Calculator
Formula used
This calculator applies Newton’s law of cooling for convection.
- q'' = h (Ts − T∞) for heat flux (W/m²)
- Q = h A (Ts − T∞) for total heat transfer rate (W)
Sign convention: if Ts > T∞, the computed heat flow is positive from the surface to the fluid.
How to use this calculator
- Select Heat flux or Heat transfer rate.
- Choose what you want to solve for.
- Enter the other known values and keep the unknown field blank.
- Pick suitable units for temperature, coefficient, and area.
- Click Calculate to view results above the form.
- Use Download CSV or Download PDF for reports.
Example data table
| Case | h (W/m²·K) | Ts (°C) | T∞ (°C) | ΔT (K) | q'' (W/m²) |
|---|---|---|---|---|---|
| 1 | 12 | 60 | 25 | 35 | 420 |
| 2 | 35 | 85 | 25 | 60 | 2100 |
| 3 | 80 | 120 | 40 | 80 | 6400 |
| 4 | 200 | 75 | 20 | 55 | 11000 |
| 5 | 10 | 30 | 50 | -20 | -200 |
Example values are illustrative; choose h from your flow regime and geometry.
1) What this calculator computes
Convection heat transfer is commonly modeled with Newton's law of cooling. The calculator evaluates the convective heat flux q'' (W/m²) using q'' = h(Ts - T∞), or it computes the total heat transfer rate Q (W) using Q = hA(Ts - T∞). You can also solve for the unknown coefficient or temperatures when the other terms are known.
2) Understanding the convection coefficient (h)
The coefficient h bundles complex boundary-layer physics into a single value. It depends on fluid properties, flow speed, surface roughness, and geometry. As a quick benchmark, natural convection in air often falls around 2 to 25 W/(m²·K), forced air flow may be 25 to 250 W/(m²·K), and liquid convection can be higher. Use values from handbooks, experiments, or correlations for your specific case.
3) Choosing representative temperatures
Ts should represent the actual surface temperature at the fluid interface, while T∞ is the bulk fluid temperature away from the surface (not the boundary-layer film value). For internal flows, T∞ is often the mixed-mean fluid temperature. Keeping the temperature basis consistent is critical when comparing to published h data.
4) Heat flux versus total heat rate
Heat flux q'' is useful for local surface checks, coatings, and thermal stress evaluations. Total heat rate Q is used for energy balances and equipment sizing. If your system has multiple surfaces or varying conditions, calculate fluxes per region and sum Q using the appropriate local areas.
5) Typical engineering magnitudes
A small temperature difference can still create significant heat transfer when h is large. For example, with h = 80 W/(m²·K) and ΔT = 20 K, the flux is q'' = 1600 W/m². For a 0.5 m² surface, that becomes Q = 800 W. Use these order-of-magnitude checks to catch unit or input mistakes early.
6) Sensitivity and uncertainty
Results scale linearly with h, area, and temperature difference. If your h estimate has a ±30% uncertainty, your flux or heat rate will typically inherit a similar uncertainty. This is why it is good practice to run low, nominal, and high scenarios for h when making design decisions.
7) Practical workflow for design checks
Start with a reliable h range from correlations (Reynolds and Nusselt based) or measured data. Enter temperatures in consistent units, then compute q'' or Q. Compare the result against allowable heat loss, required cooling capacity, or surface temperature limits. Export CSV or PDF outputs for documentation and review.
8) Common pitfalls and validation
Common issues include using the wrong reference temperature, mixing kW with W, or forgetting that negative ΔT implies heat flows from fluid to surface. Validate by checking the sign, performing a quick back-calculation, and confirming the magnitude against typical ranges. When high accuracy is needed, couple convection with conduction and radiation in a full thermal resistance model.
FAQs
1) What does a negative heat flux mean?
It means the fluid is hotter than the surface, so heat transfers from the fluid to the surface. The sign is determined by Ts - T∞.
2) How do I pick a good value of h?
Use correlations or trusted references for your geometry and flow regime. If unsure, test a plausible low-to-high range and see how sensitive q'' or Q is to that choice.
3) Can I use this for fins or extended surfaces?
Yes for the convection boundary condition, but fin performance also depends on conduction inside the fin. For accurate fin results, combine this with a fin efficiency model and use the fin surface area.
4) Is T∞ the same as the inlet temperature?
Not always. For internal flow, T∞ is usually the mixed-mean bulk temperature, which changes along the duct. Use a representative local value when evaluating a specific section.
5) Why does the calculator require area for heat rate mode?
Total heat transfer rate is Q = q''A. Without surface area, you can only compute the per-area flux, not the overall watts transferred.
6) What units should I use for engineering reports?
W/m² for heat flux and W or kW for total heat rate are common. Keep temperatures consistent and clearly state whether they are in °C, K, or °F.
7) Does this include radiation or conduction?
No. It isolates convection using Newton's law of cooling. If radiation or wall conduction is significant, add them using thermal resistances or a combined heat transfer model.