Study of the Characteristic Length for Natural Convection in Symmetric Trapezoidal Cavities

Abstract

In this work, natural convection is numerically analyzed in a symmetrical trapezoidal enclosure, which consists of two isolated vertical walls and two symmetrically inclined active walls. The inclination of the lower and upper walls varies from 0º to 30º, while the temperature difference between them varies between 1ºC and 30ºC. The smaller base of the trapezoid remains fixed, while the larger base grows as the angle of inclination increases. In previous works, the configurations have been studied: attic type and inverted attic, the results show that two types of flow are established: bottom and lateral heating; this change occurs at a critical angle. For the geometry of the symmetric trapezoid, a similar flow behavior is obtained. For different temperature jumps, as the inclination angle increases, the number of convective cells decreases. In order to study heat transfer, a potential type correlation between the Nusselt number and the Rayleigh number is used. In previous works, a characteristic length has been found for the attic and inverted attic geometries; in the present work, it is analyzed whether these lengths continue to describe the flow behavior obtained for the symmetric geometry.