Impact of Non-Uniform Heating on Flow and Heat Transfer in a Square Cavity: A DRBEM Study

This study presents a numerical investigation of natural convection and heat transfer in a square cavity subjected to non-uniform wall heating. A spatially varying heat source is imposed on the left vertical wall, while the right vertical wall is maintained at a uniform cold temperature, and the horizontal walls are assumed to be adiabatic. The main objective is to analyze the effects of heater non-uniformity and position on flow structure, fluid mixing, and convective heat transfer characteristics within the enclosure.

The governing equations, expressed in terms of stream function, vorticity, and temperature, are solved using the Dual Reciprocity Boundary Element Method (DRBEM). In this framework, the fundamental solution of the Laplace equation is employed for the stream function equation, whereas the vorticity transport and energy equations are transformed into modified Helmholtz form and solved using the corresponding fundamental solution. This transformation is achieved by introducing a relaxation parameter into the Laplacian terms, while time derivatives are discretized using a forward difference scheme. The adopted approach eliminates the need for an additional time integration procedure and provides enhanced numerical stability, in addition to the computational efficiency offered by the boundary-only discretization.

Numerical simulations are carried out for Rayleigh numbers ranging from 10³ to 10⁶ and for various values of the non-uniformity parameter β in the interval [−2, 2]. The results demonstrate that both the flow intensity and the average Nusselt number increase with increasing Rayleigh number and β, indicating a significant enhancement in convective heat transfer. Furthermore, the heater distribution is shown to have a pronounced influence on the thermal and hydrodynamic fields. These findings highlight the critical role of non-uniform heating patterns in optimizing heat transfer performance in natural convection systems.