Exact analysis of magneto‐viscous Casson fluid flow and heat transfer over a stretching sheet with PST and PHF conditions

This study provides an analytical investigation of magnetic field‐dependent viscosity (MFD) effects on the MHD boundary‐layer flow of an incompressible, steady, laminar, two‐dimensional Casson fluid over a horizontally stretching sheet. Ohmic heating and viscous dissipation are included in the formulation, and heat transfer is examined under both prescribed heat flux (PHF) and prescribed surface temperature (PST) boundary conditions. Similarity transformations reduce the governing dimensional PDEs to a coupled system of ODEs, yielding a more tractable mathematical model. An explicit analytical expression is obtained for the momentum field, while the temperature distribution is represented through Kummer's special function. Analytical relations are also derived for the non‐dimensional wall temperature (WT), local Nusselt number (NN), and local skin friction coefficient (SF). The effects of MFD viscosity and thermal parameters are explored through the resulting velocity and temperature fields and their influence on SF and NN. The results show that an increase in the Casson parameter reduces both velocity and temperature, leading to a 7.92% decrease in the local Nusselt number, whereas increasing the magnetic viscosity, magnetic parameter, and Eckert number enhances the heat transfer rate by 12.53%, 42.16%, and 76.14%, respectively. The analytical predictions exhibit excellent agreement with established benchmark results, confirming the accuracy and reliability of the present formulation The findings are relevant to applications such as biomedical flows, polymer processing, coating technologies, and cooling systems involving magnetically controlled non‐Newtonian fluids.