Viscous dissipation effect on free convection flow past a semi-infinite flat plate in the presence of magnetic field
The author analyzes the influence of different parameters on the solution to a 2D incompressible free convection flow past a continuously moving semi-infinite flat plate with magnetic field. Writing the continuity, momentum, energy and concentration balance equations and introducing a stream function and dimensionless variables, he ends with the system of ODEs \(f^{\prime \prime \prime }+\frac{1}{2}ff^{\prime \prime }+\mathrm{Gr}\theta -\mathrm{Mf}^{\prime }=0\), \(\theta ^{\prime \prime }+\frac{1}{2}\mathrm{Pr}\theta ^{\prime }+\mathrm{PrEc}(f^{\prime \prime })^{2}=0\), \(\phi ^{\prime \prime }+\frac{1}{2}\mathrm{Sc}\phi f^{\prime }=0\), with respect to a parameter \(\eta\), where \(f^{\prime }\) (resp. \(\theta ,\phi \)) is the velocity profile (resp. temperature and concentration). Initial and boundary conditions are imposed at \(\eta =0\) and \(\eta =\infty \). Here \(\mathrm{Gr}\) and \(M\) are the viscous dissipation and local magnetic field parameters and Pr, Ec and Sc are Prandtl, Eckert and Schmitt numbers. The author also introduces the Nusselt and Sherwood numbers. This system is solved using a Runge-Kutta fourth-order scheme and the shooting method in the Maple software and the author presents the results of the numerical simulations for different values of the above-indicated parameters or numbers.
scientific article; zbMATH DE number 6645005