Thermodynamic analysis of a magnetohydrodyamic oldroyd 8-constant fluid in a vertical channel with heat source and slippage

This study carried out a thermodynamic analysis of the steady-state flow and heat transfer of an Oldroyd 8-constant fluid, with consideration for the effects of heat source, velocity slip, and buoyancy force under a transverse magnetic field. A model for momentum and energy balance was numerically solved using the method of weighted residuals, and associated residuals were minimized using the partition method. The results were compared with those derived using the built-in numerical solver of MAPLE 18 to validate the method used, and the convergence of the method was determined. The results of the momentum and energy balance model were then used to compute the entropy generation rate and the irreversibility ratio. The effects of control parameters such as non-Newtonian fluid parameters, slip parameters, the Grashoff, Brinkmann, and Hartmann numbers, and heat source on non-dimensional velocity, temperature, entropy generation, and irreversibility were graphically represented. The findings revealed that the irreversibility due to fluid friction dominates over heat transfer when non-Newtonian fluid parameter ?_1 is kept constant at various values of ?_2, whereas the irreversibility due to heat transfer dominates over fluid friction when ?_2 is kept constant at various values of ?_1.