Abstract
The time evolution in the temperature field resulting from the sudden introduction of a heat source into the already fully established steady MHD flow of an electrically conducting fluid past a linearly stretching isothermal surface is considered. The problem is shown to be fully described by two dimensionless parameters, a modified magnetic field strength γ and a heat source strength Q. Numerical solutions of the initial-value problem show that there is a critical value Q c of the parameter Q, dependent on γ, such that, for Q<Q c , the solution approaches a steady state at large times and, for Q>Q c , the solutions grows exponentially large as time increases. This growth rate is determined through an eigenvalue problem which also determines the critical value Q c . The limits of Q c for both small and large values of γ are discussed.
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Merkin, J.H., Kumaran, V. The unsteady heat transfer due to a heat source in an MHD stretching sheet flow. Meccanica 47, 1837–1847 (2012). https://doi.org/10.1007/s11012-012-9556-z
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DOI: https://doi.org/10.1007/s11012-012-9556-z