Journal of Prime Research in Mathematics

# Combined effect of slip and radiation on MHD flow past a constantly moving vertical plate with variable temperature

M. A. Imran
Department of Mathematics, University of Management and Technology Lahore, Pakistan.
Shakila Sarwar
Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan.
M. Imran
Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan.
Maryam Aleem
Department of Mathematics, University of Management and Technology Lahore, Pakistan.

$$^{1}$$Corresponding Author: imran.asjad@umt.edu.pk

### Abstract

The unsteady free convection of an MHD flow of a viscous fluid passing a vertical plate which is constantly moving with variable temperature is analyzed by taking slip and radiation into consideration. The dimensionless governing equations for temperature and velocity fields are solved using Laplace transform technique. The radiative and slip effects are taken into consideration and the whole system is rotating as a rigid body with a constant angular velocity about the z-axis. Exact solutions are obtained for the two components of velocity. Some known solutions from the literature are obtained as a limiting case. The obtained solutions satisfy the initial and boundary conditions. Some physical aspects of flow parameters on the fluid motion are graphically presented.

#### Keywords:

Slip effect, Viscous fluid, MHD flow, Rotating frame, Free convection, Vertical plate.