivatives in the momentum equation. The governing boundary layer equations of continuity, momentum and energy are reduced by dimensionless variable. Numerical solutions of the momentum and energy equations are obtained by the finite difference method combined with L1-algorithm. The quantites of physical interest are graphically presented and discussed in details. It is found that particle shape, fractional derivative parameter and the Grashof number have profound influences on the the flow and heat transfer.     

Perturbation analysis of unsteady magnetohydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction

An analytical study for the problem of unsteady mixed convection with thermal radiation and first-order chemical reaction on magnetohydrodynamics boundary layer flow of viscous, electrically conducting fluid past a vertical permeable plate has been presented. Slip boundary condition is applied at the porous interface. The classical model is used for studying the effect of radiation for optically thin media. The non-linear coupled partial differential equations are solved by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field decreases the velocity, temperature and concentration profiles in the boundary layer. Also, the effects of the various parameters on the skin-friction coefficient and the rate of heat transfer at the surface are discussed.     

Hydromagnetic rotating flow of a fourth‐order fluid past a porous plate

The rotating flow in the presence of a magnetic field is a problem belonging to hydromagnetics and deserves to be more widely studied than it has been to date. In the non‐linear regime the literature is scarce. We develop the governing equations for the unsteady hydromagnetic rotating flow of a fourth‐order fluid past a porous plate. The steady flow is governed by a boundary value problem in which the order of differential equations is more than the number of available boundary conditions. It is shown that by augmenting the boundary conditions based on asymptotic structures at infinity it is possible to obtain numerical solutions of the nonlinear hydromagnetic equations. Effects of uniform suction or blowing past the porous plate, exerted magnetic field and rotation on the flow phenomena, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviours of the Newtonian fluid and second‐, third‐ and fourth‐order non‐Newtonian fluids are compared for the special flow problem, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Unsteady Slip Flow and Heat Transfer Analysis of Oldroyd-B Fluid Over the Stretching Wedge北大核心CSCD

研究了在速度滑移现象存在下,上随体Oldroyd-B流体绕加热的楔形体的非稳态流动。采用松弛-延迟热通量模型,模拟了传热过程和热延迟时间对传热的影响,通过考虑浮升力、热辐射和对流换热边界条件,进一步研究了流动及传热特性。利用同伦分析方法获得常微分方程组的近似解析解,发现滑移参数的增大可以促进流体的流动,以及流体的温度随热辐射参数增大而升高。此外还发现,温度场在热松弛时间和热延迟时间中出现相反的变化趋势。     

Flow and heat transfer of a non-Newtonian fluid past a stretching sheet with partial slip

The entrained flow and heat transfer of a non-Newtonian third grade fluid due to a linearly stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that the slip and the third grade fluid parameter have opposite effects on the velocity and the thermal boundary layers.     

Unsteady flow and heat transfer of a second grade fluid over a stretching sheet

The problem of unsteady boundary layer flow of a second grade over a stretching sheet is investigated in this paper. The governing equations of motion are reduced into a partial differential equation with two independent variables by using similarity transformations. The heat transfer analysis has been also carried out for two heating processes namely the prescribed surface temperature (PST case) and prescribed surface heat flux (PHF case). The series solutions of the problem are developed by employing homotopy analysis method (HAM). Convergence of the obtained series solutions are analyzed. It is noted that the present solutions of a second grade are valid for all dimensionless times. Finally, the results are obtained and discussed through graphs for various parameters of interest.     

Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink

An analysis has been carried out to study the flow and heat transfer characteristics for MHD viscoelastic boundary layer flow over an impermeable stretching sheet with space and temperature dependent internal heat generation/absorption (non-uniform heat source/sink), viscous dissipation, thermal radiation and magnetic field due to frictional heating. The flow is generated due to linear stretching of the sheet and influenced by uniform magnetic field, which is applied vertically in the flow region. The governing partial differential equations for the flow and heat transfer are transformed into ordinary differential equations by a suitable similarity transformation. The governing equations with the appropriate conditions are solved exactly. The effects of viscoelastic parameter and magnetic parameter on skin friction and the effects of viscous dissipation, non-uniform heat source/sink and the thermal radiation on heat transfer characteristics for two general cases namely, the prescribed surface temperature (PST) case and the prescribed wall heat flux (PHF) case are presented graphically and discussed. The numerical results for the wall temperature gradient (the Nusselt number) are presented in tables and are discussed.     

Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces

The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous electrically conducting fluid in stagnation point region of an impulsively rotating and translating sphere with a magnetic field and a buoyancy force gives a system of non-linear partial differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the homotopy analysis method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the magnetic parameter, buoyancy parameter and rotation parameter on the surface shear stresses and surface heat transfer. It is noted that the behavior of the HAM solution for the surface shear stresses and surface heat transfer is in good agreement with the numerical solution given in reference [H. S. Takhar, A. J. Chamkha, G. Nath, Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces, Heat Mass Transfer 37 (2001) 397].     

Channel flow of a Maxwell fluid with chemical reaction

This work is concerned with the two-dimensional boundary layer flow of an upper-convected Maxwell (UCM) fluid in a channel with chemical reaction. The walls of the channel are porous. Employing similarity transformations the governing non-linear partial differential equations are reduced into non-linear ordinary differential equations. The resulting ordinary differential equations are solved analytically using homotopy analysis method (HAM). Expressions for series solutions are derived. The convergence of the obtained series solutions are shown explicitly. The effects of Reynold’s number Re, Deborah number De, Schmidt number Sc and chemical reaction parameter γ on the velocity and the concentration fields are shown through graphs and discussed.     

Response of heat transfer from a moving flat plate in a parabolic flow

This paper deals with the solutions of steady as well as unsteady three-dimensional incompressible thermal boundary layer equations and the study of the response of heat transfer when there is a parabolic flow over a moving flat plate. The components of velocity in boundary layer are discussed by Sarma and Gupta and those results are used to analyse thermal boundary layer equations. A general analysis is made from which we deduce (i) Solutions of two-dimensional thermal boundary layer on a moving flat plate, (ii) Solutions of thermal boundary layer on a yawed flat plate, (iii) Solutions of thermal boundary layer when there is a parabolic flow over a moving flat plate by giving different values to β and Cx. Solutions are developed for large and small times and curves are drawn representing the variations of heat transfer from the plate with time for all the cases. The limiting time is also calculated.     

Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in presence of external magnetic field

This paper presents a mathematical analysis of MHD flow and heat transfer to a laminar liquid film from a horizontal stretching surface. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of non-linear ordinary differential equations. Numerical solution of resulting non-linear differential equations is found by using efficient shooting technique. Boundary layer thickness is explored numerically for some typical values of the unsteadiness parameter S and Prandtl number Pr, Eckert number Ec and Magnetic parameter Mn. Present analysis shows that the combined effect of magnetic field and viscous dissipation is to enhance the thermal boundary layer thickness.     

Heat and mass transfer in MHD non-Darcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with non-uniform heat source and thermal radiation

A mathematical analysis has been carried out to study magnetohydrodynamic boundary layer flow, heat and mass transfer characteristic on steady two-dimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field. Momentum boundary layer equation takes into account of transverse magnetic field whereas energy equation takes into account of Ohmic dissipation due to transverse magnetic field, thermal radiation and non-uniform source effects. An analysis has been performed for heating process namely the prescribed wall heat flux (PHF case). The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations which are then linearized by quasi-linearization method and solved very efficiently by finite-difference method. Favorable comparisons with previously published work on various special cases of the problem are obtained. The effects of various physical parameters on velocity, temperature, concentration distributions are presented graphically and in tabular form.