MAXIMIZATION OF HEAT FLOW THROUGH A CAVITY WITH NATURAL CONVECTION AND DEFORMABLE BOUNDARIES

What is it about?

The aim of this work is to try to minimize the heat transfer resistance inside an air filled vertical cavity, initially rectangular. We are dealing with initial conditions where the two-dimensional cavity has an aspect ratio (height/thickness) equal to 40. This enclosure is differentially heated, its vertical faces are thus maintained at T-H for one and T-C for the other one. Horizontal faces are chosen adiabatic. We use the classic hypothesis concerning the heat transfer by natural convection inside a cavity with a Newtonian fluid. The numerical resolution of the problem is obtained with a numerical code based on the finite volume method. We try to maximize heat transfer, while satisfying the following constraints: The thermal boundary conditions have to remain constant The height of the cavity is fixed Air is the Newtonian fluid chosen We propose an alternative to the classic route, which would be to decrease the air thickness, by modifying the geometry of the vertical faces. In this work, the vertical faces can bend inward in a symmetric way with respect to the center of the enclosure. A parabolic curvature will be used. The numerical results that we obtain, show the curvature of the vertical faces tends to stabilize the flow, while the thermal boundary conditions remain constant. The flow is first close to the transition from laminar to turbulent regime, because of the Rayleigh number and the aspect ratio chosen. The heat transfer is convective; yet it is characterized by the existence of secondary cells inside the core cavity. When the vertical faces curvature is imposed, the flow slows down at mid-height of the enclosure until becoming purely conductive at mid-height if the curvature is stronger. However, the local heat flux calculations along the cavity height, indicate that the heat transfer increases through the cavity with the curvature because of the new temperature distribution. Thinking in terms of an average thermal resistance, we obtain a decrease of this parameter from 30 to 40% depending on the thermal boundaries chosen when the curvature is maximum

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