Validation of thermal equilibrium assumption in forced convection steady and pulsatile flows over a cylinder embedded in a porous channel

Abstract

The validity of the local thermal equilibrium assumption in the forced convection steady and pulsatile flows over a circular cylinder heated at constant temperature and embedded in a horizontal porous channel is investigated. For this purpose, the Darcy–Brinkman–Forchheimer momentum and the local thermal non-equilibrium energy models are solved numerically using a spectral element method. Numerical solutions obtained over broad ranges of representative dimensionless parameters are utilized to present conditions at which the local thermal equilibrium assumption can or cannot be employed. For steady flow, the circumstances of a higher Reynolds number, a higher Prandtl number, a lower Darcy number, a lower microscopic and macroscopic frictional flow resistance coefficient, a lower Biot number, a lower solid-to-fluid thermal conductivity ratio, a lower cylinder-to-particle diameter ratio and a lower porosity, are identified as unfavorable circumstances for the local thermal equilibrium LTE condition to hold. For oscillatory flow, the degree of non-equilibrium can be decreased as pulsating amplitude increases or pulsating frequency decreases; however, such flows do not have a significant influence on satisfying the LTE.