Comparison of analytical methods and numerical methods in modeling the physical phenomenon of heat conduction with free radiation

Abstract

The development of mathematical setting for modeling heat conduction phenomena in the presence of radioactive effects is well known. The importance in the study of heat conduction in relation to radioactive effects is relevant in several engineering applications such as combustion, materials science, fluid mechanics and other areas. This research is based on the mathematical model of the heat equation to study the physical phenomenon of heat transfer along a metal bar with slightly insulated sides with the effect of free radiation. To calculate the temperature function that allows modeling the heat transfer process along the bar, the Fourier series solution is constructed step by step, in addition an alternative method of calculating the temperature by using the explicit numerical method is given. The calculation of the temperature along the bar is compared by analytical and numerical method by computing the percentage error and different temperature profiles are plotted to verify the fit of the two approaches. The methods developed throughout the research can be extended to other types of physical phenomena that are useful in related research and in education in engineering subjects such as fluid mechanics and heat transfer.