WSEAS Transactions on Heat and Mass Transfer
Print ISSN: 1790-5044, E-ISSN: 2224-3461
Volume 12, 2017
Regression Analysis to Degrade the Highly Nonlinear Lumped Equation for Coupled Natural Convection and Radiation in Gases into a Bernoulli Equation
Authors: ,
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.
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Keywords: natural convection, radiation, nonlinear lumped model, lumped Biot number criterion, Bernoulli equation
Pages: 174-179
WSEAS Transactions on Heat and Mass Transfer, ISSN / E-ISSN: 1790-5044 / 2224-3461, Volume 12, 2017, Art. #20