Question

A tube with length of 1 m is made from steel (k 15 W/m/K) having a square cross section with a circular hole through the center, as shown below Calculate the steady state temperature distribution across the cross section and the total rate of heat transfer if the inner surface is held at 20 °C, and the outer surface is held at 100 °C. How does the heat rate vary with grid resolution? Consider 9 and 17 grid points across the width of the cross section (i.e. 5 and 8 grid points across half the cross section) 1. 2. Bonus: If you extend the trend to larger numbers, for example 100, there will be a 25% bonus (applicable to other quizzes and/or exams) o 3. Compare the heat rate to an exact solution. 4. Calculate the steady state temperature distribution across the cross section and the total rate of heat transfer if the inner surface is exposed to a fluid with temperature 20 °C resulting in a heat transfer coefficient of 250 W/m2/K, the left and right outer sides are held at 100 °C, and the top and bottom outer sides are insulated Hint: Use the symmetry of the problem to reduce your work. You must use a numerical approach (for all but 3.). Look at Ch. 4 I don't want you to write the matrix solver. Use the available matrix or linear system solvers in whatever tool you're working in, e.g. Matlab Steel 150 mm 75 mm PIEASE INCLUDE: -code (e.g. in Matlab). Comment what every line is doing Any other supporting work (e.g. drawings.) Pseudocolor plots for the temperature distributions. (e.g. see the pcolor command in Matlab) - Numerical values for the heat rates

Answer 1