The development of a new computational scheme for mixed convection with using a scalar potential

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Flow fields have been solved either with a primitive variable system or with a vorticity and vector potential system. For the mixed convection, the latter scheme can not be suitally applied. In this work, it is shown that this difficulty can be resolved by introducing a scalar potnetial. This was originally proposed by Hirasaki and Hellums but there appears to be no practical computational results. At the beggining, isothermal two-dimensional through-flow in a square rectangular channel with openings near bottom was solved for Re=81.6. Computed velocity field agreed very well with the results obtained by a classical way of stream function whose gradient is given at the openings for a plug flow. Both solutions agreed in that the relative coefficient is 0.9969. Then this was applied to a two-dimensional mixed convection with heating floor and a cooling vertical wall. The flow field shown in a stream function agreed very well with the experimental streak line in a water box with the same boundary conditions. This computational scheme was also found to be applicable in a three-dimensional field. For a heat storage system two flow modes, a short-cut and a tortours modes were found to be stable depending on the Archimedes number Gr/ <Re^2> .