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51 Pages

### sm2_47

Course: MAE Heat Trans, Spring 2010
School: Seoul National
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Word Count: 288

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2.47 KNOWN: PROBLEM 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 initial, steady-state and two intermediate times, (b) Corresponding heat fluxes on q x coordinates, (c) Heat flux at locations x = 0 and x = L as a x function of...

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2.47 KNOWN: PROBLEM 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 initial, steady-state and two intermediate times, (b) Corresponding heat fluxes on q x coordinates, (c) Heat flux at locations x = 0 and x = L as a x function of time, (d) Expression for the steady-state temperature of the heater, T(0,), in terms of q , T , k, h and L. o SCHEMATIC: ASSUMPTIONS: (1) One-dimensional conduction, (2) No heat generation, (3) Constant properties. ANALYSIS: (a) For Ti < T , the temperature distributions are Note the constant gradient at x = 0 since q ( 0 ) = q . x o (b) The heat flux distribution, q ( x,t ) , is determined from knowledge of the temperature gradients, evident x from Part (a), and Fouriers law. (c) On q ( x,t ) t coordinates, the heat fluxes at the boundaries are shown above. x (d) Perform a surface energy balance at x = L and an energy balance on the wall: q cond = q conv = h T ( L, ) T (1), q cond = q . (2) o For the wall, under steady-state conditions, Fouriers law gives q = k o T ( 0, ) T ( L, ) dT =k . dx L q o . 1/h + L/k (3) Combine Eqs. (1), (2), (3) to find: T ( 0, ) = T + 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 2.48KNOWN: 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
Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
Seoul National - MAE - Heat Trans
Seoul National - MAE - Heat Trans
Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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
Seoul National - MAE - Heat Trans
PROBLEM 4.2KNOWN: Two-dimensional rectangular plate subjected to prescribed uniform temperature boundary conditions. FIND: Temperature at the mid-point using the exact solution considering the first five non-zero terms; assess error resulting from using
Seoul National - MAE - Heat Trans
PROBLEM 4.3KNOWN: Temperature distribution in the two-dimensional rectangular plate of Problem 4.2. FIND: Expression for the heat rate per unit thickness from the lower surface (0 x 2, 0) and result based on first five non-zero terms of the infinite seri
Seoul National - MAE - Heat Trans
PROBLEM 4.4 KNOWN: Rectangular plate subjected to prescribed boundary conditions. FIND: Steady-state temperature distribution. SCHEMATIC:ASSUMPTIONS: (1) Steady-state, 2-D conduction, (2) Constant properties. ANALYSIS: The solution follows the method of
Seoul National - MAE - Heat Trans
PROBLEM 4.5KNOWN: Boundary conditions on four sides of a rectangular plate. FIND: Temperature distribution. SCHEMATIC:yq sWT1T10 0 T1 LxASSUMPTIONS: (1) Two-dimensional, steady-state conduction, (2) Constant properties. ANALYSIS: This problem dif
Seoul National - MAE - Heat Trans
PROBLEM 4.14KNOWN: Tube embedded in the center plane of a concrete slab. FIND: The shape factor and heat transfer rate per unit length using the appropriate tabulated relation, SCHEMATIC:ASSUMPTIONS: (1) Two-dimensional conduction, (2) Steady-state cond
Seoul National - MAE - Heat Trans
PROBLEM 4.15 KNOWN: Dimensions and boundary temperatures of a steam pipe embedded in a concrete casing. FIND: Heat loss per unit length. SCHEMATIC:ASSUMPTIONS: (1) Steady-state conditions, (2) Negligible steam side convection resistance, pipe wall resist