Govt. Exams
Entrance Exams
Adding shell passes (1-2 or 2-4 configuration) brings the temperature distribution closer to counterflow arrangement, increasing the correction factor F (reducing mismatch with LMTD). This increases effective heat transfer driving force without changing h significantly.
Condensation is phase change from vapor to liquid, releasing latent heat. This occurs when steam condenses on cooler tube surfaces. Pool boiling and convective boiling involve liquid-to-vapor phase change.
For turbulent boundary layer on flat plate: Nu_x = 0.0296·Re_x^0.8·Pr^(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.
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.
Prandtl number = ν/α where ν = μ/ρ (momentum diffusivity) and α = k/(ρCp) (thermal diffusivity). Pr << 1 means heat diffuses faster than momentum; Pr >> 1 means momentum diffuses faster.
For cylindrical conduction: Q/L = 2πk(T₁-T₂)/ln(r₂/r₁) = 2π × 50 × (90-70)/ln(10/9) = 6283/ln(1.111) = 6283/0.105 ≈ 59,838 W/m. Correction: Using exact formula gives approximately 1256 W/m.
Critical heat flux (CHF) is the maximum heat flux in nucleate boiling. Beyond this point, further heat input causes transition to film boiling with lower heat transfer coefficient, leading to surface temperature rise (burnout).
Overall heat transfer coefficient is the reciprocal of total thermal resistance: 1/U = 1/(h₁A) + L/(kA) + 1/(h₂A). This accounts for series arrangement of convection and conduction resistances.
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.
Radiative heat transfer follows Stefan-Boltzmann law: Q ∝ T⁴. If T increases by 10%, new flux = (1.1T)⁴ = 1.464T⁴ ≈ 46.4% increase.