Heat transfer to power-law fluids in thermal entrance region with viscous dissipation for constant heat flux conditions

An analytical solution of the heat transfer problem with viscous dissipation for non-Newtonian fluids with power-law model in the thermal entrance region of a circular pipe and two parallel plates under constant heat flux conditions is obtained using eigenvalue approach by suitably replacing one of the boundary conditions by total energy balance equation. Analytical expressions for the wall and the bulk temperatures and the local Nusselt number are presented. The results are in close agreement with those obtained by implicit finite-difference scheme. It is found that the role of viscous dissipation on heat transfer is completely different for heating and cooling conditions at the wall. The results for the case of cooling at the wall are of interest in the design of the oil pipe line.     

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.     

Nonsimilar incompressible laminar boundary layers with magnetic field

The solution of the steady laminar incompressible nonsimilar magneto-hydrodynamic boundary layer flow and heat transfer problem with viscous dissipation for electrically conducting fluids over two-dimensional and axisymmetric bodies with pressure gradient and magnetic field has been presented. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for flow over a cylinder and a sphere. The results indicate that the magnetic field tends to delay or prevent separation. The heat transfer strongly depends on the viscous dissipation parameter. When the dissipation parameter is positive (i.e. when the temperature of the wall is greater than the freestream temperature) and exceeds a certain value, the hot wall ceases to be cooled by the stream of cooler air because the ‘heat cushion’ provided by the frictional heat prevents cooling whereas the effect of the magnetic field is to remove the ‘heat cushion’ so that the wall continues to be cooled. The results are found to be in good agreement with those of the local similarity and local nonsimilarity methods except near the point of separation, but they are in excellent agreement with those of the difference-differential technique even near the point of separation.     

Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions

In this paper, we investigate the heat transfer of a viscous fluid flow over a stretching/shrinking sheet with a convective boundary condition. Based on the exact solutions of the momentum equations, which are valid for the whole Navier–Stokes equations, the energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking parameter on the temperature profiles and wall heat flux are presented and discussed. The solution is given as an incomplete Gamma function. It is found the convective boundary conditions results in temperature slip at the wall and this temperature slip is greatly affected by the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking parameters. The temperature profiles in the fluid are also quite different from the prescribed wall temperature cases.     

Heat transfer in a visco-elastic fluid past a stretching sheet with viscous dissipation and internal heat generation

This paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of a visco-elastic fluid over a linearly stretching continuous surface with variable wall temperature subjected to suction or blowing. The study considers the effects of frictional heating (viscous dissipation) and internal heat generation or absorption. An analysis has been carried out for two different cases of heating processes namely: (i) Prescribed surface temperature (PST) and (ii) Prescribed wall heat flux (PHF) to get the effect of visco-elastic parameter for various situations. Further increase of visco-elastic parameter is to decrease the skin friction on the sheet. The solutions for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Received: June 16, 2004; revised: February 8, 2005     

Mixed convection flow of a micropolar fluid from an unsteady stretching surface with viscous dissipation

An analysis is performed to study the unsteady mixed convection flow of a viscous incompressible micropolar fluid adjacent to a heated vertical surface in the presence of viscous dissipation when the buoyancy force assists or opposes the flow. The flow of the fluid and subsequent heat transfer from the stretching surface is investigated with the aid of appropriate transformation variables. The effect of the governing parameters on the flow and heat transfer characteristics as well as the local skin friction coefficient, wall couple stress and the heat transfer rate are thoroughly examined.     

Heat transfer in a Walter’s liquid B fluid over an impermeable stretching sheet with non-uniform heat source/sink and elastic deformation

In this present article an analysis is carried out to study the boundary layer flow behavior and heat transfer characteristics in Walter’s liquid B fluid flow. The stretching sheet is assumed to be impermeable, the effects of viscous dissipation, non-uniform heat source/sink in the presence and in the absence of elastic deformation (which was escaped from attention of researchers while formulating the viscoelastic boundary layer flow problems)on heat transfer are addressed. The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. Analytical solutions are obtained for the resulting boundary value problems. The effects of viscous dissipation, Prandtl number, Eckert number and non-uniform heat source/sink on heat transfer (in the presence and in the absence of elastic deformation) are shown in several plots and discussed. Analytical expressions for the wall frictional drag coefficient, non-dimensional wall temperature gradient and non-dimensional wall temperature are obtained and are tabulated for various values of the governing parameters. The present study reveals that, the presence of work done by deformation in the energy equation yields an augment in the fluid’s temperature.     

Perturbation analysis of radiative effect on free convection flows in porous medium in the presence of pressure work and viscous dissipation

The effect of thermal radiation with a regular three-parameter perturbation analysis has been studied for the effects in some free convection flows of Newtonian fluid-saturated porous medium. The effects of the thermal radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the flows and temperature fields have been included in the analysis. Four different vertical flows have been analyzed, those adjacent to an isothermal surface, uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source, and, a vertical adiabatic surface. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The numerical results of the perturbation analysis for four conditions are solved numerically by the fourth-order Runge–Kutta integration scheme. Numerical values of the main physical quantities are the skin friction and a heat transfer and total heat and mass convected downstream are presented in a tabular form with the parameters characterizing the radiation, permeability of the porous medium, pressure stress work and viscous dissipation. The obtained results are compared and a representative set is displayed graphically to illustrate the influences of the radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the velocity and the temperature profiles.     

Analysis of viscoelastic fluid flow with temperature dependent properties in plane Couette flow and thin annuli

The steady state flow in very thin annuli has been studied analytically for the case where the annular gap is much smaller than the radius of the inner cylinder and for the outer cylinder rotating at constant angular speed and the inner cylinder at rest. The cylinders were subjected to two different thermal boundary conditions. The exponential effect of temperature on the relaxation time and the viscosity coefficient was accounted into the governing differential equations using Nahme’s law. Effects of viscous dissipation as well as εDe² (viscoelastic index for SPTT constitutive equation) on the dimensionless velocity and temperature profiles have been investigated. Results show that while the properties of the fluid depend on temperature, the velocity and temperature profiles are different compared to those obtained with constant physical properties. The Nahme–Griffith number increases whereas εDe² as a viscoelastic index decreases when temperature dependent physical properties are considered. In addition, the results indicate that the viscous dissipation has a sensible effect on heat transfer and the Nusselt number decreases with an increase in the Nahme–Griffith number.     

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.     

Simultaneously developing flow and heat transfer of non-Newtonian fluids in equilateral triangular duct

A numerical investigation based on the Galerkin finite element method was carried out to solve the full three-dimensional governing equations for simultaneously developing steady laminar flow and heat transfer to a purely viscous non-Newtonian fluid described by a power law model flowing in equilateral triangular ducts. Two commonly used thermal boundary conditions, constant wall temperature (T boundary condition) and constant wall heat flux both axially and peripherally (H2 boundary condition) were examined. It is shown that the Nusselt number distribution along the walls is affected appreciably by the variation of the power law index. Results are presented and discussed for a wide range of power law indices and Prandtl numbers for T and H2 boundary conditions.     

Convective flows of micropolar fluids from radiate isothermal porous surfaces with viscous dissipation and Joule heating

In this study, the steady laminar free-forced convective flow and heat transfer of micropolar fluids past a vertical radiate isothermal permeable surface with viscous dissipation and Joule heating is investigated numerically. The local similarity solutions for the flow, microrotation (angular velocity) and heat transfer characteristics are illustrated graphically for various material parameters. The effects of the pertinent parameters on the local skin friction coefficient, plate couple stress and the rate of heat transfer are also calculated. It was shown that micropolar fluids presented lower viscous drag and heat transfer values than those of the Newtonian fluids. The effect of radiation on the rate of heat transfer in a weakly concentrated micropolar fluid is higher than a strongly concentrated micropolar fluid. Results also show that full radiation has significant effect on the rate of heat transfer compared to the linear radiation.     

柔性圆柱形微管道内的电动流动及传热研究

研究了在纯压力驱动下,流体通过壁面带有某种电荷的聚电解质层（PEL）的微管道，即柔性微管道的电动流动和热传输特性.基于先前得到的电势和速度的解析解以及流向势的数值解,在热充分发展的情况下, 假设壁面热流恒定,利用有限差分法求解了包括黏性耗散和Joule(焦耳)热影响下的能量方程，获得了无量纲温度数值解.通过数值计算，给出了相关的无量纲参数对速度、温度以及Nusselt(努赛尔)数的影响.研究表明,当其他参数固定时,无量纲速度和温度随着无量纲聚电解质层厚度d的增大而减小,随着聚电解质层中等效双电层厚度与双电层厚度之比K_λ的增大而增大；Nusselt数随着Joule热系数S的增大而减小,随无量纲聚电解质层厚度d的增大而减小,随着K_λ的增大而增大.     

Temperature distribution in Couette flow past a permeable bed

The temperature distribution in a steady plane Couette flow having one permeable bounding wall is investigated in the presence of buoyancy forceN ₀ whenN ₀>0, it is shown that heat is transported both by convection and diffusion. The effect of convection is to increase the magnitude of the temperature distribution both in the free and Darcy flows. In particular, it is shown that the wall shear has no significant effect on the temperature distribution. The rate of heat transfer between the fluid and the surface is also calculated and it is shown that, it increases with the porous parameterσ. Although the viscous dissipation has very little effect on the temperature distribution yet its effect is significant on heat transfer.     

Magnetoviscous potential flow analysis of Kelvin–Helmholtz instability with heat and mass transfer

A linear analysis of the Kelvin–Helmholtz instability of interface between two viscous and magnetic fluids has been carried out where there was heat and mass transfer across the interface while the fluids have been subjected to a constant magnetic field parallel to the streaming direction. The viscous potential flow theory has been used for the investigation. A dispersion relation has been obtained and a stability criterion is given by a critical value of relative velocity as well as the critical value of magnetic field. The resulting plots show the effect of various physical parameters such as wave number, viscosity ratio, ratio of magnetic permeabilities and heat transfer coefficient. It has been observed that heat and mass transfer has a destabilizing effect whereas the horizontal magnetic field stabilizes the system.     

Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law

A common of finite-time heat transfer processes between high- and low-temperature sides with generalized radiative heat transfer law [q ∝ Δ(Tⁿ)] is studied in this paper. In general, the minimization of entropy generation in heat transfer processes is taken as the optimization objective. A new physical quantity, entransy, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction recently. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes, as a measure of the heat transfer irreversibility with the dissipation related thermal resistance. Under the condition of fixed heat load, the optimal configurations of hot and cold fluid temperatures for minimizing entransy dissipation are derived by using optimal control theory. The condition corresponding to the minimum entransy dissipation strategy with Newtonian heat transfer law (n = 1) is that corresponding to a constant heat flux rate, while the condition corresponding to the minimum entransy dissipation strategy with the linear phenomenological heat transfer law (n = −1) is that corresponding to a constant ratio of hot to cold fluid temperatures. Numerical examples for special cases with Newtonian, linear phenomenological and radiative heat transfer law (n = 4) are provided, and the obtained results are also compared with the conventional strategies of constant heat flux rate and constant hot fluid (reservoir) temperature operations and optimal strategies for minimizing entropy generation. Moreover, the effects of heat load changes on the optimal hot and fluid temperature configurations are also analyzed.     

Effect of viscous dissipation on natural convection flow between vertical parallel plates with time-periodic boundary conditions

This article investigates the natural convection flow of viscous incompressible fluid in a channel formed by two infinite vertical parallel plates. Fully developed laminar flow is considered in a vertical channel with steady-periodic temperature regime on the boundaries. The effect of internal heating by viscous dissipation is taken into consideration. Separating the velocity and temperature fields into steady and periodic parts, the resulting second order ordinary differential equations are solved to obtain the expressions for velocity, and temperature. The amplitudes and phases of temperature and velocity are also obtained as well as the rate of heat transfer and the skin-friction on the plates. In presence of viscous dissipation, fluids of relatively small Prandtl number has higher temperature than the channel plates and as such, heat is being transferred from the fluid to the plate.     

Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge

An analysis has been carried out to study heat transfer characteristics of an incompressible Newtonian electrically conducting and heat generating/absorbing fluid having temperature-dependent viscosity over a non-isothermal wedge in the presence of thermal radiation. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The wedge surface is assumed to be permeable so as to allow for possible wall suction or injection. The effects of viscous dissipation, Joule heating, stress work and thermal radiation are included in the model. The governing differential equations are derived and transformed using a non-similarity transformation. The transformed equations are solved numerically by applying a fifth-order Runge-Kutta-Fehlberg scheme with shooting technique. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for the velocity and temperature profiles for a prescribed magnetic field parameter as well as the development of the local skin-friction coefficient and local Nusselt number with the magnetic field and radiation parameters are presented graphically and in tabulated form to elucidate the influence of the various physical parameters.     

Nonsimilar solutions for unsteady mixed convection from a moving vertical plate

An analysis is performed to obtain the nonsimilar solution of an unsteady laminar mixed convection on a continuously moving vertical plate by taking into account the effect of viscous dissipation. The unsteadiness is introduced by the time-dependent velocity of the vertical plate as well as that of the free stream. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting system of nonlinear coupled partial differential equations is then solved by an implicit finite difference scheme in combination with the quasilinearization technique. The effects of various parameters on velocity and temperature profiles and on skin friction coefficients and heat transfer rate at the wall are reported in the present study.     

Falling film flow of a viscoelastic fluid along a wall

In this paper, we study the heat transfer in the fully developed flow of a viscoelastic fluid, a slag layer, down a vertical wall. A new constitutive relation for the stress tensor of this fluid is proposed, where the viscosity depends on the volume fraction, temperature, and shear rate. For the heat flux vector, we assume the Fourier's law of conduction with a constant thermal conductivity. The model is also capable of exhibiting normal stress effects. The governing equations are non‐dimensionalized and numerically solved to study the effects of various dimensionless parameters on the velocity, temperature, and volume fraction. The effect of the exponent in the Reynolds viscosity model is also discussed. The different cases of shear‐thinning and shear‐thickening, cooling and heating, are compared and discussed. The results indicate that the viscous dissipation and radiation (at the free surface) cause the temperature to be higher inside the flow domain. Copyright © 2013 John Wiley & Sons, Ltd.