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 3.14P
To determine
The daily heat loss through the wall.
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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.
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Consider a large plane wall of thickness L=0.3 m, thermal conductivity k = 2.5 W/m.K,
and surface area A = 12 m². The left side of the wall at x=0 is subjected to a net heat
flux of ɖo = 700 W/m² while the temperature at that surface is measured to be T₁ =
80°C. Assuming constant thermal conductivity and no heat generation in the wall, (a)
express the differential equation and the boundary equations for steady one-
dimensional heat conduction through the wall, (b) obtain a relation for the variation of
the temperature in the wall by solving the differential equation, and (c) evaluate the
temperature of the right surface of the wall at x=L.
Ti
до
L
X
You are asked to estimate the maximum human body temperature if the metabolic
heat produced in your body could escape only by tissue conduction and later on the surface by
convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in
radius. Further, simplify the heat transfer process inside the human body as a 1-D situation when
the temperature only depends on the radial coordinater from the centerline. The governing
dT
+q""=0
dr
equation is written as
1 d
k-
r dr
r = 0,
dT
dr
=0
dT
r=ro -k -=h(T-T)
dr
(k-0.5 W/m°C), ro is the radius of the cylinder (0.15 m), h is the convection coefficient at the
skin surface (15 W/m² °C), Tair is the air temperature (30°C). q" is the average volumetric heat
generation rate in the body (W/m³) and is defined as heat generated per unit volume per second.
The 1-D (radial) temperature distribution can be derived as:
T(r) =
q"¹'r² qr qr.
+
4k 2h
+
4k
+T
, where k is thermal conductivity of tissue
air
(A) q" can be calculated…
Chapter 3 Solutions
Introduction to Heat Transfer
Ch. 3 - Consider the plane wall of Figure 3.1, separating...Ch. 3 - A new building to be located in a cold climate is...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - A dormitory at a large university, built 50 years...Ch. 3 - In a manufacturing process, a transparent film is...Ch. 3 - Prob. 3.7PCh. 3 - A t=10-mm-thick horizontal layer of water has a...Ch. 3 - Prob. 3.9PCh. 3 - The wind chill, which is experienced on a cold,...
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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