Heat Transfer Coefficient Calculator

Background.

Stand in a breeze on a cool day and you lose heat faster than in still air at the same temperature. That difference, how readily heat crosses between a surface and a fluid for each degree of temperature gap, is what a heat-transfer coefficient measures. Still air is a poor carrier: the typical-values table in Incropera's heat-transfer textbook puts free convection in gases at 2 to 25 W/(m²·K). Blow the air and the range becomes 25 to 250; pump a liquid past the surface and it runs from 100 to 20,000; boiling or condensing fluids reach 2,500 to 100,000.

Predicting a coefficient from first principles is hard. Correlations for each geometry and flow are approximate, so engineers often work the other way round and measure: supply a known heat rate, measure the area and the temperature difference, and divide. That back-calculation is what happens here.

The result is an effective coefficient. It contains everything that happened between the two temperatures you measured. Across a heated panel in a room, that includes radiation as well as convection. Across a heat-exchanger tube, it includes both fluid films, the metal wall and any scale or deposit, which makes it an overall U value rather than a single film coefficient. Which of these you have depends entirely on where the temperatures were taken, and the arithmetic cannot tell them apart.

That is also what makes it a good diagnostic. An exchanger whose measured coefficient drifts down month after month is fouling, and plotting the figure over time shows when cleaning will pay for itself. A test rig that returns a value far outside the expected range more often has a misplaced thermocouple or an uncounted heat loss than new physics.

What is heat transfer coefficient calculator?

A heat-transfer coefficient is the rate of heat flow per unit area per kelvin of temperature difference, in watts per square metre per kelvin, W/(m²·K). A convection coefficient h describes one surface and the fluid moving past it; an overall coefficient U describes the full path through a wall or exchanger from one fluid to another. Both share the unit and the defining equation, and the reciprocal, 1/h or 1/U, is a thermal resistance per unit area in m²·K/W.

How to use this calculator.

1. 01Enter the heat-transfer rate in watts, measured once conditions are steady. For an electric heater it is the power drawn; for a fluid stream it is mass flow × specific heat × that stream's temperature change.
2. 02Enter the area heat actually crosses, in square metres. For a tube, choose the inside or the outside surface and stick with it, because the coefficient changes with that choice.
3. 03Enter the temperature difference in kelvin; a difference in °C is the same number, and one in °F should be divided by 1.8. For a surface in a fluid, use surface temperature minus bulk fluid temperature; for a heat exchanger, use the log-mean temperature difference.
4. 04Compare the result with the range expected for your situation, remembering that it includes radiation and any other path between your two measuring points.

The formula.

h = Q̇ ÷ (A × ΔT), where Q̇ is the heat-transfer rate in watts, A the area in square metres and ΔT the temperature difference in kelvin. It is Newton's law of cooling, Q̇ = h × A × ΔT, rearranged to give the coefficient. The coefficient rises in direct proportion to the heat rate and falls in inverse proportion to both area and temperature difference, so a 10% error in any one input becomes an error of roughly 9 to 10% in h. The temperature difference is usually the weakest link: with only 10 K between surface and fluid, a thermocouple reading one degree off shifts the coefficient by about 10%. All three inputs must be positive. Nothing here predicts h from fluid properties or flow speed; correlations built on Reynolds, Prandtl and Nusselt numbers do that, and measured coefficients are what those correlations are tested against. The result is rounded to 12 significant figures.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Incropera et al., Fundamentals of Heat and Mass Transfer, 8th ed. (PRINT).
2. [2]OpenStax, University Physics Volume 2, section 1.6, Mechanisms of Heat Transfer.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.