The Fourier law states that the rate of heat flow in solid is directly proportional to the cross-section area perpendicular to the flow axis and the negative of temperature gradient over the length of the path of conduction.
Now the law of heat conduction can be expressed mathematically as,
`Q=-\frac{KA.dt}{dx}`
Where,
Q = Rate of heat transfer (Watt)
K = Thermal conductivity (W/m.K)
A = Area of cross-section (`m^{2}`)
dt = Change in temperature along the direction of heat flow
dx = Thickness of the object
In the Fourier heat conduction equation, the negative sign implies that the heat is flowing from higher temperature to lower temperature, therefore it is provided to compensate for the negative nature of the temperature gradient.
Assumptions in Fourier law of heat conduction:
Following are the assumptions for the Fourier law of heat conduction.
1] The thermal conductivity of the material is constant throughout the material.
2] There is no internal heat generation that occurs in the body.
3] The temperature gradient is considered as constant.
4] The heat flow is unidirectional and takes place under steady-state conditions.
5] The surfaces are isothermal.
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