Simple computational method for conjugate conduction-natural convection along a vertical plate fin

Abstract

Conjugate conduction-natural convection for a vertical plate fin is analysed by using a simple iterative method, in which a uniform fin temperature distribution is not assumed. Governing boundary layer equations with their corresponding boundary conditions as well as one-dimensional heat conduction equations in the fin with its negligible tip leakage are cast into dimensionless forms by a non-similarity transformation. The resulting system of equations is solved numerically by using the central finite-difference approximation and the local non-similarity method, an arbitrary temperature at the fin tip can be taken to initialize the iterative process. The iterative procedure is repeated until the end surface condition is satisfied. Three or four iterations are sufficient for yielding a convergent result for the problems investigated. The main advantage of the present method is the considerable saving in computer memory. Moreover, the present results also agree well in their accuracy with other numerical results. Thus, the present method shows good accuracy and efficiency for simple conjugate conduction-convection problems along a vertical plate fin.