On temperature jump condition for turbulent slip flow in a quasi-fully developed region of micro-channel with constant wall temperature

Abstract

Temperature variation of turbulent slip flows in the quasi-fully developed region of a micro-tube were obtained numerically by solving the energy equation including the substantial derivative of pressure and viscous dissipation terms for the case of constant wall temperature. The fluid was assumed to be an ideal gas with constant density over the cross-section. The turbulent velocity profile was approximated by the three-layer model of Von Kármán. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a micro-tube with constant wall temperature when both viscous dissipation and substantial derivative of pressure terms are included in the energy equation. The total temperature in the quasi-fully developed region was lower than the wall temperature in the case of Kn ≥ 0.01.