Calculator Inputs
Run Log (for exports)
| # | Ta (°C) | Q (kW) | u (m/s) | x (m) | y (m) | z (m) | Hs (m) | Δh (m) | Stab | σy (m) | σz (m) | ΔT (°C) | Trec (°C) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 25 | 250 | 3.5 | 500 | 0 | 2 | 35 | 10 | D | 37.68 | 18.77 | 0.105 | 25.105 |
| 2 | 30 | 500 | 2.0 | 800 | 50 | 1.5 | 45 | 15 | C | 75.52 | 39.35 | 0.149 | 30.149 |
| 3 | 20 | 120 | 5.0 | 300 | 0 | 10 | 25 | 5 | E | 17.91 | 7.44 | 0.030 | 20.030 |
Formula Used
This tool uses a steady Gaussian plume to estimate temperature rise at a receptor point:
- Q is heat release rate (W), u wind speed (m/s).
- σy, σz are dispersion spreads from stability class and distance.
- H = Hs + Δh is effective stack height (m).
- Receptor temperature is T = Ta + ΔT.
Spreads are computed using common rural screening approximations for A–F stability classes.
How to Use This Calculator
- Enter ambient temperature and source heat rate in kW.
- Set wind speed representative of the plume travel height.
- Choose distance x, lateral offset y, and receptor height z.
- Provide stack height and plume rise for effective release height.
- Select stability class A–F, then press Calculate.
- Use the Run Log to export CSV or PDF for documentation.
Engineering context for plume temperature results
Thermal plume behavior and dispersion drivers
Thermal plumes cool with distance as turbulence spreads heat through ambient air. In this calculator, spread is represented by σy and σz, which increase with downwind distance and vary by stability class. Unstable air typically increases mixing, raising σ values and reducing temperature rise at any single point.
Heat release rate, density, and specific heat sensitivity
Temperature rise is proportional to heat release rate and inversely proportional to ρ·Cp. If air density drops or Cp is underestimated, predicted ΔT increases. For screening, use ρ near 1.2 kg/m³ and Cp near 1.0 kJ/kg·K, then refine with site meteorology when compliance or safety decisions depend on small margins.
Wind speed and effective stack height impacts
Higher wind speed advects heat faster, lowering ΔT because the plume volume receiving energy grows. Effective height H = Hs + Δh shifts the plume centerline upward; receptors far below H usually experience lower warming, while receptors close to H and near y = 0 produce the maximum centerline temperature rise.
Selecting stability class and interpreting σy, σz
Classes A–F approximate turbulence from very unstable to very stable conditions. Stable air (E–F) limits vertical mixing, often producing smaller σz and higher near-field ΔT at similar x. Compare multiple classes to bracket conditions, and document assumptions in exported tables to support design reviews.
Practical applications and reporting workflow
Use the tool for preliminary assessments of stack heat releases, flare screening, or localized thermal comfort checks around industrial sources. Log runs across distances and receptor heights to build an envelope of ΔT and Trec values. Export CSV for spreadsheets and PDF for appendices, keeping units consistent for traceable results.
FAQs
1) What does the calculator actually predict?
It estimates steady-state temperature rise at a receptor using a Gaussian plume approach, then adds it to the ambient temperature to report the receptor temperature.
2) Which input most strongly reduces temperature rise?
Wind speed typically reduces ΔT the most because it increases advective transport. Larger σy and σz from more mixing also reduce ΔT by spreading heat over a wider volume.
3) Why does stability class change results so much?
Stability controls turbulence. Stable air limits vertical spread (smaller σz), which can keep heat concentrated and raise ΔT. Unstable air does the opposite by enhancing mixing.
4) Is plume rise Δh required for every case?
It is optional but recommended when buoyancy or momentum lift the plume. If unknown, set Δh to zero for a conservative low release height, or test a plausible range.
5) Can I use this for regulatory compliance?
Treat it as a screening estimate. Regulatory analyses often require validated dispersion models, site-specific meteorology, and documented terrain or building effects beyond this simplified formulation.
6) Why does the result sometimes look extremely small?
Heat disperses quickly in open air. At larger x, higher wind, or high turbulence, σ values grow and ΔT can fall below 0.01 °C, which is physically plausible for many stacks.