Consider a medium in which the heat conduction equation is given in its simplest form as $$ \frac{1}{r^{2}} \frac{\partial}{\partial r}\left(r^{2} \frac{\partial T}{\partial r}\right)=\frac{1}{\alpha} \frac{\partial T}{\partial t} $$ (a) Is heat transfer steady or transient? (b) Is heat transfer one-, two-, or three-dimensional? (c) Is there heat generation in the medium? (d) Is the thermal conductivity of the medium constant or variable?

Answer: The heat transfer process is transient. Explanation: The presence of the term \(\frac{\partial T}{\partial t}\) denotes a time-dependent temperature change, indicating a transient heat transfer process. (b) Is the heat transfer process in the medium one-, two-, or three-dimensional? Answer: The heat transfer process is one-dimensional. Explanation: The given equation contains only the radial derivative term \(\frac{\partial}{\partial r}\), representing one-dimensional heat transfer in the radial direction. (c) Is there heat generation in the medium? Answer: No, there is no heat generation in the medium. Explanation: The given equation does not contain any term representing heat generation (such as Q). (d) Is the thermal conductivity of the medium constant or variable? Answer: The thermal conductivity of the medium is constant. Explanation: The given equation does not explicitly include the thermal conductivity (k). However, the thermal diffusivity term α is related to thermal conductivity. Since the equation is given in its simplest form, we can assume that the thermal conductivity (and thus, thermal diffusivity) is constant.