Numerical Solution of Nonlinear Fin Problems via Initial Value Method

In general the mathematical model for steady, one-dimensional conduction in fins appears as a nonlinear, two-point boundaryvalue problem. The nonlinearities arise due to radiative surface heat transfer, temperature dependent thermal conductivity or heat transfer coefficient etc. [i]. Often in such cases a numerical solution has to be obtained. Examining the literature reporting such solutions it appears that the most commonly used numerical scheme is based on a standard shooting technique in which a succession of guessed values of the missing initial derivative are used until the solution which satisfies the specified boundary condition at the other end is obtained. The disadvantages of this iterative process are long computing time, sensitivity of the solution to guessed initial condition and occasional lack of convergence. With the development of method of transformation groups, it has been possible, in some problems, to overcome these difficulties. The method transforms a boundary value problem into an initial value problem which can then be integrated in one