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Chapter 3: Problem 13

How does the thermal resistance network associated with a single-layer plane wall differ from the one associated with a five-layer composite wall?

Short Answer

Expert verified
Question: Explain the main difference between the thermal resistance networks of a single-layer wall and a five-layer composite wall. Answer: The main difference between the thermal resistance networks of a single-layer wall and a five-layer composite wall lies in their complexity. A single-layer wall has a simple network consisting of one resistor representing the wall's thermal resistance. In contrast, a five-layer composite wall has a more complex network with five resistors connected in series, each representing the thermal resistance of each layer. This difference in complexity affects the insulating properties and overall heat transfer through the wall.

Step by step solution

01

Understand thermal resistance

Thermal resistance is a property of an insulating material that indicates its resistance to the flow of heat energy. It depends on the material's thermal conductivity and thickness. A lower thermal resistance allows more heat energy to pass through, while a higher resistance results in better insulation.
02

Defining thermal resistance network

A thermal resistance network represents the flow of heat energy through a layered structure, like walls, with each component's thermal resistance represented as a resistor in the network.
03

Determine single-layer wall resistance network

For a single-layer wall, with a surface area A, thickness L, and thermal conductivity k, the wall's thermal resistance (R) can be calculated using the formula: R = \frac{L}{kA} Since there is only one layer, the thermal resistance network will consist of only one resistor representing the wall's thermal resistance.
04

Determine five-layer composite wall resistance network

For a five-layer composite wall, each layer will have its resistance, depending on the thickness, thermal conductivity, and surface area of each layer. In this case, the total thermal resistance (R_total) will be the sum of the resistances of the individual layers: R_{total} = R_1 + R_2 + R_3 + R_4 + R_5 The resistance network for a five-layer composite wall would include five resistors connected in series, each representing the thermal resistance of each layer.
05

Compare single-layer and five-layer resistance networks

The primary difference between the two networks lies in the complexity of the heat transfer process. In a single-layer wall, the thermal resistance network is straightforward, consisting of just one resistor. However, in a five-layer composite wall, the network becomes more complex, consisting of multiple resistors representing the different layers. This difference in complexity can impact the wall's insulating properties and overall heat transfer through the wall.

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Most popular questions from this chapter

Exposure to high concentration of gaseous ammonia can cause lung damage. To prevent gaseous ammonia from leaking out, ammonia is transported in its liquid state through a pipe \(\left(k=25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, D_{i}=2.5 \mathrm{~cm}\right.\), \(D_{o}=4 \mathrm{~cm}\), and \(L=10 \mathrm{~m}\) ). Since liquid ammonia has a normal boiling point of \(-33.3^{\circ} \mathrm{C}\), the pipe needs to be properly insulated to prevent the surrounding heat from causing the ammonia to boil. The pipe is situated in a laboratory, where the average ambient air temperature is \(20^{\circ} \mathrm{C}\). The convection heat transfer coefficients of the liquid hydrogen and the ambient air are \(100 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively. Determine the insulation thickness for the pipe using a material with \(k=\) \(0.75 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) to keep the liquid ammonia flowing at an average temperature of \(-35^{\circ} \mathrm{C}\), while maintaining the insulated pipe outer surface temperature at \(10^{\circ} \mathrm{C}\).

A turbine blade made of a metal alloy \((k=\) \(17 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) has a length of \(5.3 \mathrm{~cm}\), a perimeter of \(11 \mathrm{~cm}\), and a cross-sectional area of \(5.13 \mathrm{~cm}^{2}\). The turbine blade is exposed to hot gas from the combustion chamber at \(973^{\circ} \mathrm{C}\) with a convection heat transfer coefficient of \(538 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The base of the turbine blade maintains a constant temperature of \(450^{\circ} \mathrm{C}\) and the tip is adiabatic. Determine the heat transfer rate to the turbine blade and temperature at the tip.

A plane brick wall \((k=0.7 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) is \(10 \mathrm{~cm}\) thick. The thermal resistance of this wall per unit of wall area is (a) \(0.143 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) (b) \(0.250 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) (c) \(0.327 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) (d) \(0.448 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) (e) \(0.524 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\)

A hot surface at \(80^{\circ} \mathrm{C}\) in air at \(20^{\circ} \mathrm{C}\) is to be cooled by attaching 10 -cm-long and 1 -cm-diameter cylindrical fins. The combined heat transfer coefficient is \(30 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), and heat transfer from the fin tip is negligible. If the fin efficiency is \(0.75\), the rate of heat loss from 100 fins is (a) \(325 \mathrm{~W}\) (b) \(707 \mathrm{~W}\) (c) \(566 \mathrm{~W}\) (d) \(424 \mathrm{~W}\) (e) \(754 \mathrm{~W}\)

Obtain a relation for the fin efficiency for a fin of constant cross-sectional area \(A_{c}\), perimeter \(p\), length \(L\), and thermal conductivity \(k\) exposed to convection to a medium at \(T_{\infty}\) with a heat transfer coefficient \(h\). Assume the fins are sufficiently long so that the temperature of the fin at the tip is nearly \(T_{\infty}\). Take the temperature of the fin at the base to be \(T_{b}\) and neglect heat transfer from the fin tips. Simplify the relation for \((a)\) a circular fin of diameter \(D\) and \((b)\) rectangular fins of thickness \(t\).
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