Flow of a Casson fluid with heat transfer over a shrinking sheet and its dual solutions

Abstract

An effort has been made to examine the dual solutions of boundary layer flow of the Casson fluid over a shrinking sheet, with the effects of Joule heating and power-law heat flux. A homogeneous magnetic field is implemented in the system along a direction normal to the flow. Appropriate similarity transformations are employed to reformulate the governing equations of the present problem into a solvable set and the solution uses the three-stage Lobatto IIIa method in a developed numerical bvp4c code in MATLAB. Due to the shrinking surface, some disturbances impact the flow, which has two solutions: one that is stable and another that is unstable. Graphical results are shown to assess the velocity and temperature fields. A stability analysis is executed to characterize the stable and physically attainable solution. It is perceived that the Casson fluid parameter contributes to speed and temperature of the fluid in a time-independent case. Also, it controls the motion as well as the temperature of the fluid in the time-dependent case.

Keywords

• magnetohydrodynamics
• casson fluid
• dual solutions
• heat transfer
• joule heating
• stability analysis