EngineeringFormulaThermodynamics
Convective Heat Transfer Calculator
Calculate convective heat-transfer rate, heat flux, film coefficient, area, or temperature difference using Newton's law of cooling.
Convective heat transfer between a surface and a moving or still fluid is commonly modeled with Newton's law of cooling. This calculator covers two related forms: total heat-transfer rate, Q̇ = h A ΔT, and heat flux, q'' = h ΔT. Use Heat Rate mode when you want the total watts transferred over a known surface area. Use Heat Flux mode when you want the heat transfer per unit area or need to back-solve the film coefficient h from flux data.
h · Empirical or correlation-based coefficient that links surface heat transfer to surface-to-fluid temperature difference.
A · Exposed surface area participating in convection.
ΔT · Surface-to-fluid bulk temperature difference driving convection.
This page uses a known film coefficient `h`. It does not predict `h` from fluid flow correlations or replace overall heat-exchanger `U` calculations.
Solution
Enter the required values to calculate heat transfer rate.
Q̇ = h A ΔT
Formula Sheet
- Q̇Heat Transfer Rate
- q''Heat Flux
- hConvective Heat Transfer Coefficient
- AArea
- ΔTTemperature Difference
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| Q̇ | Heat Transfer Rate | Total convective heat-transfer rate between the surface and the surrounding fluid. | W, kW, Btu/h |
| q'' | Heat Flux | Convective heat-transfer rate per unit surface area. | W/m², kW/m², Btu/(h·ft²) |
| h | Convective Heat Transfer Coefficient | Empirical or correlation-based coefficient that links surface heat transfer to surface-to-fluid temperature difference. | W/(m²·K), Btu/(h·ft²·°F) |
| A | Area | Exposed surface area participating in convection. | cm², m², in², ft² |
| ΔT | Temperature Difference | Surface-to-fluid bulk temperature difference driving convection. | K, °C, °F |
How to Use This Calculator
- 01Choose the calculation mode first. Use Heat Rate for total watts between the surface and the fluid, or Heat Flux for watts per unit area.
- 02Select which variable to solve for. The calculator then shows only the inputs needed for that form of Newton's law of cooling.
- 03Enter positive magnitudes for the convective heat transfer coefficient h, area, temperature difference, heat-transfer rate, and heat flux. This page works with magnitudes, not directional sign.
- 04Use the surface-to-fluid bulk temperature difference, not an absolute temperature and not a fluid-to-fluid exchanger temperature difference. If you do not know h, use a tested value, handbook range, or convection correlation before relying on the result.
How the Formula Works
Newton's law of cooling expresses the convective heat-transfer rate as Q̇ = h A ΔT, where h is the convective heat transfer coefficient, A is the exposed area, and ΔT is the surface-to-fluid temperature difference. Increasing any of these increases the total heat-transfer rate proportionally.
Heat flux is simply the heat-transfer rate per unit area, so q'' = Q̇/A = h ΔT. That makes Heat Flux mode useful when area is not the main question or when you want a surface-level loading quantity instead of total watts.
Worked Example 01
Total convective heat transfer from a surface
Known
- Convective Coefficient (h): 25 W/(m²·K)
- Area (A): 2 m²
- Temperature Difference (ΔT): 15 K
Formula
Q̇ = h A ΔT
Substitution
Q̇ = 25 × 2 × 15
Result
Q̇ = 750 W
A 2 m² surface with h = 25 W/(m²·K) and a 15 K surface-to-fluid temperature difference transfers 750 W by convection.
Worked Example 02
Required area for a target cooling load
Known
- Heat Transfer Rate (Q̇): 750 W
- Convective Coefficient (h): 25 W/(m²·K)
- Temperature Difference (ΔT): 15 K
Formula
A = Q̇ / (h ΔT)
Substitution
A = 750 / (25 × 15)
Result
A = 2 m²
To transfer 750 W with that film coefficient and temperature difference, the required convecting area is 2 m².
Worked Example 03
Convective heat flux from h and temperature difference
Known
- Convective Coefficient (h): 50 W/(m²·K)
- Temperature Difference (ΔT): 12 K
Formula
q'' = h ΔT
Substitution
q'' = 50 × 12
Result
q'' = 600 W/m²
A surface-to-fluid temperature difference of 12 K with h = 50 W/(m²·K) gives a convective heat flux of 600 W/m².
Worked Example 04
Back-solve the film coefficient from flux data
Known
- Heat Flux (q''): 600 W/m²
- Temperature Difference (ΔT): 12 K
Formula
h = q'' / ΔT
Substitution
h = 600 / 12
Result
h = 50 W/(m²·K)
If the measured convective heat flux is 600 W/m² at a 12 K surface-to-fluid difference, the implied film coefficient is 50 W/(m²·K).
Applications
- 01Estimating heat loss or heat gain from a surface with a known film coefficient
- 02Back-solving exposed area or required temperature difference for cooling and heating problems
- 03Checking heat flux on plates, housings, or external surfaces when h is known from test data or correlations
- 04Back-checking whether a chosen film coefficient makes a cooling estimate physically reasonable
Assumptions
- 01The convective coefficient h is treated as known and constant over the area and temperature range used in the calculation.
- 02The page uses the standard lumped Newton's-law relation between a surface and a fluid bulk temperature.
- 03The calculator works with positive magnitudes only and does not represent heat-flow direction sign.
Where This Model Stops
- 01Does not predict h from Reynolds number, Nusselt number, geometry, orientation, or fluid properties.
- 02Does not perform transient lumped-capacitance cooling/heating time calculations.
- 03Does not use an overall heat-transfer coefficient U for multi-resistance walls or heat exchangers; use other tools if conduction and multiple resistances must be combined.
- 04Does not decide whether the flow is natural or forced convection; that choice must be reflected in the h value you enter.
References
- [1]17. Convective Heat Transfer
MIT Unified Engineering Notes
Defines the convective heat transfer coefficient and states Newton's law of cooling in heat-flux form q'' = h(Tw − T∞).
- [2]17.2 Combined Conduction and Convection
MIT Unified Engineering Notes
Shows the relation between convective heat flux and total wall heat-transfer problems and distinguishes convection from conduction resistance.
- [3]NIST Guide to the SI, Appendix B.9
National Institute of Standards and Technology
Provides official conversion factors for coefficient of heat transfer, heat flow rate, and heat-flux units used on this page.
Frequently Asked Questions
What temperature difference should I use for convection?
Use the surface temperature minus the nearby bulk-fluid temperature, expressed as a magnitude. This calculator is not for fluid-to-fluid exchanger log-mean temperature difference problems.
What is the difference between h and U?
h is a single convective film coefficient for one surface-fluid interface. U is an overall heat-transfer coefficient that combines multiple resistances such as convection on both sides and conduction through a wall.
How is this different from the Heat Conduction Calculator?
This page uses convection, where heat transfer depends on a film coefficient h between a surface and a fluid. The Heat Conduction Calculator uses Fourier's law with a material conductivity k through a solid layer.
What should I enter for h if I do not know it?
Use a value from a heat-transfer handbook, manufacturer test data, or a convection correlation for your geometry and flow regime. Natural convection in air, forced-air cooling, water flow, and boiling can differ by orders of magnitude, so h is usually the most important input.