Drag coefficients and Nusselt numbers of gas slip flow around unconfined and semi-confined spheres

• The second-order velocity slip with nonplanar modification and second-order temperature jump models are applied to simulate the gas slip flow and heat transfer around unconfined and semi-confined spheres. • The effects of rarefaction, convection, compressibility, confinement, and temperature on the drag coefficient and Nusselt number are comprehensively explored. • The dimensionless correlations for drag coefficient and Nusselt number of unconfined and semi-confined spheres are proposed, respectively. This paper numerically investigates the drag coefficients ( C D ) and Nusselt numbers ( Nu ) of gas slip flow around unconfined and semi-confined spheres using second-order velocity slip (with nonplanar modification) and temperature jump boundaries and variable gas properties. The effects of Knudsen number ( Kn ), Reynolds number ( Re ), gap ratio ( d gap / d sp ), and temperature ratio ( T sp / T ∞ ) are comprehensively analyzed. It is obtained that: (1) for the unconfined sphere, C D decreases as Kn and Re increase due to the enhanced velocity slip and weakened viscous effect; for the semi-confined sphere, C D decreases at lower Kn and Re but increases at higher Kn and Re due to the enhanced compressibility effect ( M a = 2 / π γ K n R e ); for both spheres, Nu decreases as Kn increases due to the dominant temperature jump, but increases as Re increases due to enhanced convection; for the semi-confined sphere, the enhanced compressibility effect changes the dominance from temperature jump to velocity slip. (2) C D firstly rises and then declines with narrowing d gap /d sp due to the variation of velocity gradient when the sphere moves from outside to inside and last bottom of wall boundary layer; besides, with narrowing d gap /d sp , the confinement effect weakens the rarefaction effect but enhances the compressibility effect on C D ; Nu firstly rises and then declines and last rises with narrowing d gap /d sp due to the corresponding variation in temperature gradient; furthermore, the confinement effect shifts dominance from temperature jump to velocity slip and finally back to temperature jump with narrowing d gap /d sp ; (3) for both spheres, C D and Nu increase with increasing T sp / T ∞ due to the rise in the gas viscosity, and gas temperature gradient and thermal conductivity, respectively. Consequently, C D and Nu correlations of unconfined and semi-confined spheres are proposed considering effects of convection, rarefaction, compressibility, confinement, and temperature.