Numerical Solution of the Extend Graetz Problem for a Bingham Plastic Fluid in Laminar Tube Flow

The problem of thermally laminar heat transfer based on the fully developed velocity for Bingham fluids in the entrance region of a circular duct is studied. The effect of the axial position, Peclet number, and Brinkman number are taken into account. Two cases of T (constant wall temperature) and H2 (constant heat flux) thermally boundary conditions are considered in this study. The energy equation is solved numerically by finite difference methods. The marching technique and the relaxation method are the main factors of the computer program. The results of the present work including the variation of the Nusselt number and mean temperature with the axial distance for the two cases are represented in Figures and compared with the available known results to support its accuracy.