Question

Fourier's law is applicable for

• A. Water flow in soil
• B. Airflow in soil
• C. Nutrient flow in soil
• D. Heat flow in soil

Hint:

To remember transport laws in soil:
- Water flow = Darcy's Law
- Solute/Gas diffusion = Fick's Law
- Heat flow = Fourier's Law
- Water flow in pipes = Poiseuille's Law

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Transport processes in soil are governed by physical laws that describe flux as a linear function of a driving force (gradient).
These transport equations share a common mathematical form:
\[ \text{Flux} = -\text{Conductivity} \times \text{Gradient} \] Detailed Explanation:
Let us identify the laws governing different transport processes in soil:
- Water flow in soil (A): Governed by Darcy's Law, where water flux is proportional to the hydraulic gradient.
- Airflow Nutrient diffusion in soil (B & C): Governed by Fick's Law of Diffusion, where solute or gas flux is proportional to the concentration gradient.
- Heat flow in soil (D): Governed by Fourier's Law of Heat Conduction. This law states that the rate of heat transfer through a material is proportional to the negative gradient of temperature:
\[ q_h = -\lambda \frac{dT}{dx} \] where \( q_h \) is the heat flux, \( \lambda \) is the thermal conductivity of the soil, and \( \frac{dT}{dx} \) is the temperature gradient.

Step 2: Final Answer:
Fourier's law governs heat flow in soil.