Kariuki, John King’ori2025-08-052025-08-052025-05https://ir-library.ku.ac.ke/handle/123456789/31105A Project Submitted in Partial Fulfilment of the Requirements for the Award of the Degree of Master of Science (Applied Mathematics) in the School of Pure and Applied Sciences of Kenyatta University May, 2025 Supervisor; 1.Lawrence NjauThe study investigated a Newtonian Magneto-hydrodynamic fluid flow bounded by two parallel vertical plates in a porous media with heat transfer. The fluid was considered to be flowing uniformly in the x-direction. The parallel vertical plates are impermeable and a transverse magnetic field is applied perpendicular to the plates in the positive y-direction. The plates are heated and kept at constant temperature 𝑇𝑇𝑤𝑤 and the distance between the two plates was varied. The fluid and the porous matrix are approximated to have the same temperature, 𝑇𝑇𝑓𝑓 . The effect of varying Darcy number, Hartmann number, Prandtl number, and Reynolds number on velocity and temperature profiles was discussed. The coupled non-linear PDE governing the fluid flow were non-dimensionalized to obtain a dimensionless equation. The resulting equation was discretized using the finite difference method to obtain non-linear algebraic equations which were solved using MATLAB. The obtained results were presented in graphs and then discussed. It was observed that velocity profile decreased when Hartmann number or Reynolds number was increased. On the other hand, velocity profile increased after increasing Prandtl number or Darcy number. It was also observed that temperature profile decreased when Hartmann number or Prandtl number was increased. On the other hand, temperature profile increased when Reynolds number or Darcy number was increased. These results have applications in aerodynamic heating and motor vehicle cooling.enThesis