| Summary: | 碩士 === 國立交通大學 === 機械工程學系 === 99 === An investigation of natural convection of compressible flow in a three dimensional Parallel plate with bottom side heated . The finite difference is adopted and the computational approaches are divided into two parts. One is the inviscid terms. The Roe scheme is utilized to deal with the flux of inviscid terms and the preconditioning matrix is added to let the scheme to be more effective for all speed filed. The other is viscous term and the central difference of second order is utilized to handle it. The temporal term is solved by LUSGS. Non-reflection conditions at the outlet is derived in order to resolve reflections induced by acoustic waves. In many other important natural convection problems, the temperature differences are often higher than 30 K, Boussinesq assumption is not inapplicable.
Based on the numerical results, the volume of fluid is expended due to the rising temperature, and thus leads to the fluid leaving the control volume on both ends. Then a backflow region is observed, fluid near the top half of the parallel plate flows outward, and flows inward near the bottom which is names dual-reflection phenomenon. And because of the boundary conditions, the distribution of nueeslt number of the bottom side is higher near the ends, decreases as to the center. The flow is unsteady as the heated length to the height between two parallel plate ratio gets higher. However, as the heated region gets larger, heat is accumulated, which leads to the local nusselt number decreasing and a lower heat transfer rate.
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