Effect of isoflux thermal boundary condition on mixed convective heat transfer from a sphere for liquid metals

Abstract

Numerical simulation is performed for mixed convective heat transfer past a sphere with uniform heat flux (Isoflux) thermal boundary condition for liquid metals. The steady, incompressible, laminar, axisymmetric and Newtonian fluid is considered in a vertically upward direction. A spherical geometry higher order compact scheme is utilised to solve the governing equations in stream function vorticity formulation together with the energy equation. The fourth order convergence of the current scheme is demonstrated. The velocity, streamline, isotherm contour profiles together with vorticity, pressure, local Nusselt number and average Nusselt number on the surface of the sphere are presented for the Reynolds number in the range $1\le Re\le 200$, Richardson number in the range $0\le Ri\le 5.0$ and Prandtl number in case of 0.020, 0.0208, 0.065 (liquid Gallium, liquid metal alloy $\text{Ga}68\mathrm{\%}\text{In}20\mathrm{\%}\text{Sn}12\mathrm{\%}$, liquid lithium). The critical Richardson number is identified beyond which the recirculation phenomena of the flow are completely suppressed. The rate of isoflux heat transfer is more when compare to the isothermal case for the same range of parameters.

Keywords:

• Spherical geometry higher order compact scheme
• liquid metals
• uniform heat flux boundary condition
• mixed convection
• critical Richardson number

Disclosure statement

No potential conflict of interest was reported by the authors.