Abstract
The effect of temperature dependent variable viscosity on magnetohydrodynamic (MHD) natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations are first transformed into a nondimensional form using suitable set of dimensionless variables. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the stream lines and the isotherms are shown graphically for a selection of parameters set consisting of viscosity parameter (), magnetic parameter (), and Prandtl number (Pr). Numerical results of the local skin friction coefficient and the rate of heat transfer for different values are also presented in tabular form.
Highlights
Laminar natural convection boundary layer flow and heat transfer problem from a vertical wavy surface gets a great deal of attention in various branches of engineering
We have focused our attention on the evolution of the surface shear stress in terms of local skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the stream lines and the isotherms for selected values of parameters consisting of the magnetic parameter M, Prandtl number Pr and the viscosity variation parameter ε
There are four parameters of interest in the present problem, our main aim is to determine the effects of varying ε, the temperature dependent viscosity, the strength of magnetohydrodynamic field and Prandtl number Pr
Summary
Laminar natural convection boundary layer flow and heat transfer problem from a vertical wavy surface gets a great deal of attention in various branches of engineering. If the surface is roughened, the flow is disturbed by the surface and this alters the rate of heat transfer. These types of roughened surface are taken into account in several heat transfer collectors, flat plate condensers in refrigerators and heat exchanger. Machine-roughened surface enhanced heat transfer and the interface between concurrent or countercurrent two-phase flow is another example remotely related to this problem. Such an interface is always wavy and momentum transfer across it is by no means similar to that across a smooth, flat surface and neither is the heat transfer
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