ANS:D - linear

The temperature profile in steady-state heat transfer depends on the boundary conditions and geometry of the system. Let's consider common scenarios:

1. Constant Heat Flux Boundary Condition: In this case, the temperature profile is typically linear. This means that the temperature gradient (change in temperature with respect to distance) within the material is constant, resulting in a linear temperature distribution.
2. Constant Temperature Boundary Condition: When the boundaries of the system are maintained at constant temperatures, the temperature profile within the material typically forms a parabolic shape. This is often seen in systems where heat is transferred through conduction, such as in a long rod or plate.
3. Radial Symmetry: In some systems with radial symmetry, such as heat transfer in a cylindrical object like a pipe or a sphere, the temperature profile can be asymptotic, meaning it approaches a certain value as distance from the center increases. This asymptotic behavior is due to the heat spreading outwards from the center.
4. Complex Geometries: For more complex geometries or boundary conditions, such as those involving multiple materials, shapes, or non-uniform boundary conditions, the temperature profile can take on various forms including hyperbolic or other shapes.