On identical problems of natural convection in enclosures and applications of the identity character

In this paper, a concept of "identical problemsⁿ of natural convection in enclosures is presented. A pair of problems of natural convection in enclosures is said to be identical if they look different in appearance but with appropriate selection of coordinates and appropriate definition of dimensionless variables for each problem; they will have identical geometric configurations and identical dimensionless governing equations and related boundary conditions. The identical characteristics of a pair of problems of natural convection in enclosures with an internal isolated island are demonstrated via dimensionless mathematical formulation and flow visualization results. Numerical computations are performed and the predicted streamlines agree with the flow visualization results. A number of other possible pairs of identical problems are also presented. Applications of the identical character are provided and assumptions under which the identical problems may exist are discussed.