Heat Transfer Coefficient Calculator
Calculate heat transfer rate Q, convection coefficient h, and overall U value using Newton's Law of Cooling and Nusselt number correlations. Covers air, water, oils, and common engineering fluids.
Inner conv. h=500 W/m²K (water)
Steel wall k=50 W/mK, L=0.01m
Outer conv. h=25 W/m²K (air)
| Unit | Equivalent in W/m²K | Factor |
|---|---|---|
| 1 BTU/hr·ft²·°F | 5.67826 W/m²K | ×5.67826 |
| 1 kcal/hr·m²·°C | 1.16279 W/m²K | ×1.16279 |
| 1 kW/m²K | 1,000 W/m²K | ×1000 |
| 1 W/cm²K | 10,000 W/m²K | ×10000 |
| 1 W/m²K | 0.17611 BTU/hr·ft²·°F | ÷5.67826 |
| 1 W/m²K | 0.85984 kcal/hr·m²·°C | ÷1.16279 |
| 1 W/m²K | 0.001 kW/m²K | ÷1000 |
| 1 W/m²K | 0.0001 W/cm²K | ÷10000 |
What is h in Heat and Mass Transfer?
In heat and mass transfer, h is the convective heat transfer coefficient — sometimes called the film coefficient, surface heat transfer coefficient, or simply the convection coefficient. It quantifies how effectively thermal energy moves between a solid surface and the adjacent fluid (liquid or gas) through convection.
Physical meaning: A higher h value means heat is removed (or added) more efficiently per unit area per degree of temperature difference. For example, forced convection with water (h ˜ 1,000–15,000 W/m²K) is far more effective than natural convection with air (h ˜ 2–25 W/m²K).
- Symbol: h (lowercase, not to be confused with enthalpy H)
- SI Units: W/m²K (watts per square meter per kelvin)
- Imperial Units: BTU/hr·ft²·°F
- h depends on: fluid type, flow velocity, surface geometry, temperature, viscosity
h vs k vs U vs α: h is the convection coefficient (surface-to-fluid). k is thermal conductivity of a solid. U is the overall heat transfer coefficient (all resistances combined). α is thermal diffusivity (k/ρcᵣ) — a material property, not a surface coefficient.
Heat Transfer Coefficient Formula
Formula 1 — Newton's Law of Cooling (Primary Formula)
Example: h = 25 W/m²K, A = 2 m², ?T = 30°C ? Q = 25 × 2 × 30 = 1,500 W = 1.5 kW
Formula 2 — From Nusselt Number
Example: For laminar flow over a flat plate L=0.5m, Nu=47.3, k=0.02551 W/mK (air at 20°C): h = 47.3 × 0.02551 / 0.5 = 2.41 W/m²K
Formula 3 — Overall Heat Transfer Coefficient
Formula 4 — Thermal Resistance
Heat Transfer Coefficient of Air and Water
This reference table lists typical convection coefficient h values for air, water, oils, and special fluids. These are the most commonly searched values in heat transfer engineering.
| Fluid & Condition | h (W/m²K) | h (BTU/hr·ft²·°F) | Typical Use |
|---|---|---|---|
| Natural convection — air | 2–25 | 0.35–4.4 | Passive cooling, electronics |
| Forced convection — air (low velocity) | 25–100 | 4.4–17.6 | Fans, HVAC ducts |
| Forced convection — air (high velocity) | 100–300 | 17.6–52.8 | Industrial air jets |
| Natural convection — water | 200–1,000 | 35–176 | Heating tanks |
| Forced convection — water | 1,000–15,000 | 176–2,641 | Heat exchangers, cooling systems |
| Boiling water | 2,500–35,000 | 440–6,160 | Steam generators |
| Condensing steam | 5,000–100,000 | 880–17,605 | Condensers |
| Engine oil (forced) | 50–2,000 | 8.8–352 | Lubrication systems |
| Ethylene glycol (forced) | 500–5,000 | 88–880 | Automotive cooling |
| Liquid metals | 10,000–100,000 | 1,760–17,605 | Nuclear reactors |
Film Coefficient Reference Table
| Surface / Condition | Film Coefficient h (W/m²K) |
|---|---|
| Still air (natural convection) | 5–10 |
| Air at 5 m/s (forced) | 25–35 |
| Air at 10 m/s (forced) | 40–60 |
| Water at 0.5 m/s | 500–2,000 |
| Water at 2 m/s | 2,000–8,000 |
Heat Transfer Coefficient Units
The convection coefficient h is always expressed as power per unit area per unit temperature difference. Understanding unit conversions is essential when working with international standards.
- SI unit: W/m²K — watts per square metre per kelvin. This is the international standard.
- Also written: W/m²°C — numerically identical to W/m²K for temperature differences.
- Imperial unit: BTU/hr·ft²·°F — used in US engineering and HVAC.
- Older metric: kcal/hr·m²·°C — still seen in some European and older textbooks.
- Electronics: W/cm²K — used when dealing with small surfaces and high heat flux.
| Unit | Equivalent in W/m²K | Notes |
|---|---|---|
| 1 BTU/hr·ft²·°F | 5.67826 W/m²K | US engineering standard |
| 1 kcal/hr·m²·°C | 1.16279 W/m²K | Older European metric |
| 1 kW/m²K | 1,000 W/m²K | Large heat exchangers |
| 1 W/cm²K | 10,000 W/m²K | Electronics cooling |
Why W/m²K = W/m²°C: The Kelvin and Celsius scales have the same size degree. A temperature difference of 1 K is exactly equal to a difference of 1°C. Since h involves only ?T (a difference), not an absolute temperature, the unit W/m²K and W/m²°C are identical numerically.
Overall Heat Transfer Coefficient
The overall heat transfer coefficient U accounts for all thermal resistances in series between two fluids — inner convection, wall conduction, fouling layers, and outer convection. It is always less than or equal to the smallest individual resistance's equivalent h value.
Worked Example: Hot Water Pipe in Air
- Inner convection (water): hᵢ = 2,000 W/m²K
- Steel wall: k = 50 W/mK, thickness L = 5mm = 0.005m
- Outer convection (air): hᵣ = 20 W/m²K
- Rᵢ = 1/hᵢ = 1/2,000 = 0.0005 m²K/W
- Rᵗᵢᴰᴰ = L/k = 0.005/50 = 0.0001 m²K/W
- Rᵣ = 1/hᵣ = 1/20 = 0.0500 m²K/W
- Rᵗᵓᵗᵀᴰ = 0.0005 + 0.0001 + 0.05 = 0.0506 m²K/W
- U = 1/Rᵗᵓᵗᵀᴰ = 1/0.0506 = 19.76 W/m²K
Key insight: U ˜ hᵣ = 20 W/m²K. The outer air convection dominates because it contributes 99% of total resistance. The "weakest link" controls the overall heat transfer rate.
Worked Examples
1. How to Calculate Heat Transfer Rate Using h
Use Newton's Law of Cooling: Q = h × A × ?T. Identify h in W/m²K, A in m², and ?T in K or °C. For h=25 W/m²K, A=2 m², ?T=30°C: Q = 25 × 2 × 30 = 1,500 W = 1.5 kW = 5,119 BTU/hr. This is a typical result for a fan-cooled electronic enclosure.
2. How to Find h from Nusselt Number (Flat Plate, Laminar)
For air at 20°C flowing at 5 m/s over a plate L=0.5m: Re = ?vL/µ = 1.204×5×0.5/1.825×10?5 = 165,205 (laminar, Re<5×105). Nu = 0.664×Re°·5×Pr¹/³ = 0.664×406.3×0.9006 = 242.8. h = Nu×k/L = 242.8×0.02551/0.5 = 12.39 W/m²K.
3. Calculate Overall U for a Composite Wall
Inner water film h=2,000, steel wall 5mm k=50, outer air h=20: 1/U = 0.0005+0.0001+0.05 = 0.0506. U = 1/0.0506 = 19.76 W/m²K. Note U is almost equal to h_outer (20) because air side dominates.
4. What is the Heat Transfer Coefficient of Air at Natural Convection?
For natural convection in air, h typically ranges from 2 to 25 W/m²K. This low value occurs because still or slowly moving air has poor thermal conductivity (k=0.025 W/mK) and low density, limiting convection. Forced convection raises this to 25–300 W/m²K.
5. Convection Coefficient of Water in a Pipe
Forced convection of water in a pipe yields h = 1,000 to 15,000 W/m²K — orders of magnitude higher than air. For Dittus-Boelter with Re=50,000, Pr=7.01 (water at 20°C): Nu = 0.023×50,000°·8×7.01°·4 = 0.023×1,380×2.44 = 277.4. h = 277.4×0.5978/0.025 = 6,632 W/m²K.
6. Convert h from W/m²K to BTU/hr·ft²·°F
Multiply W/m²K by 0.17611. Example: h = 25 W/m²K × 0.17611 = 4.403 BTU/hr·ft²·°F. To convert back: BTU/hr·ft²·°F × 5.67826 = W/m²K. Example: 1 BTU/hr·ft²·°F = 5.678 W/m²K.
7. How to Calculate Film Coefficient for Forced Convection
The film coefficient h is calculated via h = Nu×k/L. For forced convection over a flat plate (turbulent Re=106, air): Nu = 0.037×(106)°·8×0.7296¹/³ = 0.037×15,849×0.9006 = 527.9. h = 527.9×0.02551/1.0 = 13.47 W/m²K.
8. Difference Between h and U in Heat Transfer
h (convection coefficient) applies at a single surface between solid and fluid. U (overall coefficient) accounts for ALL resistances: inner conv + wall + outer conv + fouling. U is always = smallest h. Example: h_water=2,000, h_air=20 ? U˜19.76 — U is controlled by the weakest resistance (air side).
9. Heat Transfer Rate of Air Over a Surface
For natural convection with air: Q = h×A×?T = 10×0.5×40 = 200 W. For forced convection at 5 m/s: h˜30 W/m²K, Q = 30×0.5×40 = 600 W — three times higher just from moving the air. This demonstrates why fans improve cooling so effectively.
10. Calculate Convective Heat Flux from h
Heat flux q = h × ?T (W/m²). For h = 1,000 W/m²K (forced water) and ?T = 20°C: q = 1,000 × 20 = 20,000 W/m². For natural convection air h=5, ?T=30°C: q = 5×30 = 150 W/m². This 133× difference explains why liquid cooling dominates high-power applications.