Accurate heat transfer coefficient (HTC) calculations are fundamental to heat exchanger design. This guide covers the essential correlations and methods for various applications.
Dimensionless Numbers
Reynolds Number (Re)
Characterizes flow regime: Re = ρVD / μ = VD / ν
- Re < 2300: Laminar flow
- 2300 < Re < 10000: Transition
- Re > 10000: Turbulent flow
Prandtl Number (Pr)
Ratio of momentum to thermal diffusivity: Pr = c_p × μ / k = ν / α
- Pr < 1: Thermal diffusivity dominates (liquid metals)
- Pr ≈ 1: Similar diffusivities (gases)
- Pr > 1: Momentum diffusivity dominates (oils, water)
Nusselt Number (Nu)
Dimensionless heat transfer coefficient: Nu = hD / k
Single-Phase Internal Flow
Laminar Flow (Re < 2300)
Constant wall temperature: Nu = 3.66
Constant heat flux: Nu = 4.36
Developing flow (Sieder-Tate): Nu = 1.86 × (Re × Pr × D/L)^(1/3) × (μ/μ_w)^0.14
Turbulent Flow (Re > 10000)
Dittus-Boelter Correlation: Nu = 0.023 × Re^0.8 × Pr^n
Where n = 0.4 for heating, n = 0.3 for cooling
Gnielinski Correlation (more accurate): Nu = (f/8)(Re - 1000)Pr / [1 + 12.7(f/8)^0.5(Pr^(2/3) - 1)]
Valid for: 3000 < Re < 5×10^6, 0.5 < Pr < 2000
Single-Phase External Flow
Flow Over Flat Plate
Laminar (Re_x < 5×10^5): Nu_x = 0.332 × Re_x^0.5 × Pr^(1/3)
Turbulent (Re_x > 5×10^5): Nu_x = 0.0296 × Re_x^0.8 × Pr^(1/3)
Flow Over Tube Banks
Zukauskas Correlation: Nu = C × Re^m × Pr^0.36 × (Pr/Pr_w)^0.25
Where C and m depend on tube arrangement and Re range.
Boiling Heat Transfer
Pool Boiling (Rohsenow)
q" = μ_l × h_fg × [g(ρ_l - ρ_v)/σ]^0.5 × [c_pl × ΔT_sat / (C_sf × h_fg × Pr_l^n)]^3
Flow Boiling (Chen)
Combines nucleate and convective contributions: h_tp = h_nb × S + h_l × F
Where:
- S = suppression factor
- F = enhancement factor
- h_nb = nucleate boiling coefficient
- h_l = liquid-only coefficient
Shah Correlation
Widely used for evaporation: h_tp = h_l × E
E depends on:
- Convection number (Co)
- Boiling number (Bo)
- Froude number (Fr)
Condensation Heat Transfer
Film Condensation (Nusselt)
Horizontal tube: h = 0.725 × [ρ_l(ρ_l - ρ_v)g h_fg k_l^3 / (μ_l D ΔT)]^0.25
Vertical surface: h = 0.943 × [ρ_l(ρ_l - ρ_v)g h_fg k_l^3 / (μ_l L ΔT)]^0.25
In-Tube Condensation (Shah)
h_tp = h_l × [(1-x)^0.8 + 3.8x^0.76(1-x)^0.04 / p_r^0.38]
Air-Side Correlations for Finned Tubes
Plain Fins (Gray-Webb)
j = 0.14 × Re_Dc^(-0.328) × (Pt/Pl)^(-0.502) × (s/Dc)^0.031
Wavy Fins (Wang)
j = 0.0836 × Re_Dc^(-0.2309) × N^(-0.0311) × (Fp/Dc)^(-0.3769)
Louvered Fins
j = Re_Lp^(-0.49) × (θ/90)^0.27 × (Fp/Lp)^(-0.14) × (Fl/Lp)^(-0.29)
Practical Application Tips
1. Property Evaluation
- Use film temperature for external flow
- Use bulk temperature for internal flow
- Account for property variation
2. Fouling Factors
Add thermal resistance for fouling: 1/U = 1/h_i + R_fi + R_wall + R_fo + 1/h_o
Typical values:
- Clean water: 0.0001 m²·K/W
- River water: 0.0003 m²·K/W
- Refrigerants: 0.0001 m²·K/W
3. Enhancement Techniques
- Internal fins or inserts
- Surface roughness
- Twisted tape inserts
Conclusion
Selecting appropriate correlations and applying them correctly is essential for accurate heat exchanger design. Modern software tools incorporate these correlations with proper property databases for reliable calculations.