A liquid film of thickness δ has a component A diffusing through it with first-order reaction. The Thiele modulus is defined as:
Answer: A
For first-order reaction in a film, the Thiele modulus φ = δ√(k₁/D_AB), which compares reaction rate to diffusion rate. It determines whether the process is reaction-controlled or diffusion-controlled.
Q.42Medium
In the penetration theory of mass transfer, the mass transfer coefficient varies with contact time (t) as:
Answer: C
According to penetration theory, k_c = 2√(D_AB/(πt)), showing k_c is inversely proportional to √t. Shorter contact times give higher coefficients.
Q.43Medium
For drying of a wet solid in the constant rate period, the controlling mechanism for mass transfer is:
Answer: B
During constant rate drying period, surface moisture is continuously replenished from inside, so the external convective mass transfer from wet surface to air is the limiting step.
Q.44Medium
In a wetted wall column for gas absorption, if the gas film resistance is negligible (R_g ≈ 0), the overall mass transfer coefficient K_g is primarily controlled by:
Answer: B
When gas-film resistance is negligible, K_g ≈ k_l/H where H is Henry's constant. The liquid-phase resistance becomes dominant in overall mass transfer.
Q.45Medium
For the absorption of multiple components from a gas stream into an organic solvent, the selectivity depends on:
Answer: B
Selectivity = (k_l,A/k_l,B)·(H_B/H_A). While diffusivity ratio affects k_l, the Henry's constant ratio H_B/H_A determines preferential absorption, making partition coefficients critical.
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Q.46Medium
In reverse osmosis (RO), the membrane flux equation (Darcy's law for membranes) predicts that flux is:
Answer: D
RO flux J = (k_m/μ)·ΔP/Δx, where flux is directly proportional to pressure difference and inversely to membrane thickness, following modified Darcy's equation.
Q.47Medium
What is the Biot number (Bi) used to determine in transient heat conduction?
Answer: A
Biot number = hL_c/k determines whether lumped capacitance method is applicable. Bi << 0.1 indicates uniform internal temperature.
Q.48Medium
For fully developed laminar flow in a circular pipe with constant wall heat flux, which Nusselt number (Nu) is approximately correct?
Answer: B
For constant heat flux boundary condition (H1 type) in circular pipes with fully developed laminar flow, Nu ≈ 4.36. For constant wall temperature (H2), Nu ≈ 3.66.
Q.49Medium
In a counter-current heat exchanger with equal heat capacities, what is the maximum possible effectiveness?
Answer: A
For counter-current arrangement, maximum effectiveness can approach 1.0 (100%) with infinite NTU. For co-current, it's limited to (1-exp(-NTU(1+C_r)))/(1+C_r).
Q.50Medium
The Number of Transfer Units (NTU) is defined as which of the following?
Answer: A
NTU = UA/(ṁC_p)_min is the ratio of overall heat transfer capacity to minimum heat capacity rate, used in ε-NTU method.
Q.51Medium
The log mean temperature difference (LMTD) correction factor F is required primarily for which configuration?
Answer: B
F-correction factor is used for non-counter-current arrangements (cross-flow, 1-2 shell-tube, etc.) where LMTD doesn't directly apply without correction.
Q.52Medium
For turbulent flow in smooth pipes (Pr > 0.6), which correlation is most commonly used?
Answer: A
Dittus-Boelert correlation is the most widely used for turbulent flow with Pr > 0.6. Valid for Re > 10,000, smooth pipes, and fully developed flow.
Q.53Medium
In a shell-and-tube heat exchanger (1 shell pass, 2 tube passes), the effectiveness is lower than counter-current primarily because:
Answer: A
In 1-2 arrangement, portion of shell-side flows co-currently with tube-side, reducing overall effectiveness compared to true counter-current.
Q.54Medium
For a flat plate solar collector with selective coating, which of the following is most desirable?
Answer: B
Selective coatings should absorb solar radiation (high α_sol) but minimize thermal radiation losses (low ε_IR), maximizing collector efficiency.
Q.55Medium
For natural convection from a vertical isothermal plate in air, which correlation applies best?
Answer: A
For natural convection: Nu = C(Ra)^n where Ra = Gr×Pr. For laminar boundary layer (Ra < 10^9), n ≈ 0.25. For turbulent (Ra > 10^9), n ≈ 0.33.
Q.56Medium
In unsteady-state conduction with Bi << 0.1, what assumption is valid?
Answer: A
When Bi < 0.1, convective resistance is much larger than conductive resistance, allowing assumption of uniform temperature throughout the object.
Q.57Medium
In steady-state heat conduction through a composite wall with three layers in series, if the thermal conductivities are k₁ > k₂ > k₃, which layer will have the maximum temperature drop?
Answer: C
Temperature drop across a layer is inversely proportional to thermal conductivity (ΔT ∝ 1/k). Since k₃ is smallest, layer 3 experiences maximum temperature drop.
Q.58Medium
For a circular fin of diameter d and length L attached to a surface at temperature T₀, the fin effectiveness approaches zero when:
Answer: B
When mL → ∞, the temperature along the fin drops rapidly and efficiency decreases, approaching zero as the fin becomes ineffective.
Q.59Medium
In forced convection heat transfer, the Colburn factor (j_H) is related to which dimensionless numbers?
Answer: A
The Colburn analogy relates Stanton number to Nusselt, Reynolds, and Prandtl numbers: j_H = St·Pr^(32) = Nu/(Re·Pr^(31)).
Q.60Medium
In laminar flow through a circular tube with constant wall temperature, the Nusselt number is constant at Nu ≈ 3.66. This means:
Answer: C
Constant Nu in fully developed laminar flow indicates entrance effects are negligible and thermal profile is established.
