Homogenization of a thermal problem in the plate of a heat exchanger

In this paper we study a thermal problem with the Fourier boundary conditions on the edges of the holes in a periodically perforated plate of a heat exchanger. This problem contains several reduced parameters which can be very small (the period epsilon of the distribution of the holes, the relative thickness e of the plate and the three Blot numbers connected with the different parts of the boundary). We use the homogenization technique to estimate the field of temperatures attainable in the upper plate, depending on the relative order of magnitude of the small parameters. We use a combined asymptotic method involving the technique of multiple scales and that of matching expansions to calculate a solution of boundary layer.