Q1: In case of heat flow by conduction for a cylindrical body with an internal heat source, the nature of temperature distribution is

ANS:C - parabolic

1. Linear:
   • A linear temperature distribution would imply that the temperature increases or decreases uniformly along the length or radius of the cylindrical body. This type of temperature distribution is not characteristic of heat conduction in a cylindrical body with an internal heat source. Instead, it may occur in simpler cases like steady-state conduction through a plane wall with uniform heat generation.
2. Hyperbolic:
   • A hyperbolic temperature distribution is not typically observed in the context of heat conduction with an internal heat source in a cylindrical body. Hyperbolic temperature distributions are more commonly associated with other physical phenomena, such as certain types of wave propagation or the behavior of certain nonlinear equations.
3. Parabolic:
   • A parabolic temperature distribution is the characteristic temperature profile in the radial direction of a cylindrical body with an internal heat source. This is a consequence of Fourier's law of heat conduction and the governing heat conduction equation for cylindrical coordinates. The temperature varies quadratically with radial distance from the axis of the cylinder, with the highest temperatures occurring at the center and decreasing towards the outer surface.
4. None of these:
   • This option implies that the temperature distribution does not fit any of the provided choices. However, in the context of heat conduction in a cylindrical body with an internal heat source, the most appropriate description of the temperature distribution is parabolic.

In summary, for heat flow by conduction in a cylindrical body with an internal heat source, the nature of temperature distribution is parabolic. This reflects the characteristic behavior of heat conduction in such systems, where the temperature profile varies quadratically with radial distance from the center of the cylinder.