It is postulated that proper scaling will collapse the multiplicity of data for friction and heat transfer coefficient to a usable reasonably general formulation by choosing the hydraulic diameter as
where <m> is the average porosity and Sw is the surface area per unit volume. The chosen hydraulic diameter allows the transformation and comparison of correlation equations and experimental results obtained for diverse media morphologies. Also, it allows experimentally-determined characteristics of the media to be related to the closure relationship derived from the VAT analysis. The numerical results of closure are presented and are compared to various experimental results. The Nusselt number is based on the media internal local surface average transfer coefficient and the friction factor is the local internal value. Results obtained by VAT closure using direct numerical simulation show reasonable agreement between calculated local friction factors and local heat transfer coefficients and data confirming that the friction factor and heat transfer coefficient when correctly scaled can be computed numerically with satisfactory results. This conclusion will enable one to optimize the effectiveness of a compact heat exchanger in terms of porosity and internal surface area.
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