What does the thermal resistance of a medium represent?

Short Answer

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Answer: The thermal resistance of a medium represents its ability to resist the flow of heat through it. It is an essential parameter in understanding and analyzing heat transfer through materials and systems, primarily in construction, electronics, and heat exchange applications. A higher thermal resistance indicates that the medium offers more resistance to heat flow, whereas a lower thermal resistance implies that heat can flow through it more quickly.

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01

Definition of Thermal Resistance

The thermal resistance of a medium represents its ability to resist the flow of heat through it. It is a crucial factor in analyzing and understanding heat transfer through materials or systems. A higher thermal resistance indicates that the medium offers more resistance to heat flow, whereas a lower thermal resistance implies that heat can flow through it more quickly.
02

Importance of Thermal Resistance in Heat Transfer

Thermal resistance is essential in several practical applications involving heat transfer through materials and systems. Some of the primary areas where it plays a significant role include: 1. Construction and building design for temperature regulation and energy efficiency. 2. Thermal insulation in electronic devices to prevent overheating. 3. Design of heat exchangers and heat sinks for efficient heat dissipation.
03

Units and Calculation of Thermal Resistance

The unit of thermal resistance is kelvin per watt (K/W) or degree Celsius per watt (°C/W). It is calculated as: Thermal Resistance (R) = Temperature difference (∆T) / Heat transfer rate (Q) Mathematically, the thermal resistance of a homogeneous material can be calculated as follows: R = \frac{L}{kA} Where: R = Thermal Resistance (K/W or °C/W) L = Thickness or length of the medium through which heat is being transferred (m) k = Thermal conductivity of the medium (W/m·K) A = Cross-sectional area of the medium that is perpendicular to the direction of heat flow (m²)
04

Factors Influencing Thermal Resistance

Several factors can affect the thermal resistance of a medium, such as: 1. Material and its composition: Different materials have varying thermal conductivities, which directly influence their thermal resistance. 2. Thickness or length of the medium: A thicker or longer medium will offer more resistance to heat transfer compared to a thinner or shorter one. 3. Cross-sectional area: The larger the area, the lower the thermal resistance, as heat can flow through a more significant portion of the medium. In summary, the thermal resistance of a medium represents how effectively it can resist heat flow. It is an essential parameter in understanding and analyzing heat transfer through materials and systems, mainly in construction, electronics, and heat exchange applications.

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Most popular questions from this chapter

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 bery long, its efficiency is (a) \(0.60\) (b) \(0.67\) (c) \(0.72\) (d) \(0.77\) (e) \(0.88\)

Consider a pipe at a constant temperature whose radius is greater than the critical radius of insulation. Someone claims that the rate of heat loss from the pipe has increased when some insulation is added to the pipe. Is this claim valid?

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 \(t\).

In the United States, building insulation is specified by the \(R\)-value (thermal resistance in \(\mathrm{h} \cdot \mathrm{ft}^{2} \cdot{ }^{\circ} \mathrm{F} /\) Btu units). A homeowner decides to save on the cost of heating the home by adding additional insulation in the attic. If the total \(R\)-value is increased from 15 to 25 , the homeowner can expect the heat loss through the ceiling to be reduced by (a) \(25 \%\) (b) \(40 \%\) (c) \(50 \%\) (d) \(60 \%\) (e) \(75 \%\)

The \(700 \mathrm{~m}^{2}\) ceiling of a building has a thermal resistance of \(0.52 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\). The rate at which heat is lost through this ceiling on a cold winter day when the ambient temperature is \(-10^{\circ} \mathrm{C}\) and the interior is at \(20^{\circ} \mathrm{C}\) is (a) \(23.1 \mathrm{~kW} \quad\) (b) \(40.4 \mathrm{~kW}\) (c) \(55.6 \mathrm{~kW}\) (d) \(68.1 \mathrm{~kW}\) (e) \(88.6 \mathrm{~kW}\)

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