Heat Conduction in Infinite Elliptical Cylinder During Heating or Cooling

Abstract

Rigorous theoretical analysis of heat conduction in a very long elliptical cylinder in comparison with its cross section, i.e., an infinite elliptical cylinder, during heating or cooling is carried out using the Mathieu and modified Mathieu functions, which are the solutions of the basic heat-conduction equation expressed in terms of the elliptical cylinder coordinates. By applying the method of separation of variables, the mathematical solution is derived in the form of an infinite Mathieu function series in the most realistic and useful case that takes into consideration the internal and surface resistance of the cylinder. Two special cases of the heat conduction of an infinite elliptical cylinder, neglecting its surface resistance, and that of an infinite circular cylinder, including both its inner and surface resistance, are also discussed in detail. The temperature history and distribution within the cylinder are calculated numerically for various convective heat-transfer coefficients and aspect ratios of the elliptical cross section.