MCEN4004-Heat Transfer

A concrete duct is being designed and optimised for transportation of water, with the configuration shown in Figure.1-a. During operation, all external faces are exposed to a constant heat flux of 1000 W/m2 and water flows through two internal passages. The bulk temperature of water is assumed constant at 5°C and flow conditions induce a convective heat transfer coefficient of 120 W/m2 .K on the inside walls of the duct. The duct is long enough to consider a 2D thermal analysis of the cross-section, shown in Figure.1-b, as a reliable evaluation. Considering the geometry and thermal condition, the 2D cross-section is assumed to be symmetric about the XX’ and YY’ axes. 

a) Generate a nodal grid for the estimation of the local temperature for the 2D cross-section of concrete, considering symmetric boundaries to reduce computational nodes.

b) Explain all the boundary conditions (including corners) and derive finite difference equations for the temperature estimation of boundaries, corners and internal nodes.

c) Develop a MATLAB code to determine nodal temperatures, using Jacobi iteration method with a grid resolution of 5 mm,

d) Recalculate the temperature field with grid resolution of 1 mm

e) Compare and discuss the results obtained in part c and d, f) Modify the code to apply the Gauss-Siedel method of iteration and compare the running time with the Jacobi iteration method