Heat Transfer Calculator
Compute steady-state heat transfer by conduction, convection, or thermal radiation. Designed for engineers, students, and practitioners, this calculator outputs heat rate and heat flux using SI or Imperial units with rigorous accessibility and performance.
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.