Magnetohydrodynamics boundary layer flow of non-newtonian fluid over a permeable shrinking surface

Non-Newtonian fluids are fluids whose viscosities cannot be described by Newton’s law of viscosity and are dependent on the shear rate. The magnetohydrodynamics (MHD) boundary layer flow of three types of non-Newtonian fluids, namely, the Carreau fluid, Casson fluid and micropolar fluid are studied in this thesis. These fluids flow over a permeable shrinking surface, with different boundary conditions considered for each fluid. The MHD flow of Carreau fluid over a non-linearly shrinking sheet with thermal radiation and convective boundary condition is studied as the first problem. Then, the MHD flow of Casson fluid near a stagnation point on a linearly shrinking sheet is considered as the second problem. The effects of slip and homogeneous-heterogeneous reactions are studied in this problem. Meanwhile, the third problem discussed the effects of thermal radiation on the MHD flow of micropolar fluid over an exponentially shrinking sheet. The governing partial differential equations of these problems are transformed into ordinary differential equations using the similarity transformations. Then, these equations are solved along the boundary conditions using a numerical method called the shooting method, with the computations done in the Maple software. The effects of various parameters on the flow, concentration and thermal fields of the fluids are discussed and presented in tables and graphs. At some values of the parameters, dual solutions are obtained. Therefore, stability analysis is performed to determine the significance of these solutions to the problems. The smallest eigenvalues for the first and second solutions are computed using the bvp4c solver in MATLAB. The first solution is found to have positive smallest eigenvalues, while the second solution has negative smallest eigenvalues. Thus, the first solution is stable and significant, whereas the second solution is unstable and less significant to the problems. The presence of a magnetic field and suction are observed to boost the velocity of the fluids but causes the temperature of the fluids to drop. Besides that, the increase in these parameters enhances the concentration of reactants in the second problem and the microrotation of micropolar fluid in the third problem.

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