Chemical Engineering 6453 Heat Transfer Prof. Geoff Silcox Spring 2005 Homework Assignment 1 Due Wednesday, 19 January, by 17:00.

Problem 1.0 Problem 1-3 of text.

Problem 2.0 Problem 1-66 of text.

Problem 3.0 Problem 2-13 of text.

Problem 4.0 Problem 2-14 of text.

Problem 5.0 Consider an ordinary light bulb as shown below. Neglecting convective cooling and using a lumped formulation of the energy balance, (a) calculate the steady surface temperature of the lighted bulb, (b) find the time required for the temperature to reach 95% of the steady value, that is, find t such that

sur

ss sur

T( t ) T 0.95T T

−=

−

where Tss is the steady state temperature, (c) plot the unsteady temperature profile as a function of time, and (d) estimated the time scale for the process from the governing equation and initial condition. Use the MATLAB ODE solver, ode45, for parts b and c. Include copies of your code and output with your solution. The following data are available. P = power = 200 watts δ = thickness = 0.4 mm ρ = density = 2700 kg/m3 α = ε = absorptivity = emissivity = 0.10 c = specific heat = 850 J/(kg K) D = diameter = 8 cm Tsur = 20°C

D

δTsur

δTsur

Based on Problem 9.33, p. 504 of Arpaci (1999).

Problem 6.0 A spoon in a cup of tea is approximated as a thin rod of constant cross section. The thermal conductivity, length, perimeter, and cross-sectional area of the spoon are k, 2L, P, and A. The heat transfer coefficients are h1 (tea) and h2 (air). Assume that one-half of the spoon is in the tea, the temperature of the tea remains constant at T0, and the ends of the spoon are insulated. Using a node-centered grid and a control volume formulation, find the steady temperature distribution for stainless steel and silver spoons and discuss the results in terms of the following data. 2L = 10 cm k = 15 W/(m K) (stainless steel) and 400 W/(m K) (silver) A ≅ 0.2 cm2 h1 = 1000 W/(m2K) and h2 = 10 W/(m2K) P ≅ 2 cm T∞ = 20°C and T0 = 80°C Justify any assumptions that you make and include a copy of your MATLAB code and output with your solution. Plot both temperature profiles on the same graph. Based on Problem 3-21, p. 173 of Arpaci (1966) and Example 2.11, p. 83 of Arpaci (1999).