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LAMINAR FORCED CONVECTION WITH VISCOUS DISSIPATION IN HYDRODYNAMICALLY AND THERMALLY DEVELOPING FLOW BETWEEN PARALLEL PLATES AT UNEQUAL TEMPERATURES. : Present studies deal with the forced convection heat transfer in the entrance region of a parallel plate channel subjected to unequal temperatures including viscous dissipation. The studies involve the simultaneous development of velocity and temperature fields. In order to assess the influence of different effects, numerical results employing simpler models have been obtained first. The parameters are, A, to characterize unequal wall temperatures, the Peclet number, Pe, the Brinkman number, Br and the Reynolds number, Re or the Prandtl number, Pr. Numerical results for –1 ≤ A ≤ 1, Pe = 10, 50 and 100, –2 ≤ Br ≤ 2 and Pr = 0.1, 0.7, 10 and 100 have been obtained employing the Successive Accelerated Replacement scheme after validating the scheme. Wall heat transfer continuously varies with the axial distance for a given A, and with A up to a desired axial distance. A modified Nusselt number based on average wall temperature does not display unbounded swing and varies continuously with A. Non-dimensional bulk mean temperature and wall heat transfer are independent of A. Nusselt number for a desired A can be calculated from the values for A = 0 employing the superposition relations developed.