The finite‐difference computation of natural convection in a rectangular enclosure

Abstract

A study is made of the natural convection of a fluid contained in a long horizontal enclosure of rectangular cross section with one vertical wall heated and the other cooled. Two‐dimensional motion is assumed. The governing vorticity and energy transport equations are solved by an implicit alternating direction finite‐difference method. Transient and steady state isothermals and streamlines are obtained for Grashof numbers up to 100,000 and for height‐to‐width ratios of 1, 2, and 3.

The Turbulent Free Convection Flow Above a Heated Horizontal Circular Plate

“…This method, however, was apparently handicapped by the lack of a continuous recording technique. (9,34,43) for laminar free convection in a vertical axisymmetric enclosure with a small heated spot centrally located on the floor. He concluded that the calculated flows for all methods were similar and the required computer times were also of comparable magnitudes.…”

“…An equation similar to (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) may be obtained 152 I m, 2 from the principle of conservation of mass. This may be used to chec the results of Equation (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16).…”

“…Calculate from Equation (6)(7)(8)(9)(10)(11) for all (i,j) interior 7. Clculte i,j to the boundaries (hereafter these points will be referred to as the interior points as opposed to the boundary points) and then calculate V' jfor all interior points as follows:…”

“…Calculate u'i,j and v'i' j for all interior points using Equation (6)(7)(8)(9)(10)(11)(12)(13)(14) a the stream function just calculated.…”

Prediction of Buoyancy-Driven Flow in a Slot with Different Biot Numbers

“…The early investigations in this area include Ostrach [1], Wilkes and Churchill [2], and de Vahl Davis [3] who introduced a numerical solution for 2-D natural convection in a rectangular cavity. A large number of other studies followed examining a variety of cavities.…”