It is desired to develop and solve the governing equation for energy change in a fluid flowing through a tube as shown in Figure 1.1. The aim of the assignment is to obtain the steady-state T(r,z) temperature distribution in the fluid. Figure 1.1. Boundary layer development in a horizontal pipe The general assumptions for this problem are as follows: - The temperate at the entrance is uniform - The temperature at the wall is maintained at Tw - The flow is steady, fully-developed laminar flow - The fluid is an incompressible Newtonian fluid. - Viscous dissipation is negligible. The starting point of the analysis is the equation of energy-change: CpDtDT=q:v where is the density of the flowing fluid Cp is the specific heat capacity of the fluid T is the temperature t is time q is the flux of heat is the stress tensor v is the velocity vector Objectives (a) Make use of the listed assumptions to reduce the equation of energy-change to the appropriate form (Show all your calculations). (b) Specify the appropriate boundary conditions for the problem. (c) Develop a suitable difference equation for the problem, and justify the choice of difference quotients with the order of accuracy. (d) Perform a stability analysis of the resulting difference equation. (e) Solve the difference equation for a minimum of 10 internal nodes in both spatial coordinates (i.e., r and z )