THERMAL TAYLOR DISPERSION PHENOMENA IN NONADIABATIC SYSTEMS

This paper outlines of general 'one-dimensional' theory of convective-conductive internal energy transport phenomena in complex, multidimensional, nonadiabatic systems whose rate of heat loss to their surroundings is characterized by a 'Newton's law of cooling' heat transfer coefficient h. Taylor dispersion theory is used to effect the coarse-graining of the microscale thermal problem, therby producing an effective-medium theory of the mean thermal transport process. Both ducts ('continuous' systems) and model packed beds (spatially periodic systems) are analyzed. Expressions are derived for the macroscale thermal propagation velocity vector (U) over bar* and effective thermal dispersivity dyadic <(alpha)over bar>* in terms of the prescribed microscale data Additionally, an expression is obtained for a third macrotransport coefficient, (H) over bar*, representing the effective or overall macroscale heat transfer coefficient, and distinct from the microscale heat transfer coefficient h. (This is the same type of quantity as arises in so-called 'fin' problems.) Furthermore, it is shown that when solving the nonadiabatic macrotransport equation for the mean temperature (T) over bar, parameterized by the effective-medium phenomenological coefficients (H) over bar*, (U) over bar* and <(alpha)over bar>*, it becomes necessary to employ a fictitious mean initial temperature distribution in place of the true one. A paradigm is developed for calculating this fictitious mean initial temperature field from the prescribed initial microscale temperature field. By way of example, calculations are presented for flow in a circular tube with heat loss to isothermal surroundings. In addition to providing numerical values for (H) over bar* in terms of the pertinent microscale phenomenological data, these calculations show that (U) over bar* and <(alpha)over bar>* for nondiabatic systems may differ sensibly from their adiabatic counterparts (calculated in two previous papers), as they now also depend functionally upon the heat transfer coefficient h. Numerical results are also presented for the Darcy-scale thermophysical parameters (H) over bar*, (U) over bar* and <(alpha)over bar>* for two-dimensional pressure-driven flow through model packed beds composed of periodic arrays of circular cylinders. For both duct and porous media flow problems, the thermal propagation velocity vector (U) over bar* is shown to differ from the mean fluid velocity vector (V) over bar-that is, the mean velocity of the carrier fluid Depending upon particular circumstances, \(U) over bar*\ may be larger or smaller than \(V) over bar\.