hw1 - Homework 1 – due Friday, 8/27 1. In class 1, we...

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Unformatted text preview: Homework 1 – due Friday, 8/27 1. In class 1, we discussed a spherical, stainless steel (AISI 302) canister that was used to store reacting chemicals that provide for a uniform heat flux, q”, to its inner surface. If the canister is suddenly submerged in a liquid bath of temperature T∞ < Ti, where Ti is the initial temperature of the canister wall. Assume negligible temperature gradients in the canister wall. Values: T∞ = 350 K Ti = 500 K h = 500 ro = 0.4 m ri = 0.3 m a) develop an equation for the variation of the wall temperature with time. What is the initial rate of change of the wall temperature if q” = 105 W/m2? b) what is the steady-state temperature of the wall? c) Compute and plot the steady-state temperature as a function of h for the range 100 < h < 10,000 W/m2-K. Is there a value of h below which operation would be unacceptable? Hint: remember which processes are volumetric and which involve surface area. a) & & & Ein − Eout = Est 4 dT q1 " 4πri 2 − h 4πro2 (T − T∞ ) = ρ π ro3 − ri3 c p 3 dt 4 dT q1 " 4πri 2 − h 4πro2 (T − T∞ ) / ρ π ro3 − ri3 c p = 3 dt ( )( ) ( ) ( )( 3 ) ( ) rho ⋅ cp ⋅ ro − ri ( 3 3 ) ⋅ ⎡q ⋅ ri − h ⋅ ro ( Ti − Tinf )⎤ = −0.063 ⎣ ⎦ 2 2 b) Given rho ⋅ cp ⋅ ro − ri ( 3 3 3 ) ⋅ ⎡q ⋅ ri − h ⋅ ro ( T − Tinf )⎤ ⎣ ⎦ 2 2 0 T = 469.5 c) 12000 10000 8000 6000 4000 2000 0 300 500 700 900 1100 h Data: T h 912.5 100 462.5 500 412.5 900 393.3 1300 383.1 1700 376.8 2100 372.5 2500 369.4 2900 367 3300 365.2 3700 363.7 4100 362.5 4500 361.5 4900 360.6 5300 359.9 5700 359.2 6100 358.7 6500 358.2 6900 357.7 7300 357.3 7700 356.9 8100 356.6 8500 356.3 8900 356 9300 355.8 9700 355.6 10100 Lower h’s make T too high. 2. Consider an aluminum pan used to cook beef stew on top of an electric range. The bottom section of the pan is L = 0.3 cm thick and has a diameter of D = 20 cm. The electric heating unit on the range top consumes 800 W of power during cooking and 90 % of the heat generated in the heating element is transferred to the pan. During steady operation, the temperature of the inner surface of the inner surface of the pan is measured to be 110o C. What are the boundary conditions for the bottom section of the pan during this cooking process? @ x = 0, ‐dT/dx = q @ x = L, T = 110o C 3. Steam flows through a pipe at an average temperature of T∞ = 200 o C. The inner and outer radii of the pipe are r1 = 8 cm and r2 = 8.5 cm. The outer surface of the pipe is highly insulated. If the convection heat transfer coefficient on the inner surface of the pipe is h = 65 W/m2‐oC, express the boundary conditions on the inner and outer surfaces of the pipe during transient periods. @ r = r1, ‐k(dT(r1,t)/dr = h(T∞ ‐ T(r1)) @ r = r2, ‐k(dT(r2,t)/dr = 0 ...
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This note was uploaded on 11/12/2010 for the course CHEN 3320 at Colorado.

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