SUMMARYA new finite volume (FV) approach with adaptive upwind convection is used to predict the two-dimensional unsteady flow in a square cavity. The fluid is air and natural convection is induced by differentially heated vertical walls. The formulation is made in terms of the vorticity and the integral velocity (induction) law. Biquadratic interpolation formulae are used to approximate the temperature and vorticity fields over the finite volumes, to which the conservation laws are applied in integral form. Image vorticity is used to enforce the zero-penetration condition at the cavity walls. Unsteady predictions are carried sufficiently forward in time to reach a steady state. Results are presented for a Prandtl number (Pi-) of 0 7 1 and Rayleigh numbers equal to to3, lo4 and lo5. Both 11 x 11 and 21 x 21 meshes are used. The steady state predictions are compared with published results obtained using a finite difference (FD) scheme for the same values of Pr and Ra and the same meshes, as well as a numerical bench-mark solution. For the most part the FV predictions are closer to the bench-mark solution than are the FD predictions.

SUMMARYA new finite-volume approach is developed and applied to the two-dimensional continuity and convective4iffusive energy equations. The variation of the field variables is approximated by bi-quadratic interpolation formulae over the space occupied by the finite volume and the region surrounding it. These are used in the integral conservation laws for energy and mass. The convective transport is modelled using a new upstream-weighting approach which uses volume averages for the energy transported across the boundaries of the finite volume. The weighting is dependent on the skewness of the velocity field to the surfaces of the finite volume as well as its strength. It is adaptive to local flow conditions. Two test cases are treated which have exact solutions. The first is not new and involves a rotating shaft. The errors are less than 0.06 per cent for this case. The second case is new and involves convection past a source and sink. In contrast to the first case, the global Peclet number is a strong parameter, and cell Peclet numbers (Pe,) range from 0 to 20. The maximum error is 2.3 per cent for Pe, =4, and there is no evidence of numerical diffusion for even the largest value of Peh. For both test cases, the maximum error occurs at moderate values of Pe, and diminishes at the extreme low and high values.

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In large commercial buildings, air handlers for HVAC systems are shutdown during unoccupied periods to save on utility bills. During the shutdown time, some of the heating or cooling load accumulates and is stored in the building. Consequently, on start up, there is an added load that must be removed by the HVAC system. The stored load can be divided into preconditioning load (fast load) and storage load (slow load). In this paper, mathematical analysis is used to study the preconditioning and storage loads after system shutdown. The governing mathematical equations, that represent an analytical model, were solved using Laplace transforms. Simplifications to the analysis are presented. It is found that the ratio of storage area to the exposed area plays an important role in the determination of shutdown loads.