Numerical Study of Heat Transfer in Extended Surfaceswith Mutual Radiation Between Parallel Fins

Abstract

The present work shows the influence of the mutual heat transfer on the effectiveness of finned surfaces. Numerical simulations are carried out through a sequence of linear problems, possessing an equivalent minimum principle, that has as its limit the solution of the original problem. The original nonlinear problem is regarded as the limit (which always exists) of a sequence of linear problems like the classical conduction-convection ones. In this work the nonlinear conduction-radiation heat transfer process is considered and simulated by means of a finite difference linear scheme. Such a limit is reached in an easy way by means of standard procedures, allowing the employment of more realistic hypotheses, like some nonlinear boundary conditions, since the mathematical complexities are not a constraint for simulating the elliptic partial differential equation. This work accounts for the the steady state heat transfer process in rigid fins which experiences convective and radiative heat exchange. Some typical results are shown in order to illustrate the methodology. Results have shown both the relevance of the radiation and the importance of the thermal interaction between the fins, so that there is an effective and realistic thermal mapping. Neglecting the thermal interaction can lead to errors of up to 20 percent.