Heat Transfer Assignment 1 -

Q1. Show all assumptions, derivations and calculations.

A turbine blade 6.3 cm long with cross sectional area 4.6 x 10^-4 m² and perimeter 0.12 m is made of stainless steel (k=18 W/mK). The temperature of the root is 482^oC. The blade is exposed to a hot gas flow at 871^oC with a heat transfer coefficient 454 W/m²K.

a. Determine the temperature of the blade tip using analytical solution. Tip could be assumed to be insulated.

b. Using 11 node points and uniform node size Ax write down the finite difference equations for interior nodes and other nodes where the temperature is unknown using energy balance method.

c. Put the equations for each node into form [A][T] = [C] where [A] is the coefficient matrix, [T] is temperature column vector and [C] is the column vector of known constants.

d. Solve the resulting equation for unknown temperatures using MATLAB (or use any other similar software or write your own code) by employing matrix inversion method. Plot temperature distribution as a function of axial distance and compare with the analytical solution. Please also provide a printout of computer program you wrote.

e. Solve the unknown temperatures using MATLAB (or use any other similar software or write your own code) and employing Gauss-Seidel Iteration. Plot the temperatures as a function of number of iterations. Plot the final temperature distribution as a function of axial distance and compare with the analytical solution. Please also provide a printout of computer program you wrote.

Q2. An electronic device dissipating 30 W has a mass of 20 gm, density p = 2700 Kg/m³, a specific heat of 850 J/(kgK), and a surface area of 5 cm². The device is lightly used, and it is on for 5 min and then off several hours, during which it cools to the ambient temperature of 25^oC. Taking the heat transfer coefficient to be 12 W/(m²K) determine the temperature of the device at the end of 5 min operating period. What would the answer be if the device were attached to an aluminum heat sink (c = 903 J/(kgK), p= 2700 Kg/m³) having a mass of 200 gm and an exposed surface of 50 cm²? Assume the device and the heat sink to be nearly isothermal and have the same thermal conductivity k = 237 W/(mK) and the exposed area of device is the same as before.

Heat Transfer Assignment 2 -

Show all assumptions, derivations, integrals and calculations.

Q1. Experimental data over a very rough flat plate given in the figure shows that

Nu_x = 0.04Rex^0.9Pr^1/3

If x is measured from the leading edge, obtain an expression for the ratio of the average heat transfer coefficient h^-_x to the local coefficient h_x.

Q2. Conservation of mass, momentum and thermal energy equations for a steady, 2-D, incompressible, laminar flow with no energy generation and negligible body forces are given as: