ANS:C - both (a) and (b)

Fourier's law of heat conduction applies to non-isothermal surfaces. Explanation:

1. Fourier's Law: Fourier's law describes the heat transfer through a solid medium due to a temperature gradient. It states that the rate of heat transfer (Q) through a material is directly proportional to the temperature gradient (∇T) and the cross-sectional area (A) perpendicular to the direction of heat flow, and inversely proportional to the distance (L) over which the heat is transferred. Mathematically, it can be expressed as: Q=−kAdxdT​ where:
   • Q is the rate of heat transfer,
   • k is the thermal conductivity of the material,
   • A is the cross-sectional area,
   • dxdT​ is the temperature gradient, and
   • L is the distance over which heat is transferred.
2. Non-Isothermal Surfaces: Fourier's law applies to surfaces where there is a temperature gradient, i.e., non-isothermal surfaces. In such cases, heat transfer occurs from regions of higher temperature to regions of lower temperature.
3. Isothermal Surfaces: Isothermal surfaces, by definition, have a constant temperature throughout the surface. Since there is no temperature gradient on isothermal surfaces, heat transfer does not occur through the surface according to Fourier's law.
4. Conclusion: Therefore, Fourier's law of heat conduction applies to non-isothermal surfaces, where there is a temperature gradient across the material, allowing heat to flow from regions of higher temperature to regions of lower temperature.