Question Bank • QB_DFE_EXP_004 MCQ • 1 Mark

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Transient heat transfer in simple geometry

Question Statement:

The lumped capacitance method for transient heat conduction analysis is considered valid with negligible internal temperature gradients when the Biot number ($Bi$) satisfies:

Options:

  • (A) $Bi < 0.10$
  • (B) $Bi > 1.0$
  • (C) $0.10 < Bi < 10.0$
  • (D) $Bi = \infty$

Answer Key:

A

Step-by-Step Solution & Explanation

The lumped capacitance method assumes uniform spatial temperature throughout the body ($T(x,t) \approx T(t)$). This approximation yields errors
lt; 5\%$ only when internal conductive resistance is negligible compared to external convective resistance, represented by $Bi = \frac{h L_c}{k} < 0.10$.
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