Magnetohydrodynamics boundary layer flow and heat transfer over a permeable stretching/shrinking sheet

A theoretical study that describes boundary layer flow and heat transfer, which is induced by a moving plate in a quiescent ambient fluid has been presented herein. In this study, five problems are discussed in details. First problem related to the fluid flow and heat transfer in the boundary layers on a nonlinearly stretching sheet with a variable sheet temperature and suction, in the presence of magnetic field and nonuniform heat source. The effects of magnetic parameter, suction parameter, the temperature parameter, the space dependent heat source parameter and the temperature dependent heat source parameter have been studied. Magnetohydrodynamics (MHD) boundary layer flow and heat transfer of a viscous fluid over an exponentially permeable stretching sheet is analysed in the second problem, where the system is suppressed by thermal radiation. Velocity, thermal as well as mass slips are considered at the boundary. The boundary layer flow and heat transfer of a viscous fluid on an exponentially shrinking sheet is described in the third problem. The shrinking sheet is permeable and the system is suppressed by an exponential variation of magnetic field. The impacts of the magnetic parameter, the suction parameter and the mixed convection parameter are considered in the third problem. Fourth problem contains steady MHD mixed convection boundary layer flow of a Casson fluid over an exponentially permeable shrinking sheet. The results exhibit that the Casson fluid parameter, mixed convection parameter, magnetic parameter and suction parameter would significantly affect the number of multiple solutions obtained from numerical calculations. The final problem is about the unsteady boundary layer flow of a viscous fluid past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The effects of magnetic parameter, dimensionless curvature, suction parameter, unsteadiness parameter and mixed convection parameter are calculated numerically. For all the tested problems, the governing nonlinear partial differential equations are converted into ordinary differential equations by a similarity transformation. The converted equations are then solved numerically using the shooting method in Maple programming software. The results showed that the values of skin friction coefficient, local Nusselt number, local Sherwood number and the profiles of velocity, temperature and concentration are changed by the governing parameters on the system. Additionally, the existences of multiple solutions are contributed by the applied numerical method (shooting) and the involvement of certain parameters in the system