Topic: Heat Transfer
The temperature profile for heat conduction through a wall of constant thermal conductivity in presence of a heat source is
- A. Linear
- B. Parabolic
- C. Logarithmic
- D. Hyperbolic
Answer: B. Parabolic
Explanation: The 1D steady-state heat conduction equation with uniform heat generation is $\frac{d^2T}{dx^2} + \frac{q_g}{k} = 0$. Integrating this twice with respect to $x$ yields a second-degree polynomial equation ($T(x) = C_1 x^2 + C_2 x + C_3$), which represents a parabolic temperature profile.