Question

According to which one of the following Laws, the rate of heat transfer by conduction through a substance is directly proportional to the temperature gradient, and to the area normal to the direction of heat flow?

• A. Newton's Law
• B. Fourier's Law
• C. Boyle's Law
• D. Charle's Law

Hint:

Fourier's Law: $q = -kA \frac{dT}{dx}$ for conduction; Newton's Law of Cooling: $q = hA(T_s - T_\infty)$ for convection.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Conductive heat transfer in continuous isotropic media is governed by fundamental phenomenological transport laws.

Step 2: Key Formula or Approach:
Fourier's Law of Heat Conduction is mathematically expressed as:
\[q = -k A \frac{dT}{dx}\] where $q$ is conductive heat transfer rate ($\text{W}$), $k$ is thermal conductivity ($\text{W}/(\text{m}\cdot\text{K})$), $A$ is surface area normal to heat flow ($\text{m}^2$), and $\frac{dT}{dx}$ is the temperature gradient ($\text{K/m}$).

Step 3: Detailed Explanation:
Newton's law describes convective cooling, while Boyle's and Charles' laws describe ideal gas behavior.

Step 4: Final Answer:
Hence, the stated law is Fourier's Law.