Abstract
In this paper, an analysis is performed to explorethe transient, laminar two-dimensional, mixed convection boundary layer flow of a viscous and incompressible fluid past a vertical wedge taking into account the effect of magnetic field. With appropriate transformations the boundary layer equations are reduced to a local nonsimilarity equations and the solutions are obtained employing three distinct methods, namely, (i) perturbation method for small time; (ii) asymptotic solution method for large time; (iii) straight forward finite difference method for any time. The agreement between the solutions obtained from prescribed methods is found to be excellent. In this study the evaluation of skin-friction coefficient and the local Nusselt number with the effects of different governing parameters such as different time, τ, the exponent, m (= 0.4, 0.5, 1.0), mixed convection parameter, λ (= 0.0, 0.2, 0.4) and magnetic field parameter, M (=0.0, 1.0) for fluids having Prandtl number, Pr= 0.72, 1.0 and 7.0have been discussed. It is observed that both the local skin friction and local Nusseltnumber decreases due to an increase in the value of M. It is also found that an increase in the value of Prandtl number, Pr, leads to a decrease in the value of local skin friction coefficient and the value of local Nusselt number coefficient increases with the increasing values of Prandtl number.
Highlights
The laminar boundary layer flow of an incompressible fluid past bodies of different geometries has been studied with a great importance because it has a considerable curiosity among scientists and researchers
The governing equations have been solved by using the straight forward finite difference method for the entire time regime
Solutions of the governing local nonsimilarity equations are obtained by three distinct methodologies, namely the perturbation method for small time τ, the asymptotic solution method for large time τ and the finite difference method of all time τ
Summary
The laminar boundary layer flow of an incompressible fluid past bodies of different geometries has been studied with a great importance because it has a considerable curiosity among scientists and researchers. The skin friction and heat transfer in two-dimensional, viscous, incompressible laminar flow over wedge-shaped bodies can be calculated accurately by solving the boundary-layer equations. Hartree [5] investigated the similarity solutions of the flow in detail He obtained the solutions in terms of velocity distribution for different values of pressure gradient parameter. For flow over an arbitrary body shape with known pressure or velocity distribution where there exists no similarity, the skin friction and heat transfer are conventionally found by an approximate method, either the integral method or the equivalent wedge flow approximation. It is necessary to have the solutions of the boundary-layer equations for wedge type flows to apply the equivalent wedge flow method for the prediction of skin-friction and heat transfer. From the practical point of view, the surface mass-flux with constant velocity may be more realized than with x(m−1)/2 , where x is the distance from the leading edge, m the pressure gradient parameter
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