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Fourier law
Fourier Law of Heat Conduction: The Fourier law of heat conduction describes the distribution of heat flux (the rate at which heat is transferred from one p...
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Fourier Law of Heat Conduction: The Fourier law of heat conduction describes the distribution of heat flux (the rate at which heat is transferred from one p...
Fourier Law of Heat Conduction:
The Fourier law of heat conduction describes the distribution of heat flux (the rate at which heat is transferred from one point to another) in a material as a function of time and space. It states that the heat flux is directly proportional to the temperature gradient (the difference in temperature between two points) and inversely proportional to the distance between the points.
Formula:
q = -k(∂T/∂x)
where:
q is the heat flux in W/m²
k is the thermal conductivity in W/(m·K)
∂T/∂x is the temperature gradient in K/m
Explanation:
q represents the rate of heat transfer at a given point in the material.
k is a material property that determines how effectively heat is conducted. Higher values of k indicate better conduction.
∂T/∂x represents the rate of change of temperature with respect to position. A higher temperature gradient leads to a higher heat flux.
Examples:
In a solid at constant temperature, the heat flux is zero if there is no temperature gradient.
In a hot metal, the heat flux is higher near the surface than it is near the center.
In a fluid, the heat flux is proportional to the velocity gradient (the difference in velocity between two points).
Significance:
The Fourier law of heat conduction is a fundamental equation in heat transfer theory. It provides a quantitative relationship between the three key parameters that determine the heat flux in a material. It is used to analyze and predict heat flow in various engineering applications, such as heat exchangers, ovens, and pipes