Question Bank • QB_PARAMETRIC_DFE_CND_006MSQ • 2 Marks
Section 7: Dairy and Food Engineering
Steady-State Conduction & Shape Factors
Subtopic: Critical radius of insulation concept
Question Statement:
Which of the following statements regarding the critical radius of insulation ($r_c$) is/are TRUE? (Variation QB_PARAMETRIC_DFE_CND_006)
Options:
(A) For a circular cylinder, $r_c = k / h$, whereas for a sphere, $r_c = 2k / h$
(B) Adding insulation to a bare cylinder having outer radius $r_o < r_c$ initially increases the rate of heat loss until $r = r_c$
(C) For a plane flat wall, the concept of critical radius does not exist because surface area remains constant regardless of thickness
(D) Adding any insulation to a steam pipe always strictly decreases heat loss regardless of pipe diameter
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
1. Cylindrical $r_c = k/h$; spherical $r_c = 2k/h$ (A is true).
2. For $r_o < r_c$, the decrease in outer convective resistance ($1/hA$) outweighs added conductive resistance, peaking heat loss at $r = r_c$ (B is true).
3. In plane walls, area is invariant with thickness, so adding insulation always monotonically increases thermal resistance (C is true).
4. When $r_o < r_c$, insulation increases heat transfer; statement D is false.