Question

The heat conduction equation $\frac{dQ}{dt}=-kA\left(\frac{dT}{dx}\right)$ applied for heat transfer through a plane slab presumes:
1. Steady- state one-dimensional conduction.
2. Constant value of thermal conductivity
3. The bounding surfaces are isothermal.
4. Temperature gradient is constant.
of these statements:-

• A. $1,2,$ and $3$ are correct
• B. $2$ and $4$ are correct
• C. $2,3,$ and $4$ are correct
• D. $1$, $3$ and $4$ are correct

Answer 1

The correct option is D $1$, $3$ and $4$ are correct

The heat conduction equation $(\dot{Q}=KA\frac{dT}{dx})$ is valid only when steady state conduction is achieved i.e No change in temperature with respect to time.

From the formula we can deduce that heat flow is assumed to be one dimensional and uniform temperatures are maintained across the bounding surfaces. Termperature gradient is constant and the temperature profile is linear.
Although, thermal conductivity can be constant or variable.
Thus, option (d) is the correct answer.