Mixed convective heat transfer from a heated sphere at an arbitrary incident flow angle in laminar flows

The mixed convection from a heated sphere for an arbitrary flow incident angle (θ  ) at low to moderate Reynolds numbers (1⩽Re⩽1001⩽Re⩽100) and Richardson numbers (0⩽Ri⩽50⩽Ri⩽5) is studied by an immersed boundary method, thereby investigating the influence of different flow incident angles (0⩽θ⩽180°0⩽θ⩽180°) on the buoyancy flow and heat transfer. The numerical method is validated by comparing the results with the simulation results of pure forced convection as well as those of mixed convection with assisting flow (0° flow incident angle) published in the literature. Extensive simulations for a wide range of different incident flow angles have been performed. New correlations are obtained for the overall Nusselt number (Nu) in terms of θ, Ri, and Re, showing a quadratic decrease in Nu with respect to θ   only for 0°⩽θ⩽90°0°⩽θ⩽90° (aiding and cross flow) and a half bell-shaped decrease in Nu   for 90°<θ⩽180°90°<θ⩽180° (opposed flow). The combined treatment of mixed convection for the completely upward flow, cross flow, and completely downward flow (i.e. at incident angle 0°, 90° and 180°, respectively) was achieved showing almost linear relationships between the heat transfer rates and Ri   for Ri⩾1Ri⩾1.