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Chapter 3: Problem 43

What is thermal contact resistance? How is it related to thermal contact conductance?

Short Answer

Expert verified
Answer: The relationship between thermal contact resistance and thermal contact conductance is inverse. A decrease in thermal contact resistance corresponds to an increase in thermal contact conductance and vice versa. Mathematically, this relationship is represented as: \(R_{tc} = \frac{1}{h_c}\). The lower the contact resistance, the more efficient the thermal contact conductance and the better the heat transfer between the two materials in contact.

Step by step solution

01

Define Thermal Contact Resistance

Thermal contact resistance is the opposition to heat flow through a junction or interface between two materials that are in contact with each other. This resistance occurs due to the presence of air gaps, interstitial materials, or the roughness of the surfaces in contact.
02

Define Thermal Contact Conductance

Thermal contact conductance is a measure of the ability of materials to transfer heat across their interface. It is the reciprocal of thermal contact resistance and is typically represented by \(h_c\), where the units are W/(m²·K) or BTU/(hr·ft²·°F).
03

Relate Thermal Contact Resistance and Thermal Contact Conductance

The thermal contact resistance (\(R_{tc}\)) and thermal contact conductance (\(h_c\)) are inversely related, meaning that a decrease in thermal contact resistance corresponds to an increase in thermal contact conductance and vice versa. Mathematically, this relationship can be represented as: \[R_{tc} = \frac{1}{h_c}\] Expressed in words, the above equation illustrates that the thermal contact resistance is equal to the reciprocal of the thermal contact conductance. The lower the contact resistance, the more efficient the thermal contact conductance and the better the heat transfer between the two materials in contact.

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Most popular questions from this chapter

Consider a very long rectangular fin attached to a flat surface such that the temperature at the end of the fin is essentially that of the surrounding air, i.e. \(20^{\circ} \mathrm{C}\). Its width is \(5.0 \mathrm{~cm}\); thickness is \(1.0 \mathrm{~mm}\); thermal conductivity is \(200 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\); and base temperature is \(40^{\circ} \mathrm{C}\). The heat transfer coefficient is \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Estimate the fin temperature at a distance of \(5.0 \mathrm{~cm}\) from the base and the rate of heat loss from the entire fin.

A \(0.2\)-cm-thick, 10-cm-high, and 15 -cm-long circuit board houses electronic components on one side that dissipate a total of \(15 \mathrm{~W}\) of heat uniformly. The board is impregnated with conducting metal fillings and has an effective thermal conductivity of \(12 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). All the heat generated in the components is conducted across the circuit board and is dissipated from the back side of the board to a medium at \(37^{\circ} \mathrm{C}\), with a heat transfer coefficient of \(45 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). (a) Determine the surface temperatures on the two sides of the circuit board. (b) Now a 0.1-cm-thick, 10-cm-high, and 15 -cm-long aluminum plate \((k=237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) with \(200.2\)-cm-thick, 2-cm-long, and \(15-\mathrm{cm}\)-wide aluminum fins of rectangular profile are attached to the back side of the circuit board with a \(0.03-\mathrm{cm}-\) thick epoxy adhesive \((k=1.8 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\). Determine the new temperatures on the two sides of the circuit board.

A 1-cm-diameter, 30-cm-long fin made of aluminum \((k=237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) is attached to a surface at \(80^{\circ} \mathrm{C}\). The surface is exposed to ambient air at \(22^{\circ} \mathrm{C}\) with a heat transfer coefficient of \(11 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If the fin can be assumed to be very long, the rate of heat transfer from the fin is (a) \(2.2 \mathrm{~W}\) (b) \(3 \mathrm{~W}\) (c) \(3.7 \mathrm{~W}\) (d) \(4 \mathrm{~W}\) (e) \(4.7 \mathrm{~W}\)

In a combined heat and power (CHP) generation process, by-product heat is used for domestic or industrial heating purposes. Hot steam is carried from a CHP generation plant by a tube with diameter of \(127 \mathrm{~mm}\) centered at a square crosssection solid bar made of concrete with thermal conductivity of \(1.7 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). The surface temperature of the tube is constant at \(120^{\circ} \mathrm{C}\), while the square concrete bar is exposed to air with temperature of \(-5^{\circ} \mathrm{C}\) and convection heat transfer coefficient of \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If the temperature difference between the outer surface of the square concrete bar and the ambient air is to be maintained at \(5^{\circ} \mathrm{C}\), determine the width of the square concrete bar and the rate of heat loss per meter length.

Explain how the fins enhance heat transfer from a surface. Also, explain how the addition of fins may actually decrease heat transfer from a surface.
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