Question

Match List I with List II

Choose the correct answer from the options given below:

• A. A-III, B-II, C-I, D-IV
• B. A-II, B-III, C-I, D-IV
• C. A-I, B-II, C-III, D-IV
• D. A-IV, B-II, C-III, D-I

Hint:

Notice the mathematical similarity between the transport laws:
- Conduction (Fourier's): \(Q/A \propto -\text{d}T/\text{d}x\)
- Diffusion (Fick's): \(J \propto -\text{d}C/\text{d}x\)
- Viscosity (Newton's): \(\tau \propto -\text{d}u/\text{d}y\)
All rate equations are proportional to a negative gradient.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Transport phenomena in food engineering involve the transfer of heat, mass, and momentum.
These physical processes are governed by fundamental laws that relate the rate of transfer to their respective driving forces (temperature, concentration, or velocity gradients).

Step 2: Detailed Explanation:
Let us match the scientific laws with their mathematical equations:
- A. Fourier's law: Governs rate of heat conduction through solid materials, where heat transfer rate (\(Q\)) is proportional to the temperature gradient (\(\text{d}t/\text{d}x\)) and thermal conductivity (\(K\)):
\[ Q = -KA \frac{\text{d}t}{\text{d}x} \quad \text{(A-I)} \]
- B. Newton-Rikhman's law: Governs rate of convective heat transfer between a solid surface and a fluid, where heat transfer (\(Q\)) is proportional to the temperature difference (\(t_s - t_f\)) and convective heat transfer coefficient (\(h\)):
\[ Q = hA(t_s - t_f) \quad \text{(B-II)} \]
- C. Fick's law of diffusion: Governs molecular mass transfer of a solute (\(a\)) through a binary mixture, where mass flux (\(m_a/A\)) is proportional to the concentration gradient (\(\text{d}C_a/\text{d}x\)) and diffusion coefficient (\(D\)):
\[ \frac{m_a}{A} = -D \left(\frac{\text{d}C_a}{\text{d}x}\right) \quad \text{(C-III)} \]
- D. Stefan-Boltzmann's law: Governs rate of thermal radiation emitted by a blackbody, where emissive power (\(W_b\)) is proportional to the fourth power of absolute temperature (\(T\)) and Stefan-Boltzmann constant (\(\sigma\)):
\[ W_b = \sigma T^4 \quad \text{(D-IV)} \]

Step 3: Final Answer:
The correct matching sequence is A-I, B-II, C-III, D-IV, which corresponds to option (C).