© 1986 by Oxford University Press
ON THE EFFECTIVE DIFFUSIVITY MODEL FOR HEAT DIFFUSION IN INCLINED RANDOM LAMINATES
( Department of Engineering Mathematics, University of Newcastle upon Tyne Newcastle upon Tyne NE1 7RU )
As in (1) a laminated material occupying a half-space is subjected to an harmonic heat flux condition on the exposed face and the temperature response in the interior is sought. The laminae are taken to be inclined at an angle ½
– 
to the exposed face, and so the two cases examined in (1) are special cases of that considered here. A more general stochastic process is used to define the manner in which the laminate is formed out of the N thermally distinct types of laminae. This is so that we include laminates which have a sequential structure as well as the completely random case dealt with in (1). Other possible types are also included in our general case. The system of N coupled partial-differential equations for the expected temperature fields in each type of material is derived and solutions to them are sought for the case of ‘low’ driving frequency. The leading terms to these solutions are identical to that for the same problem involving an homogeneous material of diffusivity 
, where 
and 
are the mean conductivity and the mean thermal capacity respectively. This shows that if the diffusion is driven slowly enough then the detailed structure of the laminate is irrelevant. An estimate for the frequency range for this result to be valid is also given.