GATE AG 2019 • Q64 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Steady state heat transfer in conduction, convection and radiation

Question Statement:

Heat and Mass Transfer: Steady state heat transfer in conduction, convection and radiation; transient heat transfer in simple geometry; working principles of heat exchangers; diffusive and convective mass transfer; simultaneous heat and mass transfer in agricultural processing operations; material and energy balances in food processing systems; water activity, sorption and desorption isotherms. The steady-state mass transfer coefficient (kg) based on water vapour pressure differential (VPD), operating across stagnant, non-diffusing air, was estimated to be 0.05 g mole s⁻¹ m⁻² kPa⁻¹. If VPD varies from 12 kPa to 7 kPa over a distance of 2 mm, the mass transfer coefficient (ky') based on equimolar counter-diffusion (g mole s⁻¹ m⁻² (mole fraction)⁻¹) (rounded to 1 decimal) is ______.

Official Answer Key:

4.5 to 4.7

Step-by-Step Solution & Explanation

For diffusion through a stagnant (non-diffusing) film, the coefficient kg (pressure-difference basis) is related to the equimolar counter-diffusion coefficient ky' (mole-fraction basis) through the log-mean partial pressure of the INERT (non-diffusing) gas component, p_BM, because the stagnant-film case includes a 'bulk flow' correction factor that the equimolar case does not: ky' = kg × p_BM Total pressure, P = 101.325 kPa (1 atm). Partial pressures of water vapour: p_A1 = 12 kPa, p_A2 = 7 kPa. Partial pressures of the inert (dry-air) component: p_B1 = P − p_A1 = 101.325−12 = 89.325 kPa; p_B2 = P − p_A2 = 101.325−7 = 94.325 kPa. p_BM = (p_B2 − p_B1)/ln(p_B2/p_B1) = (94.325−89.325)/ln(94.325/89.325) = 5.0/ln(1.0560) = 5.0/0.05445 = 91.83 kPa. ky' = 0.05 × 91.83 = 4.59 ≈ 4.6 g mol s⁻¹ m⁻² (mole fraction)⁻¹. Answer: within 4.5–4.7. (The 2 mm diffusion-path distance is extraneous data not needed for this particular unit-conversion step; it would be used if kg itself needed to be derived from Fick's law rather than given directly.)

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