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Homework_2_Spring_2010_SOLUTIONS(2)

# Homework_2_Spring_2010_SOLUTIONS(2) - MAE 105 Introduction...

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Unformatted text preview: MAE 105: Introduction to Mathematical Physics -—«”""‘" 0 FDU“;5 Homework 2 Z ’_'\ Posted: April 8, 2010, DUE: April 16, 2010 1. Determine the equilibrium temperature distribution for a one-dimensional rod of length “L”, assuming the following boundary conditions: th*q In each case, sketch, very approximately, the temperatme proﬁle in the rod (a) No internal heat sources. The temperature of the left end of the rod is “T” and the temperature at the right end is ‘ zero. 6 ﬂb‘ (b) An internal heat source generates “Q” units of heat per unit volume and unit time. The temperature of the left end of the rod is “T1” and the temperature at the right end is “T2”. ? f”;— (c) No internal heat sources. The temperature of the left end of the rod is “T1” and the temperature gradient at the right end is equai to a constant, “a” 7ft HOMENOZK 2 - bOLuTlONS szx' © NO ken-1“ 5W Q Tot: 0,13) =T(O) =. 7; “L 31!. WWW.“ Noah-bah: =9 ”(XI—(319:0 2 50—54“. TONI)? T(x)= CI‘JL't-CL 'au“ 95va {in ‘9me WII‘. cum; m comma [email protected])4(C;J :3 T(x=o,t)=T(0) = T, = c.(o)+ CL =) 6-HT: 9T(1‘L) __._ C1 :6. r; Cl=é "7" 69¢ +Tl 1—(1) (aw) “3' 6 *6 PM‘M '1': 1:0 1:}: 9C 700 T. % 6 @WM @LH.) 7‘0 “Le-L at ...
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Homework_2_Spring_2010_SOLUTIONS(2) - MAE 105 Introduction...

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