Numerical Heat Transfer · 1985 · 24 citations · 10 references
EngineeringComputational EngineeringMechanical EngineeringComputational Fluid DynamicsFluid DynamicsHeat TransferAnnular FlowConvection DynamicsHeat Transfer AnalysisHeat Transfer FundamentalsHeat Transfer ModelingThermal Boundary LayersConvection ModelingFinite Difference DiscretizationFinite Difference SchemesNatural ConvectionNatural Convection In EnclosuresSpherical CoordinatesTemperature Field AnalysisVector Potential
The three-dimensional equations of conservation in spherical coordinate were solved by a finite-difference method for natural convection in a spherical annulus. The vorticity-vector potential formulation and the alternating-direction-implicit method were utilized. Two sets of boundary conditions were considered. In the first the inner sphere was insulated, and a continuous sinusoidal temperature field was imposed on the outer sphere such that one vertical half was heated and the other cooled. In the second the inner sphere was cooled at uniform temperature, the same temperature distribution as before was imposed on the heated half of the outer sphere, and the previously cooled half was insulated. The computations were carried out for Ra = 500 and Pr = 1.0. The computed velocity and temperature fields are illustrated graphically. The streaklines were found to consist of pairs of double helices just as in rectangular and cylindrical enclosures.
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