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ISRO Scientist ME 2011 Paper

- \(kA\frac{{dT}}{{dx}}\)
- \(kA\frac{{d{T^2}}}{{d{x^2}}}\)
- \(k\frac{{dx}}{{dT}}\)
- \(kA\frac{{dx}}{{dT}}\)

Option 1 : \(kA\frac{{dT}}{{dx}}\)

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**Concept:**

According to Fourier’s Law of heat conduction, the rate of heat flow, Q through a homogeneous solid is directly proportional to the area A, of the section at the right angles to the direction of the heat flow, and to the temperature difference dT along the path of heat flow.

\(Q = \frac{{kAdT}}{{dx}}\)

**Assumptions of Fourier equation:**

- Steady-state heat conduction
- One directional heat flow
- Bounding surfaces are isothermal in character that is constant and uniform temperatures are maintained at the two faces
- Isotropic and homogeneous material and thermal conductivity ‘k’ is constant
- Constant temperature gradient and linear temperature profile
- No internal heat generation

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