1. Use the finite-difference implicit method and derive finite-difference energy balance equations for a 1-D hollow cylinder during the transient with the following BCs (see problem 5.9): Let m = 1, 2, 3, 4, 5; time step = p = 0, 1, 2 = hT1
r=r
2. For hot-gas flow (velocity Vo, temperature To) over a cooled convex surface (surface temperature Ts), answer the following questions (see chapter 6):
a. Sketch the thermal boundary-layer thickness distribution on the entire convex surface and explain the results.
b. Sketch the possible local heat transfer coefficient distribution on the convex surface and explain the results.
c. Define the similarity parameters (dimensionless parameters) that are important to determine the local heat transfer coefficient on the convex surface.
d. Write down the relationship among those similarity parameters and give explanations.
e. Write down how to determine the local heat flux from the convex surface.
3. Similarity Method for Laminar Flow over a Flat Plate (see problem 7.11): U.o - free stream velocity, Tco - free stream temperature, Tw - flat plate wall temperature.
(a) Write down the similarity variable, differential equations, and boundary conditions for velocity and temperature, respectively. Then, determine velocity (u) and temperature T (if Pr = 1) at: (x, y) = (2cm, 1/3 8) = (4cm, 1/3 8) = (6cm, 1/3 8)
(b) At any given x: if Uo increases, the friction factor will be increased or decreased? Why? How about shear stress? At any given Uoo: if x increases, the heat transfer coefficient will be increased or decreased? Why? How about the heat transfer rate?
