Development of the three-dimensional finite analytic method for simulation of fluid flow and conjugate heat transfer

In this study, a new three-dimensional Finite Analytic Method is introduced. The new method is then applied in the development of a program named FANS-3D (Finite Analytic Numerical Simulation-3 Dimensional) to solve conjugate heat transfer problems in three-dimensional geometries. Finally, as an example of the use and capabilities of the program, some relevant engineering problems are solved.; The new 19-point finite analytic discretization equation for three dimensional convection diffusion equation is derived from superposition of three two-dimensional finite analytic solutions. This new discretization equation is fully tested for stability and accuracy using previous analytic and numerical solutions, as well as experimental results.; Several new developments are made in this study. First, the efficiency in solving the coupled Navier-Stokes equations is greatly enhanced with the introduction of a new staggered algorithm to reduce the effort of evaluation of the discretization coefficients to almost one third of the original staggered algorithms. Second, a new conjugate element is created for the solution of conjugate heat transfer problems. The discretized equations based on the conjugate element in the new staggered arrangement are examined for stability and consistency. Furthermore, a unique grid is used to compute all modes of heat transfer.; FANS-3D is designed to solve any incompressible fluid flow with the Boussinesq approximation and heat transfer problem that involves conduction and convection modes of heat transfer in laminar flow, with provisions for radiation and turbulent flows. It can solve singular or conjugate modes of heat transfer. FANS-3D solves heat transfer associated with one, two and three dimensional geometry that can be represented in any orientation by orthogonal planes in a Cartesian coordinate system. It can solve internal and external flows using appropriate boundary conditions such as symmetric, periodic and user defined.; FANS-3D program is fully tested using analytic, numerical and experimental results. A variety of geometries and orientations are considered and used as benchmarks. The program is applied to solve conjugate heat transfer problems with application to heat exchangers, cooling of electronic components, and other engineering problems. In these examples all modes of heat transfer are considered.