Comprehensive investigation of heat transfer in non-newtonian fluid flow over a stretching surface: Influence of MHD, bioconvection, porous media and slip effects

This research explores the steady, two-dimensional motion of an incompressible bioconvective Casson fluid over a permeable, linearly stretching surface. The mathematical formulation accounts for velocity slip, convective surface heating, and nonlinear drag effects through the Forchheimer law. The impact of several physical phenomena, magnetic field application, suction, internal heat generation, chemical reactions and viscous dissipation on the thermal and solutal behavior of the fluid is comprehensively analyzed. The fluid’s viscosity and diffusivity are modeled as functions of temperature and concentration, respectively. The heat generation and viscous dissipation substantially intensify the thermal boundary layer, leading to elevated heat transfer rates. Through appropriate similarity transformations, the governing nonlinear partial differential equations are reduced to a set of ordinary differential equations. These equations are then solved numerically using the shooting method coupled with a suitable iteration scheme. Moreover, parametric investigations show how key dimensionless quantities affect the velocity field, thermal distribution, concentration and microorganism density. The graphical representation of results provides a deeper understanding of the influence of controlling parameters on flow and transport phenomena. The following results are generated by fixing values as [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. These findings have practical relevance in the design of bio-inspired cooling systems, polymer processing and biomedical flows involving magnetic regulation. The presented results contribute to engineering applications where control of thermal and mass transport in complex fluids is essential.