HEAT TRANSFER ANALYSIS INSIDE A DUCT UNDER LAMINAR FLOW CONDITION USING VARIATIONAL METHOD

摘要

When a fluid flows through a pipe line, the velocity and temperature distribution across the pipe cross section is required to be determined in order to properly utilize the fluid and its associated energy in a process plant. In the present paper, a variational method has been used to determine this distribution in a pipeline of rectangular as well as square cross section under laminar condition. The mathematical equations have been developed describing the velocity and temperature distributions under two cases. In the first case, the heat flow rate is taken to be uniform along the axial direction and in the second case, the wall temperature has been taken to be uniform. In both the cases, the velocity and temperature distribution curves have been drawn from the mathematical equations derived. The distribution curves are presented for a variety of thermal boundary conditions around the periphery of the duct cross section.