Thermal conductivity k is a measure of the ability of a material to conduct heat. For conduction heat transfer in the x-direction through a surface normal to the x-direction, Fourier’s law of heat conduction is expressed as: Q=-kA.dT/dx where ?̇ is the rate of heat transfer and A is the area normal to the direction of heat transfer. Determine the primary dimensions of thermal conductivity (k). Look up a value of k and verify that its SI units are consistent with your result. Write a set of primary SI units for k. The diagram illustrates the flow of heat through a rectangular material with the following labeled components:- **A**: Represents the cross-sectional area through which heat flows.- **k**: Denotes the thermal conductivity of the material, a measure of its ability to conduct heat.- **x**: Indicates the thickness or distance between the two sides where the temperature difference is applied.- **T₁** and **T₂**: Represent the temperatures on either side of the material, with T₁ being higher than T₂, causing heat to flow from left to right.- **Q̇**: Symbolizes the rate of heat transfer through the material, often measured in watts.The heat conduction can be described using the formula:\[ Q̇ = \frac{k \times A \times (T₁ - T₂)}{x} \]This formula is derived from Fourier's law of heat conduction, indicating that the heat transfer rate is proportional to the thermal conductivity, the cross-sectional area, and the temperature difference, and inversely proportional to the thickness.

Given Data: Fourier’s law of heat conduction is expressed as: Q=-kA.dTdx Primary dimensions:…

Answered: Thermal conductivity k is a measure of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Thermal conductivity k is a measure of the ability of a material to conduct heat. For conduction heat transfer in the x-direction through a surface normal to the x-direction, Fourier’s law of heat conduction is expressed as: Q=-kA.dT/dx

where ?̇ is the rate of heat transfer and A is the area normal to the direction of heat transfer. Determine the primary dimensions of thermal conductivity (k). Look up a value of k and verify that its SI units are consistent with your result. Write a set of primary SI units for k.

The diagram illustrates the flow of heat through a rectangular material with the following labeled components:

- **A**: Represents the cross-sectional area through which heat flows.
- **k**: Denotes the thermal conductivity of the material, a measure of its ability to conduct heat.
- **x**: Indicates the thickness or distance between the two sides where the temperature difference is applied.
- **T₁** and **T₂**: Represent the temperatures on either side of the material, with T₁ being higher than T₂, causing heat to flow from left to right.
- **Q̇**: Symbolizes the rate of heat transfer through the material, often measured in watts.

The heat conduction can be described using the formula:

\[ Q̇ = \frac{k \times A \times (T₁ - T₂)}{x} \]

This formula is derived from Fourier's law of heat conduction, indicating that the heat transfer rate is proportional to the thermal conductivity, the cross-sectional area, and the temperature difference, and inversely proportional to the thickness.

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