Heat Transfer and Solar Energy — Formula Sheet

Q = K·A·(Tₕ - Tᶜ)·t / d

Rate of heat flow = dQ/dt = K·A·(Tₕ - Tᶜ) / d

λₘ · T = 2.884 × 10⁻³ m·K (Wien's Displacement Law)

E = A·e·σ·T⁴ (Stefan-Boltzmann Law)

E_net = A·e·σ·(T₁⁴ - T₂⁴)

Kirchhoff's Law: eλ / aλ = Eλ (constant for all bodies at same T)

Q = 2πRₑ² × C

E = (r/R)² · σT⁴ (Solar constant at distance R)

E'/E = (R/R')² (Ratio of solar constants)

SOLAR CONSTANT

The energy received per unit area per second on Earth from the Sun = 1.36 × 10³ Wm⁻² (= 1360 Wm⁻²).

Total solar energy received by Earth per second

Q = 2πRₑ²C ≈ 3.5 × 10¹⁷ W (only illuminated half is counted).

Solar constant for another planet at orbital distance R' from Sun: E'/E = (R/R')² where R = Earth's orbital radius.

Fourier's Law

Q = KA(T_h - T_c)t / d. K is the thermal conductivity of the material.

Kirchhoff's Law

e_λ / a_λ = E_λ. Good emitters are also good absorbers at any given temperature.

Solar constant C = 1.36 × 10³ Wm⁻². It is the solar energy received per unit area per second at Earth's mean distance from the sun.

Total solar power received by Earth ≈ 3.5 × 10¹⁷ W.

Solar constant varies inversely with the square of distance from the sun: E'/E = (R/R')².