Prescribed Surface Heat Flux Research Articles

Momentum and Heat Transfer in MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet

In this paper we present a mathematical analysis for the magneto hydrodynamic (MHD) axi-symmetric stagnation-point flow and heat transfer over a shrinking sheet which shrinks axi-symmetrically in its own plane. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then these equations are solved numerically by shooting technique. Thermal conductivity is assumed to vary linearly with the temperature. Temperature profiles are obtained for two different types of heating process namely (i) the sheet with prescribed surface temperature (PST) and (ii) the sheet with prescribed surface heat flux (PHF). The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.

Buongiorno Model for Nanofluid Blasius Flow with Surface Heat and Mass Fluxes

The Buongiorno model is used to investigate the effects of Brownian motion and thermophoresis on the flow, heat, and mass transfer from a flat plate with prescribed surface heat flux. The experimental correlations for the effective density, thermal conductivity, and viscosity of nanofluid are incorporated in the governing equations. Governing partial differential equations are transformed into a set of ordinary differential equations by using similarity transformations. These equations are solved numerically using the Runge–Kutta–Fehlberg method, which produces a fifth-order-accurate solution. The results for the dimensionless velocity, temperature, wall shear stress, and Nusselt and Sherwood numbers are presented graphically and compared for water-based nanofluids with ethylene-glycol-based nanofluids.

Natural convection on a vertical plate with variable heat flux in supercritical fluids

The present article investigates laminar free convection with uniform or non-uniform prescribed surface heat flux over a vertical flat plate in supercritical fluid, numerically. A new equation for thermal expansion coefficient in a supercritical fluid is derived based on Redlich–Kwong equation of state as a function of pressure, temperature and the compressibility factor. Calculated values of thermal expansion coefficient have been compared with the experimental results which show better accuracy in comparison with van der Waals ones. The governing systems of partial differential equations were solved numerically using the finite difference method. The local Nusselt number was calculated and plotted as a function of the local Rayleigh number. Using supercritical fluids in constant heat flux free convection, decrease wall temperature in comparison with under critical fluids. It was observed that positive and negative slopes of surface heat flux distribution increases and decreases the heat transfer coefficient, respectively.

Second law analysis for free convection in non-newtonian fluids over a horizontal plate embedded in a porous medium: (prescribed heat flux)

Second law characteristics of heat transfer and fluid flow due to free convection of non-Newtonian fluids over a horizontal plate with prescribed surface heat flux in a porous medium are analyzed. Velocity and temperature fields are obtained numerically using an implicit finite difference method under the similarity assumption and these results are used to compute the entropy generation rate Ns, irreversibility ratio φ and the Bejan number Be for both Newtonian and non-Newtonian fluids. The effects of power-law index n, heat flux variation parameter λ , and modified duty parameter, G on the dimensionless entropy generation rate Ns, and the Bejan number Be are investigated and presented graphically.

Analytic heat and mass transfer of the mixed hydrodynamic/thermal slip MHD viscous flow over a stretching sheet

In this paper, the heat and mass transfer characteristics of the magnetohydrodynamic (MHD) viscous flow over a permeable stretching surface is solved analytically. The flow considered is under both the hydrodynamic and thermal slip conditions. The magnetohydrodynamic flow and heat transfer of an electrically conducting fluid, taking into account the effects of Joule and viscous dissipation, internal heat generation/absorption, work done due to deformation and thermal radiation is studied. The solution is expressed in a closed form equation and is an exact solution of the full governing Navier–Stokes and energy equations. Thermal transport is analyzed for two types of non-isothermal boundary conditions, i.e. prescribed surface temperature (PST) and prescribed surface heat flux (PHF) varying as a power of the distance from the origin. Results for some special cases of the present analysis are in excellent agreement with those existing in the literature. The effects of various physical parameters, such as magnetic parameter, thermal radiation parameter, heat source/sink parameter, Prandtl number, Eckert number and suction/injection parameter on the velocity and temperature profiles, skin friction coefficient and Nusselt number are examined and discussed in detail. Results show that there is only one physical solution for any combination of the slip together with all the parameters. The velocity/shear stress profiles and the temperature/heat transfer profiles are greatly influenced by these parameters.

Mixed Convection Stagnation-Point Flow Over a Vertical Plate with Prescribed Heat Flux Embedded in a Porous Medium: Brinkman-Extended Darcy Formulation

This article considers the problem of mixed convection stagnation-point flow towards a vertical plate embedded in a porous medium with prescribed surface heat flux. It is assumed that the free stream velocity and the surface heat flux vary linearly from the stagnation point. Using a similarity transformation, the governing system of partial differential equations is transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and the heat transfer characteristics are analyzed and discussed. It is found that dual solutions exist for both buoyancy assisting and opposing flows.

Boundary layer flow and heat transfer of a dusty fluid flow over a stretching sheet with non-uniform heat source/sink

The present paper deals with the analysis of boundary layer flow and heat transfer of a dusty fluid over a stretching sheet with the effect of non-uniform heat source/sink. Here we consider two types of heating processes namely (i) prescribed surface temperature and (ii) prescribed surface heat flux. The momentum and thermal boundary layer equations of motion are solved numerically using Runge Kutta Fehlberg fourth–fifth order method (RKF45 Method). The effects of fluid particle interaction parameter, Eckert number, Prandtl number, Number of dust particle and non-uniform heat generation/absorption parameter on temperature distribution are analyzed and also the effect of wall temperature gradient function and wall temperature function are tabulated and discussed.

MHD flow of a micropolar fluid towards a vertical permeable plate with prescribed surface heat flux

The problem of a steady mixed convection stagnation point flow towards a permeable vertical plate with prescribed surface heat flux immersed in an incompressible micropolar fluid is studied numerically. The governing partial differential equations are first transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by a finite-difference scheme known as the Keller-box method and the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter, buoyancy parameter, suction/injection parameter and the Prandtl number on the fluid flow and heat transfer characteristics are discussed. It is found that dual solutions exist for both assisting and opposing flows. The skin friction coefficient and the local Nusselt number increase in the presence of suction and magnetic field. Moreover, suction as well as fluids with larger Prandtl number widens the range of the buoyancy parameter for which the solution exists.

Effects of slip on sheet-driven flow and heat transfer of a non-Newtonian fluid past a stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian fluid due to a stretching surface subject to partial slip is considered. The constitutive equation of the non-Newtonian fluid is modeled by that for a third grade fluid. The heat transfer analysis has been carried out for two heating processes, namely, (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHFcase) in presence of a uniform heat source or sink. 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. The important finding in this communication is the combined effects of the partial slip, magnetic field, heat source (sink) parameter and the third grade fluid parameters on the velocity, skin friction coefficient and the temperature field. It is interesting to find that slip decreases the momentum boundary layer thickness and increases the thermal boundary layer thickness, whereas the third grade fluid parameter has an opposite effect on the thermal and velocity boundary layers.

Hydromagnetic flow and heat transfer over a bidirectional stretching surface in a porous medium

In this study, we present a steady three-dimensional magnetohydrodynamic (MHD) flow and heat transfer characteristics of a viscous fluid due to a bidirectional stretching sheet in a porous medium. The heat transfer analysis has been carried out for two heating processes namely (i) the prescribed surface temperature (PST) and (ii) prescribed surface heat flux (PHF). In addition the heat transfer rate varies along the surface. The similarity solution of the governing boundary layer partial differential equations is developed by employing homotopy analysis method (HAM). The quantities of interest are velocity, temperature, skin-friction and wall heat flux. The results obtained are presented through graphs and tabular data. It is observed that both velocity and boundary layer thickness decreases by increasing the porosity and magnetic field. This shows that application of magnetic and porous medium cause a control on the boundary layer thickness. Moreover, the results are also compared with the existing values in the literature and found in excellent agreement.

New analytical solution for natural convection of Darcian fluid in porous media prescribed surface heat flux

A new analytical method called He's Variational Iteration Method is introduced to be applied to solve nonlinear equations. In this method, general Lagrange multipliers are introduced to construct correction functional for the problems. It is strongly and simply capable of solving a large class of linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term and also is very user friend because it reduces the size of calculations besides; its iterations are direct and straightforward. In this paper the powerful method called Variational Iteration Method is used to obtain the solution for a nonlinear Ordinary Differential Equations that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. The obtained Variational Iteration Method solution in comparison with the numerical ones represents a remarkable accuracy.

Falkner–Skan problem for a static and moving wedge with prescribed surface heat flux in a nanofluid

An analysis is carried out to study the problem of the steady flow and heat transfer over a static or moving wedge with a prescribed surface heat flux in a nanofluid. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using similarity transformation, before being solved numerically by the Keller box method and the Runge–Kutta–Fehlberg method with shooting technique. The features of the flow and heat transfer characteristics are analyzed and discussed. Three different types of nanoparticles are considered, namely copper Cu, alumina Al 2O 3 and titania TiO 2 with water as the base fluid. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for copper–water nanofluid compared to the alumina–water and titania–water nanofluids. Moreover, the heat transfer rate at the surface increases with the Falkner–Skan power law parameter m.

Boundary Layer Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet with Prescribed Surface Heat Flux

The steady two-dimensional flow adjacent to a vertical, continuously stretching sheet in a viscous and incompressible fluid is studied. It is assumed that the sheet is stretched with a power-law velocity and is subjected to a variable surface heat flux. The governing partial differential equations are reduced to nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by the Keller-box method. Results showed that the heat transfer rate at the surface increases as the velocity exponent parameter, mixed convection parameter and the Prandtl number are increased. Keywords: Similarity solution; heat transfer; numerical solution; stretching sheet.

The laminar free‐convection boundary‐layer flow about a heated and rotating down‐pointing vertical cone in the presence of a transverse magnetic field

AbstractThis paper deals with the study of the laminar free‐convection boundary‐layer flow about a heated and rotating down‐pointing vertical cone in the presence of a transverse magnetic field. Two cases of heat transfer analysis are discussed. These are: (i) the rotating cone with prescribed surface temperature and (ii) the rotating cone with prescribed surface heat flux. By means of similarity transformation, the governing partial differential equations are reduced into highly non‐linear ordinary differential equations. The resulting non‐linear system has been solved analytically using a very efficient technique, namely homotopy analysis method. Expressions for velocity and temperature fields are developed in a series form. The influence of various pertinent parameters is also seen on the velocity and temperature fields. Copyright © 2010 John Wiley & Sons, Ltd.

Effects of slip on sheet-driven flow and heat transfer of a third grade fluid past a stretching sheet

The entrained flow and heat transfer of an electrically conducting non-Newtonian fluid due to a stretching surface subject to partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). The constitutive equation of the non-Newtonian fluid is modeled by that for a third grade fluid. The heat transfer analysis has been carried out for two heating processes, namely, (i) with prescribed surface temperature (PST case) and (ii) prescribed surface heat flux (PHF case). 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. The important finding in this communication is the combined effects of the partial slip, magnetic field and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that slip decreases the momentum boundary layer thickness and increases the thermal boundary layer thickness, whereas the third grade fluid parameter has an opposite effect on the thermal and velocity boundary layers.

On the analytic solution of MHD flow and heat transfer for two types of viscoelastic fluid over a stretching sheet with energy dissipation, internal heat source and thermal radiation

In this paper we study the magneto-hydrodynamic flow and heat transfer of an electrically conducting, viscoelastic fluid past a stretching surface, taking into account the effects of Joule and viscous dissipation, internal heat generation/absorption, work done due to deformation and thermal radiation. Closed-form solutions for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walters’ liquid B fluids. Thermal transport is analyzed for two types of non-isothermal boundary conditions, i.e. prescribed surface temperature (PST) and prescribed surface heat flux (PHF) varying as a power of the distance from the origin. Results for some special cases of the present analysis are in excellent agreement with the existing literature. The effects of various physical parameters, such as viscoelasticity, magnetic parameter, thermal radiation parameter, heat source/sink parameter, Prandtl number, Eckert number and suction/injection parameter on the velocity and temperature profiles, skin friction coefficient and Nusselt number are examined and discussed in detail.

Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet with prescribed surface heat flux

The similarity solution for the problem of mixed convection boundary layer flow adjacent to a stretching vertical sheet in an incompressible electrically conducting fluid in the presence of a transverse magnetic field is presented. It is assumed that the sheet is stretched with a power-law velocity and is subjected to a variable surface heat flux. The governing partial differential equations are first transformed into a system of non-linear ordinary differential equations, before being solved numerically by the Keller-box method. The numerical results obtained are then compared with previously reported cases available in the literature as well as the series solution for certain values of parameters, to support their validity. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed.

Heat transfer in a viscoelastic boundary layer flow over a stretching sheet

Abstract Studies are made on the viscoelastic fluid flow and heat transfer characteristics over a stretching sheet with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for the cases of prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The momentum equation is decoupled from the energy equation for the present incompressible boundary layer flow problem with constant physical parameters. Exact solution for the velocity field and the skin-friction are obtained. Also, the solutions for the temperature and heat transfer characteristics are obtained in terms of Kummer’s function. The work due to deformation in energy equation, which is essential while formulating the viscoelastic boundary layer flow problems, is considered. This paper examines the effect of viscoelastic parameter, Eckert number, Prandtl number and non-uniform heat source/sink parameter on temperature distribution, wall temperature gradient for PST-case and wall temperature for PHF-case.

Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux

In this paper, a powerful analytical method, called homotopy analysis method (HAM) is used to obtain the analytical solution for a nonlinear ordinary deferential equation that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. Nonlinear ODE which is obtained by similarity solution has been solved through homotopy analysis method (HAM). The main objective is to propose alternative methods of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The obtained analytical solution in comparison with the numerical ones represents a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region.

Heat transfer in unsteady axisymmetric second grade fluid

This work looks at the heat transfer effects on the flow of a second grade fluid over a radially stretching sheet. The axisymmetric flow of a second grade fluid is induced due to linear stretching of a sheet. Mathematical analysis has been carried out for two heating processes, namely ( i) with prescribed surface temperature (PST case) and ( ii) prescribed surface heat flux (PHF case). The modelled non-linear partial differential equations in two dependent variables are reduced into a partial differential equation with one dependent variable. The resulting non-linear partial differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence is properly discussed. The series solutions and graphs of velocity and temperature are constructed. Particular attention is given to the variations of emerging parameters such as second grade parameter, Prandtl and Eckert numbers.