Heat transfer optimization and rheological features of Buongiorno nanofluid in a convectively heated inclined annulus with nonlinear thermal radiation using response surface methodology

The theoretical analysis of the mixed convective Buongiorno nanofluid flow in an inclined annular microchannel with convectively heated walls subjected to the effects of nonlinear thermal radiation, exponential heat source (EHS), thermal dependent heat source (THS) is carried out. The description of the Buongiorno nanofluid is implemented to analyze the Brownian diffusion and thermo-migration mechanisms. The general boundary conditions for the velocity, thermal, and nanoparticle volume fraction (NVF) are considered. Numerical solutions for fully developed governing equations are obtained using bvp5c solver and verify with FEM. The optimization of heat transport rates is made by using the Box-Behnken design-based response surface method. It is found that the Lorentz force and the angle inclination of the annulus significantly affect the rheological characteristics of the nanofluid. Nanoparticles increase thermal energy in the system through Brownian diffusion and thermophoresis, resulting in increased temperature field. Internal heat sources would serve as an important tool for modulating the thermal field in microchannel, as they are directly associated. At low-level values of the thermal Biot number, the exponential heat source, and the thermal radiation parameter, it is possible to attain the maximum Nusselt number on both walls of the annulus.