Mixed convection of a viscous dissipating fluid about a vertical flat plate (original) (raw)
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The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a vertical plate is studied numerically, taking into account the effects of Ohmic heating and viscous dissipation. A uniform magnetic field is applied perpendicular to the plate. The resulting governing equations are transformed into the non-similar boundary layer equations and solved using the Keller box method. Both the aiding-buoyancy mode and the opposing-buoyancy mode of the mixed convection are examined. The velocity and temperature profiles as well as the local skin friction and local heat transfer parameters are determined for different values of the governing parameters, mainly the magnetic parameter, the Richardson number, the Eckert number and the suction/injection parameter, f w. For some specific values of the governing parameters, the results agree very well with those available in the literature. Generally, it is determined that the local skin friction coefficient and the local heat transfer coefficient increase owing to suction of fluid, increasing the Richardson number, Ri (i.e. the mixed convection parameter) or decreasing the Eckert number. This trend reverses for blowing of fluid and decreasing the Richardson number or decreasing the Eckert number. It is disclosed that the value of Ri determines the effect of the magnetic parameter on the momentum and heat transfer.
PLoS ONE, 2013
The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.
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The effect of temperature dependent viscosity on laminar mixed convection boundary layer flow and heat transfer on a continuously moving vertical surface is studied. The fluid viscosity is assumed to vary as an inverse linear function of temperature. Local similarity solutions are obtained for the boundary layer equations subject to isothermally moving vertical surface with uniform speed. The effect of various governing parameters, such as Prandtl number Pr, the mixed convection parameter λ = S Gr x /Re 2 x , and the viscosity/temperature parameter θ r which determine the velocity and temperature distributions, the local heat transfer coefficient, and the local shear stress coefficient at the surface are studied. Significant changes are obtained in dimensionless local heat transfer and shear stress coefficient at the surface when the magnitude of θ r has small values for each λ. Critical values of λ are obtained for predominate natural convection and buoyancy shear stress for assisting and opposing flow for various θ r .
JOURNAL OF ADVANCES IN PHYSICS, 2014
The steady mixed convection flow from a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of thermal radiation as well as Newtonian heating effects. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in conjunction with the quasi-linearization technique. Computations are performed and representative set is displayed graphically to illustrate the influence of the mixed convection parameter ( ), Prandtl number (Pr), the ratio of free stream velocity to the composite reference velocity ( ) and the radiation parameter (R) on the velocity and temperature profiles. The numerical results for the local skinfriction coefficient ( ) and surface temperature ( ) are also presented. The results show th...
Mixed convection of non-Newtonian fluids along a heated vertical flat plate
"Mixed convective heat transfer of non-Newtonian fluids on a flat plate has been investigated using a modified power-law viscosity model. This model does not contain physically unrealistic limits of zero or infinite viscosity as are encountered in the boundary-layer formulation with traditional models of viscosity for power-law fluids. These unrealistic limits can introduce an irremovable singularity at the leading edge; consequently, the model is physically incorrect. The present modified model matches well with the measurement of viscosity, and does not introduce irremovable singularities. Therefore, the boundarylayer equations can be solved by marching from the leading edge downstream as for Newtonian fluids. The numerical results are presented for a shear-thinning fluid in terms of the velocity and temperature distribution, and for important physical properties, namely the wall shear stress and heat transfer rates."
Asian Research Journal of Mathematics, 2021
A heated vertical flat plate in the presence of heat generation is an extremely significant technological issue, and many academics have studied this sort of problem. A vertical plate submerged in a fluid with varying viscosity will be used in this research to investigate the effects of variable viscosity and thermal conductivity on heat generation free convection flow. The boundary layer equations in this section are two-dimensional, laminar, and unstable. The fundamental governing equations are turned into non-dimensional governing equations by using the necessary variables. Using the Crank-Nicolson implicit finite-difference technique, these equations are solved numerically. Viscosity and thermal conductivity are temperature-dependent properties of a viscous, incompressible fluid. Variations in the study's numerous parameters will reveal and compare the velocities, temperatures, local skin friction, and local heat transfer co-efficient profiles. There will be a comparison bet...
Journal of Computational Engineering, 2014
The purpose of this study is to investigate the natural convection laminar flow along an isothermal vertical flat plate immersed in a fluid with viscosity which is the exponential function of fluid temperature in presence of internal heat generation. The governing boundary layer equations are transformed into a nondimensional form and the resulting nonlinear system of partial differential equations is reduced to a convenient form which are solved numerically using an efficient marching order implicit finite difference method with double sweep technique. Numerical results are presented in terms of the velocity and temperature distribution of the fluid as well as the heat transfer characteristics, namely, the wall shear stress and the local and average rate of heat transfer in terms of the local skin-friction coefficient, the local and average Nusselt number for a wide range of the viscosity-variation parameter, heat generation parameter, and the Rayleigh number. Increasing viscosity ...
The effect of viscous dissipation and boundary conditions of the third kind on fully developed mixed convection for the laminar flow in a parallel plate vertical channel filled with two immiscible viscous fluids is studied analytically. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperatures of external fluid are considered. Separate solutions are matched at the interface using suitable matching conditions. First, the simple cases of the negligible Brinkman or negligible Grashof numbers are solved. Then, the combined effects of buoyancy forces and viscous dissipation are analyzed by the perturbation series method (PM), valid for small values of the perturbation parameter, and by the differential transform method (DTM), valid for all values of perturbation parameter. Numerical results are presented graphically for the distribution of velocity and temperature fields for varying physical parameters, such as the mixed convection parameter, perturbation parameter, viscosity ratio, width ratio, conductivity ratio, and Biot numbers. The effect of these parameters on the Nusselt number at the walls is also presented graphically. It is found that the mixed convection parameter and perturbation parameter enhance the flow field; whereas, the viscosity ratio, width ratio, and conductivity ratio suppress the flow field. It is also found that both PM and DTM solutions agree very well for small values of the perturbation parameter.
International Journal of Heat and Technology, 2021
Received: 5 March 2020 Accepted: 14 December 2020 This paper elucidates heat together with mass transfer through a flat plate and variable temperature as well as dissipative effects. The flow assumptions resulted to steady flow equations which were simplified with appropriate similarity variables. The simplified equations were numerically solved and results are presented both in graphs and tabular form. Effects of physical quantities of interest were presented graphically. The local skin friction is observed to increase because of increase in Schmidt number. Also, increase in Prandtl number is found to boast the local Nusselt number. The behaviour of increase in Prandtl number is found to be unstable within the boundary layer regime while increase in Eckert number produces heat energy within the fluid layers. Finally, the validation of the present problem is done by comparing with previous works and was in perfect agreement.
In the present study we investigate the effect of viscous dissipation on natural convection from a vertical plate placed in a thermally stratified environment. The reduced equations are integrated by employing the implicit finite difference scheme of Keller box method and obtained the effect of heat due to viscous dissipation on the local skin friction and local Nusselt number at various stratification levels, for fluids having Prandtl numbers of 10, 50, and 100. Solutions are also obtained using the perturbation technique for small values of viscous dissipation parameters ξ and compared to the finite difference solutions for 0 ≤ ξ ≤ 1. Effect of viscous dissipation and temperature stratification are also shown on the velocity and temperature distributions in the boundary layer region.