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58 Pages

### sm2_41

Course: MAE Heat Trans, Spring 2010
School: Seoul National
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Word Count: 455

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2.40 PROBLEM (Cont.) q ro, z = 16 W / m K 2 150C / m 1 m 12C /1 m = 4608 W / m r () 2 2 &lt; &lt; q r ( ro ) = A r q ro, z r () 2 where A r = 2 ro ( 2z o ) q r ( ro ) = 4 1 m 2.5 m 4608 W / m = 144, 765 W Note that the sign of the heat flux and heat rate in the positive r-direction is negative, and hence the heat flow is into the cylinder. (d) The heat fluxes and the heat rates at...

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2.40 PROBLEM (Cont.) q ro, z = 16 W / m K 2 150C / m 1 m 12C /1 m = 4608 W / m r () 2 2 < < q r ( ro ) = A r q ro, z r () 2 where A r = 2 ro ( 2z o ) q r ( ro ) = 4 1 m 2.5 m 4608 W / m = 144, 765 W Note that the sign of the heat flux and heat rate in the positive r-direction is negative, and hence the heat flow is into the cylinder. (d) The heat fluxes and the heat rates at end faces, z = + zo and zo, may be calculated using Fouriers law. The direction of the heat rate in or out of the end face is determined by the sign of the heat flux in the positive z-direction. At the upper end face, z = + zo: q ( r, + z o ) = k z T z z o < = k [ 0 + 0 + 0 + 2dz o ] q ( r, + z o ) = 16 W / m K 2 300C / m z q z ( + z o ) = A z q ( r, + z o ) z q z ( + z o ) = 1 0.2 2 ( 2 ( 2 )m ) 2.5 m = +24, 000 W / m where A = (r 2 z 2 < 2 2 o ri ) < < 2 24, 000 W / m = +72, 382 W Thus, heat flows out of the cylinder. At the lower end face, z = - zo: q ( r, z o ) = k z T z = k [ 0 + 0 + 0 + 2d( z o ) ] zo 2 2 q ( r, z o ) = 16 W / m K 2 ( 300C / m )( 2.5 m ) = 24, 000 W / m z q z ( z o ) = 72, 382 W < < Again, heat flows out of the cylinder. (e) The heat rates from the surfaces and the volumetric heat generation can be related through an overall energy balance the on cylinder as shown in the sketch. Continued Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. PROBLEM 2-40 (Conti.) E in E out + E gen = 0 where E gen = q = 0 E in = q r ( ro ) = ( 144, 765 W ) = +144, 765 W < < E out = + q z ( z o ) q z ( z o ) = [ 72, 382 ( 72, 382 )] W = +144, 764 W The overall energy balance is satisfied. COMMENTS: When using Fouriers law, the heat flux q denotes the heat flux in the positive zz direction. At a boundary, the sign of the numerical value will determine whether heat is flowing into or out of the boundary. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
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Seoul National - MAE - Heat Trans
PROBLEM 2.42KNOWN: Temperature distribution in a spherical shell. FIND: Whether conditions are steady-state or transient. Manner in which heat flux and heat rate vary with radius. SCHEMATIC:ASSUMPTIONS: (1) One-dimensional conduction in r, (2) Constant
Seoul National - MAE - Heat Trans
PROBLEM 2.43 KNOWN: Spherical container with an exothermic reaction enclosed by an insulating material whose outer surface experiences convection with adjoining air and radiation exchange with large surroundings. FIND: (a) Verify that the prescribed tempe
Seoul National - MAE - Heat Trans
PROBLEM 2.44 KNOWN: One-dimensional system, initially at a uniform temperature Ti, is suddenly exposed to a uniform heat flux at one boundary, while the other boundary is insulated. FIND: (a) Proper form of heat equation and boundary and initial condition
Seoul National - MAE - Heat Trans
PROBLEM 2.45 KNOWN: Plate of thickness 2L, initially at a uniform temperature of Ti = 200C, is suddenly quenched in a liquid bath of T = 20C with a convection coefficient of 100 W/m K. FIND: (a) On T-x coordinates, sketch the temperature distributions for
Seoul National - MAE - Heat Trans
PROBLEM 2.46KNOWN: Plane wall, initially at a uniform temperature, is suddenly exposed to convective heating. FIND: (a) Differential equation and initial and boundary conditions which may be used to find the temperature distribution, T(x,t); (b) Sketch T
Seoul National - MAE - Heat Trans
PROBLEM 2.47KNOWN: Plane wall, initially at a uniform temperature Ti, is suddenly exposed to convection with a fluid at T at one surface, while the other surface is exposed to a constant heat flux q . o FIND: (a) Temperature distributions, T(x,t), for in
Seoul National - MAE - Heat Trans
PROBLEM 2.48KNOWN: Plane wall, initially at a uniform temperature To, has one surface (x = L) suddenly exposed to a convection process (T &gt; To,h), while the other surface (x = 0) is maintained at To. Also, wall experiences uniform volumetric heating q su
Seoul National - MAE - Heat Trans
PROBLEM 2.49KNOWN: Plane wall, initially at a uniform temperature To, has one surface (x = L) suddenly exposed to a convection process (T &lt; To, h), while the other surface (x = 0) is maintained at To. Also, wall experiences uniform volumetric heating q s
Seoul National - MAE - Heat Trans
PROBLEM 2.50KNOWN: Size and thermal conductivities of a spherical particle encased by a spherical shell. FIND: (a) Relationship between dT/dr and r for 0 r r1, (b) Relationship between dT/dr and r for r1 r r2, (c) Sketch of T(r) over the range 0 r r2. SC
Seoul National - MAE - Heat Trans
PROBLEM 2.51KNOWN: Temperature distribution in a plane wall of thickness L experiencing uniform volumetric heating q having one surface (x = 0) insulated and the other exposed to a convection process characterized by T and h. Suddenly the volumetric heat
Seoul National - MAE - Heat Trans
PROBLEM 3.2KNOWN: Temperatures and convection coefficients associated with air at the inner and outer surfaces of a rear window. FIND: (a) Inner and outer window surface temperatures, Ts,i and Ts,o, and (b) Ts,i and Ts,o as a function of the outside air
Seoul National - MAE - Heat Trans
PROBLEM 3.3KNOWN: Desired inner surface temperature of rear window with prescribed inside and outside air conditions. FIND: (a) Heater power per unit area required to maintain the desired temperature, and (b) Compute and plot the electrical power require
Seoul National - MAE - Heat Trans
PROBLEM 3.4KNOWN: Curing of a transparent film by radiant heating with substrate and film surface subjected to known thermal conditions. FIND: (a) Thermal circuit for this situation, (b) Radiant heat flux, q (W/m2), to maintain bond at o as a function of
Seoul National - MAE - Heat Trans
PROBLEM 3.7 KNOWN: A layer of fatty tissue with fixed inside temperature can experience different outside convection conditions. FIND: (a) Ratio of heat loss for different convection conditions, (b) Outer surface temperature for different convection condi
Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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PROBLEM 4.1KNOWN: Method of separation of variables for two-dimensional, steady-state conduction. FIND: Show that negative or zero values of 2, the separation constant, result in solutions which cannot satisfy the boundary conditions. SCHEMATIC:ASSUMPTI