Heat transfer characteristics of slip flow over solid spheres

Abstract

In this study, heat transfer characteristics of slip flow over an isolated impermeable solid sphere are investigated numerically. An isothermal solid sphere is considered at intermediate Reynolds numbers (0 ≤ Re ≤ 50) for Prandtl numbers in the range of 0.7–7.0. The Navier–Stokes and energy equations are solved by a control volume technique in conjunction with the velocity slip and temperature jump boundary conditions. It was found that the size of the thermal wake region according to the Knudsen number depends on the Prandtl number. At lower Prandtl numbers (0.7 ≤ Pr ≤ 2.0), the thermal wake region shrinks as the Knudsen number increases, while at higher Prandtl numbers, it grows as the Knudsen number increases. The maximum temperature jump occurs at the front stagnation point where the local Nusselt is itself maximum, owing to the maximum temperature gradient at this point. The results show that due to the opposing effects of the velocity slip and temperature jump, the average Nusselt number variation with the Knudsen number depends nonlinearly on both the Prandtl and Reynolds numbers. Furthermore, for the limiting case of Re → 0, an analytical solution for the problem is presented which has also served as a validation case.

A numerical study on drag reduction of underwater vehicles using hydrophobic surfaces

“…The fluid might slip on wall at two circumstances: 30 (a) slip flow regime, due to rarefaction effects, 31 and (b) liquid flow over hydrophobic surfaces, where slip occurs as a surface phenomenon due to the surface properties of the solid. 30 Yet, numerous researches have been reported considering velocity slip boundary condition on walls, especially for micron-sized particles in rarefied gas flows. [30][31][32][33][34][35][36][37] It has been postulated by Navier in 1827 38 that the slip velocity, tangent to a wall, is proportional to the tangential wall shear rate as follows…”

“…30 Yet, numerous researches have been reported considering velocity slip boundary condition on walls, especially for micron-sized particles in rarefied gas flows. 30–37…”