Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 3, Problem 3.97P
The cross section of a long cylindrical fuel element in a nuclear reactor is shown. Energy generation occurs uniformly in the thorium fuel rod, which is of diameter
- It is proposed that, under steady-state conditions, the system operates with a generation rate of
- Explore the effect of variations in
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A plane wall of thickness 2L = 30 mm and thermal conductivity k = 7 W/m-K experiences uniform volumetric heat generation at a
rate q, while convection heat transfer occurs at both of its surfaces (x = − L, + L), each of which is exposed to a fluid of
temperature T = 20°C. Under steady-state conditions, the temperature distribution in the wall is of the form
T(x) = a + bx + cx² where a = 82.0°C, b = -210°C/m, c = -2x 10°C/m², and x is in meters. The origin of the x-coordinate is at
the midplane of the wall.
(a) What is the volumetric rate à of heat generation in the wall?
(b) Determine the surface heat fluxes, q" (L)and q ( + L).
(c) What are the convection coefficients for the surfaces at x = - Land x = + L?
The volumetric rate of heat generation in the wall, in W/m³:
q = i
W/m³
The surface heat flux, in W/m²:
qx ( - L) = i
The surface heat flux, in W/m²:
q (+ L) = i
W/m²
W/m²
The convection coefficients for the surface at x = - L, in W/m²-K:
h(- L) = i
W/m².K
The convection…
In a cylindrical fuel element for a gas-cooled nuclear reactor, the heat generation rate within the fuel element due to fission can be approximated by the relation: g(r) = g_0 [1 - (r/b)^2] W/m^3 where b is the radius of the fuel element and g_0 is constant. The boundary surface at r = b is maintained at a uniform temperature T_0. Assuming one-dimensional, steady-state heat flow, develop a relation for the temperature drop from the centerline to the surface of the fuel element. For radius b = 2 cm, the thermal conductivity k = 10 W/m middot K and g_0 = 2 times 10^7 W/m^3, calculate the temperature drop from the centerline to the surface.
How long should it take to boil an egg? Model the egg as a sphere with radius of 2.3 cm that has properties similar to water with a density of = 1000 kg/m3 and thermal conductivity of k = 0.606 Watts/(mC) and specific heat of c = 4182 J/(kg C). Suppose that an egg is fully cooked when the temperature at the center reaches 70 C. Initially the egg is taken out of the fridge at 4 C and placed in the boiling water at 100 C. Since the egg shell is very thin assume that it quickly reaches a temperature of 100 C. The protein in the egg effectively immobilizes the water so the heat conduction is purely conduction (no convection). Plot the temperature of the egg over time and use the data tooltip in MATLAB to make your conclusion on the time it takes to cook the egg in minutes.
Chapter 3 Solutions
Fundamentals of Heat and Mass Transfer
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