LAMINAR FLOW HEAT TRANSFER IN A CYLINDER WITH CIRCUMFERENTIAL TUBES

Abstract

Employing a special class of basis functions of Laplace and biharmonic equations, the problems of laminar flow heat transfer in a cylinder with a ring of N equally spaced circumferential tubes are solved. It is assumed that the outer boundary of the cylinder is subject to convection, while the inner tube boundaries are subject to either convection or a uniform temperature. It is also assumed that the fully developed kinematics and thermal states have been reached by the viscous fluid, and that all of its properties are independent of temperature. The aforementioned basis functions, which automatically satisfy the outer boundary conditions are obtained in closed form for all outer Biot numbers as integers greater than 1. For non integer values of the outer Biot numbers, the basis functions are developed in the form of series with rapid convergence properties. The inner boundary conditions are numerically satisfied and some examples for the temperature distributions and the rates of heat transfer are given.