Abstract: The heat transfer rate of the thermal Marangoni convective flow of a hybrid nanomaterial is optimized by using the response surface methodology (RSM). The thermal phenomenon is modeled in the presence of a variable inclined magnetic field, thermal radiation, and an exponential heat source. Experimentally estimated values of the thermal conductivity and viscosity of the hybrid nanomaterial are utilized in the calculation. The governing intricate nonlinear problem is treated numerically, and a parametric analysis is carried out by using graphical visualizations. A finite difference-based numerical scheme is utilized in conjunction with the 4-stage Lobatto IIIa formula to solve the nonlinear governing problem. The interactive effects of the pertinent parameters on the heat transfer rate are presented by plotting the response surfaces and the contours obtained from the RSM. The mono and hybrid nanomaterial flow fields are compared. The hybrid nanomaterial possesses enhanced thermal fields for nanoparticle volume fractions less than 2%. The irregular heat source and the thermal radiation enhance the temperature profiles. The high level of the thermal radiation and the low levels of the exponential heat source and the angle of inclination (of the magnetic field) lead to the optimized heat transfer rate (Nu_x=7.462 75).

Key words: inclined magnetic field, Marangoni boundary layer flow, sensitivity analysis, hybrid nanofluid, exponential heat source, response surface methodology (RSM)