Unsteady magnetohydrodynamic stagnation point flow—closed-form analytical solutions
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This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic (MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes (NS) equations are transformed into a similarity nonlinear ordinary differential equation, and a closed form solution is obtained for the unsteadiness parameter of 2. The boundary layer energy equation is transformed into a similarity equation, and is solved for a constant wall temperature and a time-dependent uniform wall heat flux case. The solution domain, velocity, and temperature profiles are calculated for different combinations of parameters including the Prandtl number, mass transfer parameter, wall moving parameter, and magnetic parameter. Two solution branches are obtained for certain combinations of the controlling parameters, and a stability analysis demonstrates that the lower solution branch is not stable. The present solutions provide an exact solution to the entire unsteady MHD NS equations, which can be used for validating the numerical code of computational fluid dynamics.
Key wordsunsteady stagnation point flow stretching/shrinking sheet magnetohydrodynamic (MHD) Navier-Stokes (NS) equation
Chinese Library ClassificationO3613
2010 Mathematics Subject Classification76W05
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- MAGYARI, E. and WEIDMAN, P. D. Comment on “Unsteady stagnation-point flow over a plate moving along the direction of flow impingement” by Y. Zhong and T. Fang. Internatioal Journal Heat Mass Transfer, 54, 3103–3108 (2011)”. International Journal of Heat and Mass Transfer, 55(4), 1425–1426 (2012)CrossRefzbMATHGoogle Scholar
- FANG, T. and ZHONG, Y. Reply to “Comment on “Unsteady stagnation-point flow over a plate moving along the direction of flow impingement” by Y. Zhong and T. Fang. Internatioal Journal Heat Mass Transfer, 54, 3103–3108 (2011)”. International Journal of Heat and Mass Transfer, 55(4), 1425–1426 (2012)CrossRefzbMATHGoogle Scholar
- SOID, S. K., ISHAK, A., and POP, I. MHD stagnation point flow over a stretching/shrinking sheet. 2015 International Symposium on Mathematical Sciences and Computing Research, 355–360 (2015)Google Scholar
- ZAIB, A., BHATTACHARYYA, K., UROOJ, S. A., and SHAFIE, S. Dual solutions of an unsteady magnetohydrodynamic stagnation-point flow of a nanofluid with heat and mass transfer in the presence of thermophoresis. Proceedings of the Institution of Mechanical Engineers (Part E: Journal of Process Mechanical Engineering), 232(2), 155–164 (2018)CrossRefGoogle Scholar