- The present work describes the thermal profile of a single dissipation fin, where their surfaces reject heat to the environment. The problem happens in steady state, which is, all the analysis occurs after the thermal distribution reach heat balance considering that the fin dissipates heat by conduction, convection and thermal radiation. Neumann and Dirichlet boundary conditions are established, characterizing that heat dissipation occurs only on the fin faces, in addition to predicting that the ambient temperature is homogeneous. Heat transfer analysis is performed by computational simulations using appropriate numerical methods. The most of solutions in the literature consider some simplifications as constant thermal conductivity and linear boundary conditions, this work addresses this subject. The method applied is the Kirchhoff Transformation, that uses the thermal conductivity variation to define the temperatures values, once the thermal conductivity variate as a temperature function. For the real situation approximation, this work appropriated the silicon as the fin material to consider the temperature function at each point, which makes the equation that governs the non-linear problem. Finally, the comparison of the results obtained with typical results proves that the assumptions of variable thermal conductivity and heat dissipation by thermal radiation are crucial to obtain results that are closer to reality.

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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.

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 presented tools allow the employment of realistic hypotheses. The problems are simulated with the aid of a finite difference approximation. 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 indicate that mutual radiation can significantly impact the actual heat transfer response of a fin.

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