A thorough investigation into the impacts of the fluid’s characteristics and the permeability of the sheet was conducted to examine the heat transfer (HT) in the boundary layer (BL) flow of an incompressible couple stress fluid over a permeable, linearly stretched sheet. There is an incidental static magnetic field that restricts fluid flow. The case where the heating procedure involves a prescribed surface temperature has been studied in relation to the heat transfer problem. Since these phenomena typically occur in the production of magnetic materials, the energy couple stress phenomenon and viscous dissipation effects are considered. A nonlinear set of coupled ODEs with boundary conditions is created from the governing equations by similarity transformations. By implementing the Keller Box Method (KBM), the resultant equations are numerically solved. The discussion revolves around how relevant parameters affect the fluid’s temperature and velocity profiles. Quantitatively, increasing the couple stress parameter can enhance the skin friction coefficient by about 8.2% while reducing the Nusselt number by nearly 25.8%, whereas raising the magnetic field parameter can increase surface friction by approximately 44.0% and decrease the heat transfer rate by around 31.3%. The technique’s effectiveness is shown through a table comparison, indicating good alignment with existing data and highlighting its accuracy.
Khader et al. (Sat,) studied this question.