Radiation Heat Transfer Calculator
Radiation exchange grows with T⁴: a 1 m² surface of emissivity 0.8 at 500 K in 300 K surroundings loses 2467.75 W.
2467.7469471488 W
Full answer, then cut to fewer decimals (not rounded):
- 2467.7469471488 W
- 2467.746947148 W
- 2467.74694714 W
- 2467.7469471 W
- 2467.746947 W
- 2467.74694 W
- 2467.7469 W
- 2467.746 W
- 2467.74 W
- 2467.7 W
- Heat flux q
- 2467.75 W/m²
- Black-body emissive power σT₁⁴
- 3543.98 W/m²
- Wien peak wavelength λmax = 2897.8/T₁
- 5.79554 µm
- Radiation coefficient hr
- 12.3387 W/m²·K
Step-by-step solution
- Q = εσA(T₁⁴ − T₂⁴)
- σ = 5.670374 × 10⁻⁸ W/m²·K⁴
- Q = 2467.75 W/m² × 1 m² = 2467.75 W
Radiation Heat Transfer Formula
Q = εσA(T₁⁴ − T₂⁴)
σ = 5.670374 × 10⁻⁸ W/m²·K⁴; plates: σ(T₁⁴ − T₂⁴)/(1/ε₁ + 1/ε₂ − 1)
Worked Example
A 1 m² surface (ε = 0.8) at 500 K in large surroundings at 300 K:
- Q = εσA(T₁⁴ − T₂⁴)
- σ = 5.670374 × 10⁻⁸ W/m²·K⁴
- Q = 2467.75 W/m² × 1 m² = 2467.75 W
Black-body emissive power σT₁⁴: 3543.98 W/m² · Wien peak wavelength λmax = 2897.8/T₁: 5.79554 µm · Radiation coefficient hr: 12.3387 W/m²·K
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Example: A 200 mm wall (k = 0.8 W/m·K, 10 m²) with faces at 40 °C and 10 °C: Heat transfer rate Q = 1200 W.
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(T − T∞)/(Tᵢ − T∞) = e^(−t/τ), τ = ρcLc/h
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Example: A 1 mm thermocouple bead (ρ = 8500, c = 400, k = 20) at 25 °C plunged into gas at 200 °C with h = 400 W/m²·K, reaching 199 °C: Time to reach T, t = 7.31678 s.
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LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁/ΔT₂)
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Example: Counter-flow: hot 150 → 100 °C, cold 30 → 70 °C, Q = 200 kW, U = 500 W/m²·K: LMTD = 74.8888 °C.
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ε = [1 − e^(−NTU(1 − Cr))] ÷ [1 − Cr e^(−NTU(1 − Cr))]
NTU = UA/Cmin, Cr = Cmin/Cmax (counter-flow)
Example: UA = 3000 W/K, Ch = 4000 W/K, Cc = 2000 W/K, hot in at 120 °C, cold in at 20 °C: Effectiveness ε = 0.690785.
Frequently asked questions
Why must radiation temperatures be in kelvin?
Emissive power is proportional to absolute temperature to the fourth power; °C would give wrong results.
What is Wien’s displacement law?
λmax T = 2897.8 µm·K: the sun (5800 K) peaks near 0.5 µm, a 300 K surface near 9.7 µm.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Radiation Heat Transfer Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/radiation-heat-transfer-calculator/
IEEE
Scientific Converters, "Radiation Heat Transfer Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/radiation-heat-transfer-calculator/