Influence of magnetic field and thermal radiation by natural convection past vertical cone subjected to variable surface heat flux

A numerical study is performed to examine the heat transfer characteristics of natural convection past a vertical cone under the combined effects of magnetic field and thermal radiation.The surface of the cone is subjected to a variable surface heat flux.The fluid considered is a gray,absorbing-emitting radiation but a non-scattering medium.With approximate transformations,the boundary layer equations governing the flow are reduced to non-dimensional equations valid in the free convection regime.The dimensionless governing equations are solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent,accurate,and unconditionally stable.Numerical results are obtained and presented for velocity,temperature,local and average wall shear stress,and local and average Nusselt number in air and water.The present results are compared with the previous published work and are found to be in excellent agreement.     

Nonsimilar solutions for free convection from a vertical plate in porous media

A nonsimilar boundary layer analysis has been presented for the free convection along a vertical plate embedded in a fluid-saturated porous medium in the presence of surface mass transfer and internal heat generation. The transformed conservation laws are solved numerically for the cases of variable wall temperature and variable wall heat flux boundary conditions. Results are presented for the details of the velocity and temperature fields as well as Nusselt number. Received on 13 December 1996     

Mixed convection heat transfer from a horizontal plate with variable surface heat flux in a porous medium

In this article nonsimilarity solution for mixed convection from a horizontal surface in a saturated porous medium was obtained for the case of variable surface heat flux. The entire mixed convection regime, ranging from pure forced convection to pure free convection, is considered by introducing a single nonsimilarity parameter. Heat transfer results are predicted by employing four different flow models, namely, Darcy's law, the Ergun model, and the Brinkman-Forchheimer-extended Darcy model with constant and variable porosity. The variable porosity effect is approximated by an exponential function. Effects of transverse thermal dispersion are taken into consideration in the energy equation, along with variable stagnant thermal conductivities. The formulation of the present problem shows that the flow and heat transfer characteristics depend on five parameters, that is, the power in the variation of surface heat flux, the nonsimilarity mixed-convection parameter, the inertia effect parameter, the boundary effect parameter, and the ratio of thermal conductivity of the fluid phase to that of the solid phase. Numerical results for the local Nusselt number variations, based on the various flow models, are presented for the entire mixed convection regime. The impacts␣of different governing parameters on the heat transfer results are thoroughly investigated. Received on 7 August 1997     

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

This 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.     

Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium

Unsteady laminar mixed convection flow (combined free and forced convection flow) along a vertical slender cylinder embedded in a porous medium under the combined buoyancy effect of thermal and species diffusion has been studied. The effect of the permeability of the medium as well as the magnetic field has been included in the analysis. The partial differential equations with three independent variables governing the flow have been solved numerically using a implicit finite difference scheme in combination with the quasilinearization technique. Computations have been carried out for accelerating, decelerating and oscillatory free stream velocity distributions. The effects of the permeability of the medium, buoyancy forces, transverse curvature and magnetic field on skin friction, heat transfer and mass transfer have been studied. It is found that the effect of free stream velocity distribution is more pronounced on the skin friction than on the heat and mass transfer. The permeability and magnetic parameters increase the skin friction, but reduce the heat and mass transfer. The skin friction, heat transfer and mass transfer are enhanced due to the buoyancy forces and curvature parameter. The heat transfer is strongly dependent on the viscous dissipation parameter and the Prandtl number, and the mass transfer on the Schmidt number.     

Mixed convection flow over a vertical wedge embedded in a highly porous medium

 The steady mixed convection flow over a vertical wedge with a magnetic field embedded in a porous medium has been investigated. The effects of the permeability of the medium, surface mass transfer and viscous dissipation on the flow and temperature fields have been included in the analysis. The coupled nonlinear partial differential equations governing the flow field have been solved numerically using the Keller box method. The skin friction and heat transfer are found to increase with the parameters characterizing the permeability of the medium, buoyancy force, magnetic field and pressure gradient. However the effect of the permeability and magnetic field on the heat transfer is very small. The heat transfer increases with the Prandtl number, but the skin friction decreases. The buoyancy force which assists the forced convection flow causes an overshoot in the velocity profiles. Both the skin friction and heat transfer increase with suction and the effect of injection is just the reverse. Received on 21 May 1999     

Steady mixed convection flow of Maxwell fluid over an exponentially stretching vertical surface with magnetic field and viscous dissipation

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.     

Combined convection in non-Newtonian fluids along a nonisothermal vertical plate in a porous medium with lateral mass flux

 A boundary layer analysis has been presented for interaction of combined convection from vertical surface in a porous medium saturated with a power-low type non-Newtonian fluid with presence suction and injection. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The effect of fluid suction/injection on the heat transfer rate is discussed. Received on 21 December 1999     

Mixed convection in non-Newtonian fluids along a vertical plate with variable surface heat flux in a porous medium

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along a vertical plate with power-law surface heat flux distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate. Received on 13 October 1998     

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.     

Finite-difference solution of unsteady natural convection flow past a nonisothermal vertical cone under the influence of a magnetic field and thermal radiation

An analysis is performed to study the heat transfer characteristics of natural convection over a vertical cone under the combined effects of a magnetic field and thermal radiation. The cone surface is subjected to a variable surface temperature. The fluid considered is a gray absorbing/emitting, but non-scattering medium. The boundary layer equations governing the flow are reduced to non-dimensional equations using non-dimensional quantities valid in the free-convection regime. The resulting non-dimensional governing equations are solved by an implicit finite-difference method of the Crank-Nicolson type, which is rapidly convergent and unconditionally stable. Numerical results are obtained for velocity, temperature, local and average skin friction, and local and average Nusselt numbers for various values of parameters occurring in the problem and are presented in the graphical form. Excellent agreement of the results obtained with available data is demonstrated.     

Effect of variable viscosity on non-Darcy free or mixed convection flow on a vertical surface in a fluid saturated porous medium

This paper analyzes the variable viscosity effects on non-Darcy free or mixed convection flow on a vertical surface in a fluid saturated porous medium. The viscosity of the fluid is assumed to be a inverse linear function of temperature. Velocity and heat transfer are found to be significantly affected by the variable viscosity parameter, Ergun number, Peclet number or Rayleigh number.     

Natural convection flow over a vertical frustum of a cone for constant wall heat flux

Laminar natural convection flow and heat transfer over a vertical frustum of a cone has been studied. The governing boundary layer equations are solved using local non-similarity method for constant wall heat flux. The local similarity and the local non-similarity two and three-equation models are constructed and the resulting equations are solved numerically. Results obtained from two and three-equation models are in good agreement. The numerical values of the flow and temperature functions required to calculate the surface skin friction and heat transfer rate are reported for various values of Prandtl numbers.     

Free convection in non-newtonian fluids along a horizontal plate in a porous medium

A similarity solution is presented for the problem of free convection boundary layer in power-law type non-Newtonian fluids along a horizontal plate with variable wall temperature or heat flux distribution. The effects of surface mass transfer are included. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.     

Natural convection with evaporation in a vertical cylindrical cavity under the effect of temperature-dependent surface tension

The effect of surface tension on laminar natural convection in a vertical cylindrical cavity filled with a weak evaporating liquid has been analyzed numerically. The cylindrical enclosure is insulated at the bottom, heated by a constant heat flux from the side, and cooled by a non-uniform evaporative heat flux from the top free surface having temperature-dependent surface tension. Governing equations with corresponding boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The influence of Rayleigh number, Marangoni number, and aspect ratio on the liquid flow and heat transfer has been studied. Obtained results have revealed that the heat transfer rate at free surface decreases with Marangoni number and increases with Rayleigh number, while the average temperature inside the cavity has an opposite behavior; namely, it growths with Marangoni number and reduces with Rayleigh number.     

Unsteady mixed convection boundary layer flow over a vertical cone with non-uniform slot suction (injection)

The non-similar solution of an unsteady mixed convection laminar boundary layer flow over a vertical cone in the presence of non-uniform surface mass transfer through slot has been obtained while the axis of cone is inline with the flow. The unsteadiness is caused by the time dependent free stream velocity. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting coupled non-linear partial differential equations have been solved numerically by the combination of quasi-linearization technique and an implicit finite difference scheme. Numerical computations are performed for different values of the parameters to display the velocity and temperature profiles graphically. Both accelerating and decelerating free stream velocities are considered. Numerical results are reported to display the effects of non-uniform single and double slot suction (injection) on skin friction and heat transfer coefficients at the wall. Further, the effects of Prandtl number, buoyancy and mass transfer (suction or injection) parameters at different stream-wise locations for various times on velocity and temperature profiles, and on skin friction and heat transfer coefficients are also presented in this paper.     

Free convection flow over an uniform-heat-flux surface with temperature-dependent viscosity

The role of temperature-dependent viscosity is studied in laminar free convection flow adjacent to a vertical surface with uniform heat flux. The resulting non-similar equations are solved by using a suitable variable transformation and employing an implicit finite difference method. It is shown that the constant viscosity results evaluated at the ambient fluid temperature underestimate the Nusselt number and overestimate the drag coefficient. The heat transfer predictions for large values of the viscosity parameter may be two times the constant viscosity parameter prediction. The present analysis is in good agreement with the corresponding correlation of previous experimental investigation.     

Similarity solution of free convective boundary-layer behavior at a stretching surface

In the present study, free convection and heat transfer behavior of electrically conducting fluid in the boundary layer over a vertical continuously stretching surface is investigated. The effects of free convection, magnetic field, suction/blowing at the surface and the stretching speed of the surface on the flow and heat transfer characteristics are considered. By applying one-parametric group theory to analysis of the problem, a similarity solution is found. The governing equations of continuity, momentum and energy are solved numerically by a fourth-order Runge-Kutta scheme. The numerical results, which are obtained for the flow and heat transfer characteristics, reveal the influences of the parameters. Received on 9 September 1998     

Effects of viscous dissipation on a power-law fluid over plate embedded in a porous medium

The present study is devoted to investigate the influences of viscous dissipation on buoyancy induced flow over a horizontal or a vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained with prescribed variable surface temperature (PT) or with prescribed variable surface heat flux (PHF) for the horizontal plate case. While, the similarity solutions are obtained with prescribed variable surface heat flux for the vertical plate case. Different similar transformations, for each case, are used. Numerical results for the details of the velocity and temperature profiles are shown on graphs. Nusselt number associated with temperature distributions and excess surface temperature associated with heat flux distributions which are entered in tables have been presented for different values of the power-law index n and the exponent as well as Eckert number.     

Mixed Convection-Radiation in Power-Law Fluids Along a NOn-Isothermal Wedge in a Porous Medium with Variable Permeability

A boundary layer analysis has been presented for the interaction of mixed convection with thermal radiation in laminar boundary flow from a vertical wedge in a porous medium saturated with a power-law type non-Newtonian incorporating the variation of permeability and thermal conductivity. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. The combined convection non-similar parameter we note that =0 and 1 correspond to pure free and forced convection cases. The Rosseland approximation is used to describe the radiative heat flux in energy equation. Velocity and temperature profiles as well as the local Nusselt number are presented.