Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 3, Problem 3.95P
To determine
The temperature distribution
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Conduction
1. A thermodynamic analysis of a proposed Brayton cycle gas turbine yields P=
5 MW of net power production. The compressor, at an average temperature
of T. = 400°C, is driven by the turbine at an average temperature of T₁ =
1000°C by way of an L = 1m-long, d= 70mm - diameter shaft of thermal
conductivity k = 40 W/m K.
Compressor
min
T
Combustion
chamber
Shaft
L
Turbine
Th
out
(a) Compare the steady-state conduction rate through the shaft connecting the hot
turbine to the warm compressor to the net power predicted by the thermodynamics-
based analysis.
(b) A research team proposes to scale down the gas turbine of part (a), keeping all
dimensions in the same proportions. The team assumes that the same hot and cold
temperatures exist as in part (a) and that the net power output of the gas turbine is
proportional to the overall volume of the device. Plot the ratio of the conduction through
the shaft to the net power output of the turbine over the range 0.005 m s Ls 1 m. Is a…
Example 4.13. A thermocouple junction is in the form of 8 mm diameter sphere. Properties of
material are:
40 W/M2°C.
= 8000 kg/m³; k = 40 W/m°C and h
This junction is initially at 40°C and inserted in a stream of hot air at 300°C. Find:
%3D
420 J/kg°C; p
C =
(i) Time constant of the thermocouple;
(ii) The thermocouple is taken out from the hot air after 10 seconds and kept in still air at
30°C. Assuming the heat transfer coefficient in air 10 W/M²°C, find the temperature attained
by the junction 20 seconds after removing from hot air.
(P.U.)
5.6 Steel balls 12 mm in diameter are annealed by heating to
1150 K and then slowly cooling to 400 K in an air envi-
ronment for which T325 K and h = 20 W/m².K.
Assuming the properties of the steel to be k = 40 W/mK,
p= 7800 kg/m³, and c = 600 J/kg K, estimate the time
required for the cooling process.
Chapter 3 Solutions
Introduction to Heat Transfer
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Ch. 3 - Prob. 3.11PCh. 3 - A thermopane window consists of two pieces of...Ch. 3 - A house has a composite wall of wood, fiberglass...Ch. 3 - Prob. 3.14PCh. 3 - Prob. 3.15PCh. 3 - Work Problem 3.15 assuming surfaces parallel to...Ch. 3 - Consider the oven of Problem 1.54. 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