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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Question
Chapter 3, Problem 3.7P
To determine
The value of heat gain per unit surface area.
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1. Find the heat transfer per unit area through the composite wall in Figure below. Assume
one-dimensional heat flow.
k₁= 150 W/m-°C
kg = 30
kc=50
A = 0.1 m²
kD=70
B
AB=AD
D
7.5 cm
T=370°C
2.5 cm
H
4
5.0 cm
T = 66°C
Q1/ Consider a large plane wall of thickness L=0.03 m. The wall surface at x =0
is insulated, while the surface at x =L is maintained at a temperature of 30°C. The
thermal conductivity of the wall is k=25 W/m °C, and heat is generated in the
wall at a rate of g = 9oe0.5x/L W/m³ Where g, = 8 x 10 W /m². Assuming
steady one-dimensional heat transfer, (a) express the differential equation and the
boundary conditions for heat conduction through the wall, (b) obtain a relation for
the variation of temperature in the wall by solving the differential equation, and (c)
determine the temperature of the insulated surface of the wall.
Q1.
Consider a plane wall (thermal conductivity, k = 0.8 W/mK, and thickness, fb1 = 100 mm) of a
house as shown in Fig. Q1(a). The outer surface of the wall is exposed to solar radiation and has
an absorptivity of a = 0.5 for solar energy, or=600 W/m². The temperature of the interior of
the house is maintained at T1 = 25 °C, while the ambient air temperature outside remains at
T2 = 5 °C. The sky, the ground and the surfaces of the surrounding structures at this location
can be modelled as a surface at an effective temperature of Tsky = 255 K for radiation exchange
on the outer surface. The radiation exchange inside the house is negligible. The convection heat
transfer coefficients on the inner and the outer surfaces of the wall are h₁ = 5 W/m²-K and
/1₂ = 20 W/m².K, respectively. The emissivity of the outer surface is = 0.9.
T1 = 25 °C
Ţ₁
Too1 = 25 °C
T₁
k
100 mm
Fig. Q1(a)
Assuming the heat transfer through the wall to be steady and one-dimensional:
(a) Solve the steady 1D heat…
Chapter 3 Solutions
Introduction to Heat Transfer
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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 Xarrow_forwardQ2/ The wall of a refrigerator is constructed of fiberglass insulation (k=0.035 W/ m. C) sandwiched between two layers of 1-mm-thick sheet metal (k-15.1 W/m.°C). The refrigerated space is maintained at 3°C, and the average heat transfer coefficients at the inner and outer surfaces of the wall are 4 W/m2.C and 9 W/m2.°C, respectively. The kitchen temperature averages 25°C. It is observed that condensation occurs on the outer surfaces of the refrigerator when the temperature of the outer surface drops to 20°C. Determine the minimum thickness of fiberglass insulation that needs to be used in the wall in order to avoid condensation on the outer surfaces. Sheet metal Kitchen Refrigerated air space 3°C 25°C Insulation 10°C 1 mm mmarrow_forwardQ1: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m °C, and surface area A= 20 m2. The left side of the wall at x= 0 is subjected of T1 = 80°C. while the right side losses heated by convection to the surrounding air at T-15 °C with a heat transfer coefficient of h=24 W/m2 C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall Ans : (c) 6030 Warrow_forward
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