AUTHORS: Antonio Campo, Miguel Cortina

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ABSTRACT: Within the framework of the lumped model, unsteady heat conduction takes place in a quasi-isothermal body whose mean temperature changes with time only. Fundamentally, the lumped model subscribes to the notion that the internal conductive resistance in a solid body is negligible with respect to the external convective resistance at the solid/fluid interface. The short technical paper seeks to establish an alternate basis for the utilization of the lumped model embodying heat interaction by coupled natural convection and radiation between a simple solid body and a quiescent gas. The governing lumped equation is highly nonlinear and needs to be solved by numerical methods, like the Runge-Kutta-Fehlberg algorithm. Utilizing regression analysis for the total heat transfer coefficient varying with the temperature excess, nonlinear lumped equation is conveniently transformed into a milder nonlinear Bernoulli equation. Despite that the latter equation is still nonlinear, it admits an exact analytic solution. The step-by-step computational procedure is developed in a case study centered in a horizontal solid cylinder cooled by air.

KEYWORDS: natural convection, radiation, nonlinear lumped model, lumped Biot number criterion, Bernoulli equation

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