TED-AJ03-158 OPTIMAL BOUNDARY CONTROL OF CONVECTION HEAT TRANSFER PROBLEMS

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An inverse analysis based on adjoint formulation of convection heat transfer is proposed to obtain the optimal boundary conditions for heat transfer characteristics; such as a total heat transfer rate or a temperature at a specific location. In the inverse analysis via adjoint formulation, the heat flow is reversed in both time and space. Thus, using the numerical solution of the adjoint problem, we can inversely predict the boundary condition effects on the heat transfer characteristics. As a result, we can obtain the optimal boundary conditions in both time and space to control the heat transfer at any given time. In order to illustrate the concept of the adjoint approach, let us consider a simple steady problem. Figure A(a) shows a model flow field usually called a lid-driven cavity flow. The purpose of this example is to raise the temperature at the center of cavity by heating somewhere on the walls. Using a conventional numerical technique, we can easily obtain the center temperature by solving energy equation, if the boundary conditions are specified. For example, Fig. A(b) shows the temperature distribution in the cavity when the bottom wall is uniformly heated. However, is this the best heating to raise the center temperature? Probably not. Because the ordinary numerical method gives us only a particular solution under specific boundary conditions. In the adjoint computation, on the other hand, the heat flow is reversed as mentioned above; this means that the heat flow is transferred from the center to the boundary in this example. To achieve this process, we set an imaginary heat source at the center of cavity, and reverse the flow direction as shown in Fig. A(c). This can be done by numerically solving an adjoint energy equation which will be derived later. The adjoint temperature distribution shown in Fig. A(c) indicates that the adjoint heat flow generated at the center of cavity goes toward the upper part on the right wall; this location is depicted by an oval in Fig. A(c). This inversely means that the most effective heating location to raise the center temperature exists in the oval. Thus, if we install a heater, this location is the best. In this paper, the basic idea mentioned above will be extended to unsteady optimal control problems.[figure]
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TED-AJ03-158 OPTIMAL BOUNDARY CONTROL OF CONVECTION HEAT TRANSFER PROBLEMS

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