Buoyant flow calculations with non‐orthogonal curvilinear co‐ordinates for vertical and horizontal parallelepiped enclosures

A control‐volume‐based finite‐difference formulation is developed for heat transfer and fluid flow in arbitrary three‐dimensional parallelepiped enclosures. The governing equations in Cartesian co‐ordinates are first transformed to those in non‐orthogonal curvilinear co‐ordinates by tensor transformations. After introducing the properties of the parallelepiped geometry, equations are obtained in the primitive variables for which all vectors and tensors are based on the curvilinear co‐ordinates. With proper treatment of the heat flux and stress tensor terms, the finite‐difference equations, analogous to those in the Cartesian coordinates, are formed. Examples are utilized to show the validity of the methodology and the results are found to compare well with existing experimental data. The differences in heat transfer and fluid flow inside parallelepiped enclosures and rectangular enclosures are delineated and discussed from a physical point of view.