Subtopic: Fourier number definition and Heisler charts
Question Statement:
Which of the following statements regarding transient heat conduction in foods is/are TRUE?
Options:
(A) Fourier number is dimensionless time defined as $Fo = \frac{\alpha t}{L_c^2}$, where $\alpha = \frac{k}{\rho c_p}$
(B) Heisler charts are analytical graphical solutions used when $Bi > 0.1$ and $Fo > 0.2$
(C) In lumped capacity analysis, the thermal time constant is $\tau = \frac{\rho V c_p}{h A}$
(D) When $Bi \to \infty$, the surface of the body immediately reaches the ambient fluid temperature
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
All four statements are foundational principles of transient food engineering:
1. $Fo = \alpha t / L_c^2$ scales diffusion time (A).
2. Heisler charts neglect higher Fourier terms when $Fo > 0.2$ (B).
3. Temperature decay follows $\exp(-t / \tau)$ with time constant $\tau = \frac{\rho V c_p}{h A}$ (C).
4. $Bi \to \infty$ represents negligible surface convective resistance ($h \to \infty$), pinning surface to fluid temperature instantaneously (D).
All options A, B, C, D are correct.