Heat Transfer Calculator

Three modes: conduction (Fourier's law), convection (Newton's law), and radiation (Stefan-Boltzmann).

Material (thermal conductivity k)

Area A (m²)

Thickness d (m)

Temperature Difference ΔT (°C)

Composite Layers (series)

1–3 layers in series (same k)

Output Power Unit

Heat Flow Rate Q250000.00 W

Heat Flux q = Q/A250000.00 W/m²

Thermal Resistance R = d/(k·A)0.000200 K/W

Conductivity k used50 W/(m·K)

What This Calculator Does

Heat transfer occurs by three fundamental mechanisms. Conduction (Fourier's law) governs heat flow through solids. Convection (Newton's law) governs heat exchange between a surface and a fluid. Radiation (Stefan-Boltzmann) governs heat emission from hot surfaces. This calculator handles all three with material presets, unit conversion, and a composite wall option for conduction.

It combines Mass, Specific Heat, Temperature Change to estimate Heat Energy (Q = m·c·ΔT), Also.

Formula & Method

Conduction (Fourier):

Q = k \cdot A \cdot \frac{\Delta T}{d}, \quad R_{th} = \frac{d}{kA}

Convection (Newton):

Q = h \cdot A \cdot (T_s - T_\infty)

Radiation (Stefan-Boltzmann):

Q = \varepsilon \sigma A (T_s^4 - T_{amb}^4)

where

\sigma = 5.670 \times 10^{-8}

W/(m²·K⁴).

Notation used in the formulas: $R$ = Heat Energy (Q = m·c·ΔT); $x_{1}$ = Mass; $x_{2}$ = Specific Heat; $x_{3}$ = Temperature Change.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Worked Examples

Conduction through steel wall — 50°C temperature difference

k_steel = 50 W/(m·K), A = 2 m², thickness d = 0.01 m, ΔT = 50°C Q = 50 × 2 × (50/0.01) = 500,000 W = 500 kW Thermal resistance R = 0.01/(50×2) = 0.0001 K/W

Radiation from hot surface at 200°C

ε = 0.85, A = 1 m², Ts = 200°C = 473.15 K, Tamb = 25°C = 298.15 K Q = 0.85 × 5.67×10⁻⁸ × 1 × (473.15⁴ − 298.15⁴) = 0.85 × 5.67×10⁻⁸ × (5.01×10¹⁰ − 7.90×10⁹) ≈ 2,012 W = 6,866 BTU/hr

Inputs Used

Mass: Used directly in the calculation.
Specific Heat: Used directly in the calculation.
Temperature Change: Used directly in the calculation.

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