Heat Transfer Coefficient Calculations: Correlations and Methods

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.