Solution+Conduction+Mid+Term+Spring+2011 (1)

Solution+Conduction+Mid+Term+Spring+2011 (1) - S O L U -...

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\ HEAT FLUX S OL U -r/O,J Midterm Exam ME 3345 Heat Transfer Spring 2011 Hesketh TIME ALLOWED 55 MINUTES Name: _________ Grade: Question 1 (30 pts): LENGTH = 1m INSIDE Q("=100W/m 2 HEAT GENERATION q=104fVlm 3 The cylindrical pipe shown above has heat generation in the annular region and an inside boundary condition ofradial heat flux. (1) From the heat diffusion equation in cylindrical co-ordinates calculate the temperature distribution as a function ofradius, (2) Indicate control volume and calculate the outside surface temperature. Assume: Steady state conditions, neglect radiation heat transfer, uniform, constant properties. ...r 7 c::7iP y- J 7/'ffE - Ii ( k r~) -+- :i -== 0 d-r. f ~ (krE) jr=- J tjrdr- d r ;}r t 2- l k rJT _ c -#+ I Tr 2- J- \ {f + Jr - - Page 1
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----------- g 0 (/ tJ {)/j/(y C (;7 tJ 0 cIT ION :;;. r -=- I) - k L7 _I b 0 dr - 1;/~ -{;' +'/~j r:::::-G C, :::::= 0, 0..2. S- [I;) ~/V'~~lry e,4L-/l)1/~E O/l/ C Vl-I/V/JtS7( ,. , .. .f~:0. C? J're;w;y ;::=/r-- - EOvJb- -I-£:j -= ge =- -~T.A17?: 7 ~ 2/T1) - /... 21/r". (7.,- 19b) + p'x 7T! f2
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Solution+Conduction+Mid+Term+Spring+2011 (1) - S O L U -...

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