Volumetric heat transfer coefficients in solid–fluid porous media: closure problem, thermal analysis and model improvement with fluid flow

Abstract This paper presents a detailed investigation on the volumetric transfer coefficient (VHTC) model in solid–fluid porous media based on the volume averaging method (VAM). The VHTC is obtained by solving the closure problem with the control-volume finite difference method. A thermal analysis is conducted to illustrate the thermal nature of the VHTC, based on which, an improved VHTC model has been proposed by taking into account the effects of the thermal entrance and the non-uniformity of the velocity field. With this model, the applicability of the VAM has been extended to large Peclet number laminar regime for convection heat transfer in porous media characterized by straight ducts.

[1]  Stephen Whitaker,et al.  Heat conduction in multiphase systems—I: Theory and experiment for two-phase systems , 1985 .

[2]  J. Whitelaw,et al.  Convective heat and mass transfer , 1966 .

[3]  Jacob Bear,et al.  Fundamentals of transport phenomena in porous media , 1984 .

[4]  M. Kaviany,et al.  Slip and no-slip temperature boundary conditions at interface of porous, plain media'conduction , 1991 .

[5]  Stephen Whitaker,et al.  Heat and Mass Transfer in Porous Media , 1984 .

[6]  S. Whitaker,et al.  One- and Two-Equation Models for Transient Diffusion Processes in Two-Phase Systems , 1993 .

[7]  R. Carbonell,et al.  Development of Transport Equations for Multiphase Systems—III: Application to heat transfer in packed beds , 1984 .

[8]  R. G. Carbonell,et al.  Development of transport equations for multiphase system—I: General Development for two phase system , 1984 .

[9]  E. Sparrow,et al.  Fully Developed Flow and Heat Transfer in Ducts Having Streamwise-Periodic Variations of Cross-Sectional Area , 1977 .

[10]  S. Whitaker,et al.  Heat transfer in packed beds: interpretation of experiments in terms of one- and two-equation models , 1994 .

[11]  Massoud Kaviany,et al.  Principles of convective heat transfer , 2001 .

[12]  Michel Quintard,et al.  Local thermal equilibrium for transient heat conduction: theory and comparison with numerical experiments , 1995 .

[13]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.