Heat Transfer Calculator
Estimate heat transfer using conduction, convection, or radiation inputs.
Results
Data Source and Methodology
Authoritative references:
- F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, 7th ed., Wiley, 2011.
- NIST CODATA 2018 recommended values for physical constants (Stefan–Boltzmann constant σ), https://physics.nist.gov/cuu/Constants/.
- VDI Heat Atlas, 2nd Edition, Springer, 2010 (empirical ranges for h and emissivity).
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formulas Explained
Conduction (Fourier’s law for a plane wall)
Q = k A ΔT / L
q'' = Q / A
In LaTeX:
Q = k\,A\,\frac{\Delta T}{L}, \quad q'' = \frac{Q}{A}
Convection (Newton’s law of cooling)
Q = h A ΔT
q'' = h ΔT
In LaTeX:
Q = h\,A\,\Delta T, \quad q'' = h\,\Delta T
Thermal radiation (Stefan–Boltzmann, diffuse-grey surfaces)
Q = ε σ A (T_h^4 − T_c^4)
q'' = ε σ (T_h^4 − T_c^4)
In LaTeX:
Q = \varepsilon \,\sigma\,A \left(T_h^{4}-T_c^{4}\right), \quad q'' = \varepsilon \,\sigma \left(T_h^{4}-T_c^{4}\right)
Glossary of Variables
- A — Area exposed to heat transfer (m² or ft²)
- k — Thermal conductivity (W/(m·K) or Btu/(hr·ft·°F))
- L — Thickness of the conductive path (m or ft)
- h — Convective heat transfer coefficient (W/(m²·K) or Btu/(hr·ft²·°F))
- ε — Emissivity (0–1)
- T_h, T_c — Hot-side and cold-side temperatures (K or R internally; user may enter °C/°F/K/R)
- ΔT — Temperature difference T_h − T_c (K or °F)
- Q — Heat transfer rate (W or Btu/hr)
- q″ — Heat flux per unit area (W/m² or Btu/(hr·ft²))
How It Works: A Step-by-Step Example
Scenario: A 10 mm aluminum plate (k = 205 W/(m·K)) with area A = 1.0 m² separates a hot chamber at 80 °C from ambient at 20 °C.
- Choose Conduction and SI.
- Enter A = 1.0 m², k = 205 W/(m·K), L = 0.01 m, T_hot = 80 °C, T_cold = 20 °C.
- Compute ΔT = 80 − 20 = 60 K.
- Apply Fourier’s law: Q = k A ΔT / L = 205 × 1.0 × 60 / 0.01 = 1,230,000 W.
- Heat flux: q″ = Q / A = 1,230,000 / 1.0 = 1,230,000 W/m².
In real systems, contact resistances, multi-layer walls, or non-uniform temperatures may reduce this idealized value.
Frequently Asked Questions (FAQ)
Do I need absolute temperature (K or R) for conduction and convection?
No. Only the difference ΔT matters, so °C or °F work equivalently. The tool handles this automatically.
Does the radiation formula require view factors?
This simplified calculator assumes a large surrounding at T_c with a view factor of 1 and a diffuse-grey surface. For enclosure radiation, view factors are required.
What if I have multiple layers in a wall?
Compute the total thermal resistance R_total = Σ(L_i/(k_i A)), then Q = ΔT / R_total. A multi-layer module will be added in a future update.
How should I pick h (heat transfer coefficient)?
h depends on geometry, flow, and properties. Use correlations from textbooks or vendor data. Typical natural convection in air is 2–10 W/(m²·K).
Is emissivity constant with temperature?
It can vary. Use data for the relevant temperature range. Polished metals often have low ε that changes as they oxidize.
Can I compute heat loss direction?
Yes. The sign follows T_hot − T_cold. This tool reports the magnitude; heat flows from hot to cold.
How precise are the constants?
The Stefan–Boltzmann constant uses CODATA 2018 value. Unit conversions are performed in double precision.
Formula (LaTeX) + variables + units
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= (sel, ctx=document) => Array.from(ctx.querySelectorAll(sel)); const inputs = { area: el('area'), k: el('k'), thickness: el('thickness'), h: el('h'), emissivity: el('emissivity'), tHot: el('tHot'), tCold: el('tCold') }; const modeRadios =
('input[name="units"]'); const tempUnitRadios =
('.mode-conduction-only'); const groupConvection =
('.mode-radiation-only'); const unitArea = el('unit-area'); const unitK = el('unit-k'); const unitL = el('unit-thickness'); const unitH = el('unit-h'); const unitTemp1 = el('unit-temp'); const unitTemp2 = el('unit-temp-2'); const resMode = el('res-mode'); const resDt = el('res-dt'); const resQ = el('res-q'); const resQflux = el('res-qflux'); const resExtra = el('res-extra'); const resExtraLabel = el('res-extra-label'); const resExtraValue = el('res-extra-value'); const tooltipButtons =
Conduction (Fourier’s law for a plane wall) Q = k A ΔT / L q'' = Q / A In LaTeX: Q = k\,A\,\frac{\Delta T}{L}, \quad q'' = \frac{Q}{A} Convection (Newton’s law of cooling) Q = h A ΔT q'' = h ΔT In LaTeX: Q = h\,A\,\Delta T, \quad q'' = h\,\Delta T Thermal radiation (Stefan–Boltzmann, diffuse-grey surfaces) Q = ε σ A (T_h^4 − T_c^4) q'' = ε σ (T_h^4 − T_c^4) In LaTeX: Q = \varepsilon \,\sigma\,A \left(T_h^{4}-T_c^{4}\right), \quad q'' = \varepsilon \,\sigma \left(T_h^{4}-T_c^{4}\right)
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- Engineering — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/engineering - Mechanical — calcdomain.com · Accessed 2026-01-19
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Last code update: 2026-01-19
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