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A new approach for local similarity solutions of an unsteady hydromagnetic free convective heat transfer flow along a permeable flat surface. (English) Zbl 1360.76350

Summary: In this study a new class of similarity transformations is used to obtain local similarity solutions for an unsteady hydromagnetic free convective heat transfer flow along a permeable vertical plate. The resulting local similarity equations are solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Steady solutions are compared with previously published results which show excellent agreement. The results show that this new similarity approach has the advantage that one can separately obtain the steady and unsteady solutions. The results also show that unsteadiness is found to reduce the hydrodynamic as well as thermal boundary layer growths.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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