| In this study, a numerical simulation is developed for analyzing incompressible fluid flow and conjugate heat transfer problems involving complex geometries. In the context of this work, conjugate heat transfer refers to coupled conduction in the solid domain and forced convection in the fluid domain. In conjugate heat transfer analysis, the energy equations in the solid and fluid domains are coupled by the interface boundary condition, which is a heat flux balance across the interface.;The simulation developed in this work is called DIATEMP (Diagonal Cartesian Method for Temperature Analysis). DIATEMP utilizes a Cartesian grid and models complex geometries with the diagonal Cartesian method, which uses diagonal line segments as well as Cartesian line segments. The transport equations are discretized with the finite analytic (FA) method, using 9-point FA elements throughout the solution domain except near complex boundaries, where the 5-point FA element is employed to allow the use of diagonal line segments.;The current work is validated by simulating several conjugate heat transfer problems, and accurate results are obtained for both regular and complex geometries. DIATEMP is then used in the design of a heat exchanger. Flow and conjugate heat transfer in heat exchangers with different fin geometries are simulated, and the resulting pressure drop and heat transfer characteristics are used to determine the best designs with respect to minimum pressure drop and maximum heat transfer. It is also found that a convection-only analysis of the heat exchanger assuming constant wall temperature leads to an overestimation of the heat transfer.;This study achieves the following contributions: (1) the diagonal Cartesian method yields a more accurate geometrical representation of complex bodies than the traditional Cartesian method, but retains the simplicity, robustness and speed inherent in the Cartesian grid; (2) DIATEMP is capable of modeling conjugate heat transfer problems involving arbitrary geometries; and (3) the applications investigated in this work demonstrate the ability of DIATEMP to increase physical understanding of conjugate heat transfer problems. |
