Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with constant velocity and the lower plate is kept stationary. The flow is assumed to be laminar, both hydro-dynamically and thermally fully developed, taking into account the effect of viscous dissipation of the flowing fluid. Both the plates being kept at specified and at different constant heat fluxes are considered as thermal boundary conditions. The solutions obtained from energy equation are in terms of Brinkman number, dimensionless velocity and heat flux ratio. These parameters greatly influence and give complete understanding on heat transfer rates that has potentials for designing and analyzing energy equipment and processes.

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O. Aydin, “Effects of Viscous Dissipation on the Heat Transfer in a Forced Pipe Flow. Part 2: Thermally Developing Flow,” Energy Conversion Management, Vol. 46, No. 18-19, 2005, pp. 3091-3102.
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S. H. Hashemabadi, S. Gh. Etemad and J. Thibault, “Forced Convection Heat Transfer of Couette-Poiseuille Flow of Nonlinear Visco-Elastic Fluids between Parallel Plates,” International Journal of Heat and Mass Transfer, Vol. 47, No. 17-18, 2004, pp. 3985-3991.
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M. Lewandowska and L. Malinowski, “An Analytcal Solution of the Hyperbolic Heat Conduction Equation for the Case of a Finite Medium Symmetrically Heated on Both Sides,” International Communications in Heat Mass Transfer, Vol. 33, No. 1, 2006, pp. 61-69.
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