Finite element solution of heat transfer for gas flow through a tube

An analysis is performed of the axial temperature distribution along the wall of a circular tube. A transparent gas in forced convection enters a tube with variable heat-transfer coefficient, axial wall heat conduction, and internal radiation exchange. The nonlinear intergro-differential equation describing the process of energy exchange is solved using the Galerkin finite element technique with isoparametric, quadratic elements. Depending on the particular physical problem, an arbitrary heat generation distribution in the tube wall as a function of axial position can be taken into this model. However, only the uniform and the sinusoidal heat generation cases are considered here. The tube interior surface is assumed to be black, and the gas transparent.