Inexpensive Computations Using Computational Fluid Dynamics Combined With Asymptotics Applied to Laminar Mixed Convection in a Vertical Channel

Abstract

In this work, a solution technique is proposed by synergistically combining asymptotics and computational fluid dynamics to ascertain a problem of laminar mixed convection heat transfer in a vertical channel. First, numerical simulation is carried out on a vertical channel that consists of an aluminum heater plate assembly at the center of the channel. The numerical model is treated as a conjugate heat transfer problem, and the concept of perturbation and blending is incorporated wherein the limiting solution of natural and forced convection is obtained in terms of average Nusselt number. These correlations are then blended to find a unified composite correlation that work very well for extreme limits of mixed convection. The Richardson number is chosen as an independent variable in the present analysis; as a result, the Nusselt number correlation is cogent for the mixed convection region. Upon performing the numerical simulations, the results of the mixed convection are then compared with experimental results available in the literature for the purpose of validation of the numerical solution. The results of the present work emphasize that, with minimum computational fluid dynamics (CFD) solutions, one can obtain a reasonably good composite correlation for the Nusselt number for mixed convection and also a substantial reduction of computations is possible ensuing an asymptotically flawless solution.