Investigating Hydromagnetic Casson Fluid Flow over a Shrinking Sheet
Athanas, Julian Nthenya
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Casson fluid has vast applications in numerous fields such as in processing of foods, drilling operations, the field of metallurgy and many more. This study investigates the flow of Casson fluid over a shrinking surface in presence of a magnetic field. The partial differential equations governing the steady flow are transformed to a system of ordinary differential equations by similarity transformation. The transformed non-dimensional equations are solved using the three stage Lobbatolla scheme. The numerical results for the flow variable: velocity and temperature profiles are displayed graphically for several parameters and discussed in details. The graphical results depict the effects of magnetic field parameter, Biot number and Prandtl number on fluid temperature and velocity. The results show that, an increase in Biot number results to a decrease in the secondary velocity and a consequent decrease of the boundary layer, and a decrease in the temperature profile. A combined effect of magnetic field strength and Prandtl number on flow properties are graphically represented. Increase in the magnetic field strength and Prandtl number lead to a decrease in both the secondary velocity and primary velocity at the boundary layer, and this is due to the fact that Lorentz force (generated from the magnetic field) act adversely to the flow. An increase in Prandtl number means an increase in momentum diffusivity, which causes a reduction in the flow velocity at the boundary layer but increases the velocity at the free stream. Also, increasing both the magnetic field strength and the Prandtl number have an adverse effect on the flow temperature.