Heat Transfer Coefficient Calculations

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  • The heat transfer coefficient (h) is a measure of the convective heat transfer between a surface and a fluid (gas or liquid) in contact with it.
  • It’s typically expressed in units of W/m²·K.

Basic Formula for Heat Transfer Rate

Q=h⋅A⋅ΔT

Where:

  • Q = heat transfer rate (W)

  • h = convective heat transfer coefficient (W/m²·K)

  • A = surface area of heat transfer (m²)

  • ΔT = temperature difference between the surface and the fluid (K or °C)

                    Nu=C⋅Re^m⋅Pr^n

Methods to Determine h

  1. Experimental Method:

    • Measure Q, A, and ΔT, then apply the above formula.

    • Used in lab or industrial test setups.

  2. Empirical Correlations (for convection):
    Use dimensionless numbers for forced or natural convection

Typical Values of h

Type of Convection Heat Transfer Coefficient (W/m²·K)
Free convection (gas) 2 – 25
Free convection (liquid) 50 – 1,000
Forced convection (gas) 25 – 250
Forced convection (liquid) 100 – 20,000
Boiling / condensation 2,500 – 100,000+
Heat transfer coefficient for boiler evaporator tubes

his is typically forced convection with phase change (boiling/evaporation). The heat transfer coefficient is very high due to the latent heat of vaporization and boiling dynamics.

 Typical range:

h_water-steamside≈5000−25,000 W/m2⋅Kh

Outside the Tubes (Flue Gas Side)

This is typically forced convection from hot combustion gases, sometimes with radiation component added.

h_gas​≈30−250 W/m2⋅K

nfluencing Factors:

  • Gas velocity (higher velocity → higher Re → higher h)

  • Gas temperature

  • Tube pitch and arrangement (in-line or staggered)

  • Fouling/ash deposits on tube surfaces

Summary Table

Side Heat Transfer Coefficient (h) Notes
Water/steam inside 5,000 – 25,000 W/m²·K Due to boiling
Flue gas outside 30 – 250 W/m²·K Convective + some radiation
Overall U-value 40 – 300 W/m²·K Combined effect

 

Heat Transfer Properties of Common Gases at ~300 K

Gas Thermal Conductivity (k) W/m·K Prandtl Number (Pr) Typical h (W/m²·K) Remarks
Air 0.0262 0.71 10 – 100 Standard ambient gas
Hydrogen (H₂) 0.1805 0.71 50 – 250 Very high k, fast heat transfer
Helium (He) 0.1513 0.67 20 – 300 Low density, high thermal conductivity
Nitrogen (N₂) 0.0259 0.72 10 – 90 Similar to air
Oxygen (O₂) 0.0263 0.68 10 – 100 Similar to air
Carbon Dioxide (CO₂) 0.0166 0.72 10 – 80 Lower k, dense gas
Steam (H₂O vapor) 0.0190 1.00 25 – 150 High Pr → lower diffusivity
Ammonia (NH₃) 0.0219 1.00 20 – 80 High latent heat in condensation
Methane (CH₄) 0.0346 0.70 20 – 90 Higher k than air
Sulfur Dioxide (SO₂) 0.0136 0.96 5 – 40 Toxic, heavy gas
Argon (Ar) 0.0179 0.67 5 – 30 Inert, low k

Explanation of Parameters:

  • Thermal Conductivity (k):

    • Governs how well the gas conducts heat.

  • Prandtl Number (Pr):

    Pr=μcp/k

    • Describes the ratio of momentum diffusivity to thermal diffusivity.

    • Gases have Pr≈0.7

    •  steam and vapors often have Pr>1, > 1.

  • Heat Transfer Coefficient (h):

    • Depends on k, flow velocity, geometry, and turbulence.

    • This is a typical range for moderate forced convection (e.g., ~2–5 m/s flow across tubes or plates).