The paper describes a topology optimization procedure to obtain optimal structures which maximize a chosen quantity of interest (QoI). Conduction heat transfer is assumed to govern the underlying physics. The numerical solution is performed using a finite volume formulation. The computational domain is divided into structured quadrilateral or hexahedral cells. Associated with each cell is a design variable that is intended to be driven to a binary value of either 0 or 1. The binary value determines which of two materials fill the cell. Thus the optimization problem seeks to find a structure, i.e., a spatial distribution of the design variable that maximizes a global QoI under specified constraints. A gradient-based optimization technique is developed within the framework of the finite volume formulation. We demonstrate the efficacy of the technique using a variety of test cases specifically for conduction heat transfer applications. The underlying procedure is, however, applicable to more general problems involving fluid flow and convective thermal transport as well as other physics.

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