Matrix heat exchangers, invented forty years ago, have found widespread applications during the last two decades. Because of their unique construction, they satisfy the diverse requirements of high compactness, high transfer coefficient, low axial conductivity, and uniform flow distribution. The heat transfer mechanism in these exchangers is quite complex. Convective heat transfer takes place in the pores as well as in the front and rear faces of the plates. Conduction heat transfer takes place in two directions: between the streams through the perforated plates, and along the separating wall in the axial direction. The five sources of heat transfer are strongly coupled with each other. The governing equations have been derived and simplified using well-justified assumptions. The discrete structure of the exchanger helps in reducing the partial differential equations to sets of algebraic and ordinary differential equations. A numerical scheme is presented for solving these equations. Its use is illustrated with two examples.

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