The thermal characteristics of nanofluids, arising from progressive mechanisms, present an intriguing phenomenon with significant implications for energy production, cooling processes, and heat transfer devices. This study investigates the magnetohydrodynamic combined convection of Maxwell nanofluids, focusing on heat transport properties over an exponentially stretching sheet. The effects of activation energy, nonlinear thermal radiation, Cattaneo–Christov heat flux, suction/injection, Joule heating, solutal energy, and viscous dissipation in the presence of swimming microorganisms are incorporated. To elucidate these phenomena, the study examines the impacts of bioconvection, magnetic fields, and thermophoresis under extended boundary conditions. The partial differential equations (PDEs) of the problem related to momentum, energy, concentration, and density are transformed into ordinary differential equations (ODEs) through the application of similarity variables. The resulting dimensionless nonlinear ODEs are solved using the shooting method. Numerical results for key parameters are presented in the form of tabular and graphical trends for both steady and unsteady flow cases, utilizing MATLAB for computational analysis. Notable improvements in the velocity profile are observed with increasing values of the Maxwell parameter. Conversely, a rise in the mixed convection parameter leads to a deterioration in both the temperature and concentration fields.
Waseem et al. (2026) studied this question.