Shooting Method for Numerical Simulation of Free Convection Flow in Porous Medium

摘要

In the analysis and optimal control of the systems, one often encounters a two-point boundaryvalue problem. In our work natural convection heat transfer along a vertical flat plate embedded in a fluid saturated porous medium is considered. The prescribed wall temperature and heat fluxes are boundary conditions in the form of some power functions. The mathematical model of the phenomena is a set of partial derivative equations. The theory of distributed-parameter systems can be applied in our case but the computational complexity is a motivation for finding simplified models. In our study we reduce the distributed-parameter system to a lumpedparameter system. This approach is based on assumptions that the physical properties of the medium are constant except the fluid density related to buoyancy term. The governing equations of the phenomenon that are partial derivative equations are transformed in ordinary differential equations by using the similarity method. Similarity solutions can be obtained by solving the simplified models based on Prandtl boundary layer equations. In the study of the simplified model one encounters what is called a two-point boundaryvalue problem. The existence and uniqueness of the solution can be quite difficult so that a numerical solution can offer an approach for this problem.