Composite walls with no heat generation may also be characterized by series-parallelconfigurations, as shown in the following figure. Although the heat flow is nowmultidimensional, it is often reasonable to assume one-dimensional conditions. Subject to thisassumption, two different thermal circuits may be used. For case (a), it is presumed thatsurfaces normal to the x-direction are isothermal, while for case (b), it is assumed that surfacesparallel to the x-direction are adiabatic. Different results are obtained for the total thermalresistance for conduction. Here important geometrical information and thermal conductivityinformation are as follows.Length: LE-LF-LG=LH=L=1 mArea perpendicular to x-axis: A for sections E and H, 4/2 for sections F and G where A=1 m²Thermal conductivity: ke-ke-ku-k and ke-a-k where k-50 W/(mK) and a-10.1-1) What is the total thermal resistance between T₁ and T2 for case (a), Rtota. The answershould be given in the unit of K/W.1-2)What is the total thermal resistance between Ti and 72 for case (b), Rtot,b. The answershould be given in the unit of K/W.1-3)If a is infinitely large, what is the ratio between the total thermal resistances for cases(a) and (b), Rtot,a/Rtot,b?1455-4 = 46°Area, AT₁-Lake42OTI LECA/25wwGFL(2)kg (4/2)(a)k(A/2)4(1/2)H44444k(A/2)44(472)/2

Let us denote LKA by the symbol R R = LkA= 150=0.02

1-1) What is the total thermal resistance between T₁ and 72 for case (a), Ruota. The answer should be given in the unit of K/W. 1-2) What is the total thermal resistance between Ti and 72 for case (b), Rtot,b. The answer should be given in the unit of K/W.

1-1) What is the total thermal resistance between T₁ and 72 for case (a), Ruota. The answer should be given in the unit of K/W. 1-2) What is the total thermal resistance between Ti and 72 for case (b), Rtot,b. The answer should be given in the unit of K/W.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.3P

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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

Composite walls with no heat generation may also be characterized by series-parallel
configurations, as shown in the following figure. Although the heat flow is now
multidimensional, it is often reasonable to assume one-dimensional conditions. Subject to this
assumption, two different thermal circuits may be used. For case (a), it is presumed that
surfaces normal to the x-direction are isothermal, while for case (b), it is assumed that surfaces
parallel to the x-direction are adiabatic. Different results are obtained for the total thermal
resistance for conduction. Here important geometrical information and thermal conductivity
information are as follows.
Length: LE-LF-LG=LH=L=1 m
Area perpendicular to x-axis: A for sections E and H, 4/2 for sections F and G where A=1 m²
Thermal conductivity: ke-ke-ku-k and ke-a-k where k-50 W/(mK) and a-10.
1-1) What is the total thermal resistance between T₁ and T2 for case (a), Rtota. The answer
should be given in the unit of K/W.
1-2)
What is the total thermal resistance between Ti and 72 for case (b), Rtot,b. The answer
should be given in the unit of K/W.
1-3)
If a is infinitely large, what is the ratio between the total thermal resistances for cases
(a) and (b), Rtot,a/Rtot,b?
1455
-4 = 46°
Area, A
T₁-
La
ke
42
OTI LE
CA/25
ww
G
F
L
(2)
kg (4/2)
(a)
k(A/2)
4
(1/2)
H
444
44
k(A/2)
44
(472)
/2

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