Dimensionless Correlating-Equations for Predicting the Optimal Tilting Angle of Water-Filled Square and Shallow Enclosures Differentially Heated at Sides

Abstract

Laminar natural convection heat transfer inside water-filled, tilted square and shallow cavities heated at one side and cooled at the opposite side, is studied numerically. A computational code based on the SIMPLE-C algorithm is used to solve the system of the mass, momentum and energy transfer governing equations. Simulations are performed using the Rayleigh number based on the length of the heated and cooled sides, the height-to-width aspect ratio of the enclosure, and the positive tilting angle with respect to the gravity vector (which corresponds to configurations with the heated wall facing upwards), as independent variables. It is found that the heat transfer performance has a peak at an optimal tilting angle which increases as the Rayleigh number is decreased and the aspect ratio is increased. On the basis of the results obtained, a set of dimensionless correlations is developed.