ANS:C - material is anisotropic.

Fourier's law of heat conduction states that the rate of heat transfer through a material is directly proportional to the negative temperature gradient and the cross-sectional area, and inversely proportional to the material's thermal conductivity. The statement "Steady state one-dimensional heat flow by conduction as given by Fourier's law does not assume that the material is anisotropic" is incorrect. Anisotropic materials have different thermal conductivities in different directions. Fourier's law assumes that the material is isotropic, meaning its thermal conductivity is the same in all directions. Therefore, the assumption of isotropy is implicit in Fourier's law. If the material were anisotropic, the relationship between the temperature gradient and the heat flux would be more complex and would require additional considerations beyond Fourier's law. The other statements listed are not assumptions of Fourier's law:

• "There is no internal heat generation": Fourier's law does not explicitly assume or exclude internal heat generation. It simply describes the relationship between the temperature gradient and the heat flux in a material.
• "Boundary surfaces are isothermal": While the temperature gradient is typically applied across a material's thickness, Fourier's law does not specifically require or assume isothermal boundary surfaces.
• "Constant temperature gradient exists": Fourier's law describes the relationship between the temperature gradient and the heat flux, but it does not assume that the temperature gradient is constant. It applies to any situation where there is a temperature gradient, whether it is constant or variable.