Turbulent temperature profile in the quasi-fully developed region of a micro-tube

Abstract

Turbulent temperature profiles 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. The temperature profiles were compared with the laminar flow and previous numerical solutions. The total temperature was higher than the wall temperature depending on the Mach number. The static temperature in the quasi-fully developed region agrees well with the temperature results for an ideal gas flow obtained by solving the Navier-Stokes and energy equations.