Numerical analysis of natural convection in parallel, convergent, and divergent open‐ended channels

Abstract

PurposeTo investigate the natural convection in open‐ended parallel, convergent, and divergent channels using a fully elliptic procedure without extending the domain outside the channel for the application of the boundary conditions at the inlet and outlet of the channels.Design/methodology/approachThe model is two‐dimensional and fully elliptic in x and y directions, and the equations are solved only inside the channel by the finite volume method using a co‐located arrangement with a segregated procedure and boundary fitted coordinates. The pressure‐velocity coupling is solved by the PRIME algorithm.FindingsThe results are shown in terms of velocity vectors, streamlines, isotherms, and the local and the average Nusselt number for all fluids and configurations investigated. For high values of the Rayleigh number, a recirculation region in the outlet of all investigated configurations and Prandtl numbers was observed. Based on the results, a single correlation is proposed to evaluate the average Nusselt number for all fluids and configurations analyzed.Research limitations/implicationsThe shown results are based on the following hypothesis: steady‐state, two‐dimensional, laminar flow, and Boussinesq's aproximation. The results are presented in following range of parameters: 105<(Smax/L)RaSmax<108, where Smax denotes the maximum distance between the plates and Ra denotes the Rayleigh number; half angle of convergence or divergence (θ): 5° and 15°; and Prandtl numbers: 0.7, 5.0, and 88.Originality/valueLocal and average Nusselt numbers, for Prandtl numbers varying from 0.70 to 88, and a correlation for the average Nusselt number for all fluids and configurations are presented. The results presented in this paper are useful to engineers and researchers involved in thermal design and numerical methods.