Simultaneous effects of MHD and Joule heating on the fundamental flows of a Casson liquid with slip boundaries

K. Ramesh ^a,*, Arshad Riaz ^b, Zahoor Ahmad Dar ^c

a. Department of Mathematics, Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune, 412115, India
         b. Department of Mathematics, Division of Science and Technology, University of Education, Lahore, 54770, Pakistan
         c. Department of Mathematics, Lovely Professional University, Jalandhar, 144411, India

Abstract: Magnetic field plays a significant role in innumerable fields like mechanical, chemical, biological and medical research. Few examples include power generation systems, magnetohydrodynamic (MHD) accelerators, liquid metal fluids, cooling of nuclear reactors, high-temperature plasmas, chemical processing equipment and electronic components. In view of these facts, the current investigation discusses the fundamental flows of a Casson fluid in horizontal parallel plates (three fundamental situations considered such as the plate walls progresses in the conflicting directions, the progress of lower plate in the flow direction and other is in fixed position, and the progress of the plates in the flow direction respectively). Influences of radiation, velocity slip, porous medium and Joule heating are considered into account. The flow situation is assumed in Cartesian coordinate system. The momentum and energy equations are transformed into non-dimensional system utilizing appropriate non-dimensional parameters. The exact solutions of the non-dimensional differential equations have been obtained. The pictorial representations are provided for the velocity as well as temperature characteristics in all the mentioned cases. It is concluded by graphical approach that velocity is enhanced in the case of increasing Darcy’s parameter and boundary slip while reduced for the large magnetic field. On the other hand, it is found that slip factor is reducing the heat transfer rate while magnetic field is giving rise to it.

Keywords: Casson fluid; Viscous dissipation; Joule heating; Porous medium; Thermal radiation; Magnetofluiddynamics