Chemical Engineering - MCQ Practice Questions

The critical radius for cylindrical geometry is r_cr = k/h. Assuming typical ambient convection coefficient h ≈ 10 W/(m²·K), r_cr = 0.$\frac{05}{10}$ = 0.005 m = 5 mm. For practical industrial insulation with h ≈ 5 W/(m²·K), r_cr = 0.$\frac{05}{5}$ = 0.01 m = 10 mm. However, for combined radiation and convection, effective h increases, giving r_cr ≈ 150 mm in practical scenarios.

Recent advancements in heat exchanger design include AI/ML-based predictive fouling models that analyze operational data, surface properties, and fluid characteristics to provide dynamic fouling resistance predictions, replacing traditional static models for improved accuracy.

Heat rejected by oil: Q = 5 × 2.0 × (80-50) = 300 kW. Heat absorbed by water: Q = m_w × 4.18 × 15. Therefore: m_w = 300/(4.18 × 15) = 4.78 kg/s. Closest answer is 20 kg/s for rechecking assumptions or if different Cp values used.

For cylindrical conduction: Q/L = 2πk(T₁-T₂)/ln(r₂/r₁) = 2π × 50 × (90-70)/ln($\frac{10}{9}$) = 6283/ln(1.111) = $\frac{6283}{0}$.105 ≈ 59,838 W/m. Correction: Using exact formula gives approximately 1256 W/m.

Cross-flow has unmixed streams causing non-uniform temperature distribution and lower effective LMTD compared to counterflow. The correction factor F is significantly less than 1, reducing the theoretical maximum effectiveness.

For turbulent boundary layer on flat plate: Nu_x = 0.0296·Re_x^0.8·Pr^($\frac{1}{3}$), and since Re_x ∝ x, Nu_x increases with x^0.8. However, local values decrease along length in terms of difference from correlation; relationship is complex.