Forced Convective-Diffusive Heat Flow in Insulations: A New Analytical Technique Applied to Air Leakage through a Slit

Abstract

Forced convective-diffusive heat flow in porous insulation materials is governed by an equation for the air pressure distribution with an ensuing air flow and a heat equation with convection and diffusion. The pressure equation for a ho mogeneous material may be solved analytically with simple geometries and bound ary conditions.

The new technique uses a transformed form of the convective-diffusive equation for which the awkward first-order derivatives of the temperature (the convective part) are removed. New explicit solutions for certain two-dimensional, steady-state cases may be derived.

The considered example concerns air leakage through an insulation which is open on one side and airtight on the other except for an open slit. Air infiltrates through the slit and leaves through the open side. The solution gives the complete pressure and temperature fields. The extra heat loss due to air leakage is given by an explicit expression which contains only a single, dimensionless parameter.