Heat Transfer: Conduction, Convection, Radiation

Conduction & Convection

Your skin measures heat flow, not temperature. Conduction, convection, and radiation are the three highways that flow takes. Engineering a thermos simply blocks all three.

Conduction is heat transfer via molecular collisions. Governed by Fourier's law:

$$\frac{dQ}{dt} = -kA\frac{dT}{dx}$$

Where $k$ is thermal conductivity in $W/(m \cdot K)$, $A$ is area, and $\frac{dT}{dx}$ is the temperature gradient.

For a slab of thickness $L$, we define thermal resistance:

$$R_{\text{th}} = \frac{L}{kA}, \quad \frac{dQ}{dt} = \frac{\Delta T}{R_{\text{th}}}$$

Convection is heat carried by fluid motion. Governed by Newton's law of cooling:

$$\frac{dQ}{dt} = hA(T_s - T_\infty)$$

Where $h$ is the convective heat transfer coefficient, $T_s$ is surface temperature, and $T_\infty$ is fluid temperature.

Radiation & Thermal Rules

Radiation emits thermal energy via electromagnetic waves. Governed by the Stefan-Boltzmann law:

$$P = \varepsilon\sigma A T^4$$

Wien's displacement law finds the peak wavelength of blackbody radiation:

$$\lambda_{\max} T = 2.898\times 10^{-3}\;\text{m K}$$

Physics link: The Sun ($5778$ K) peaks at $\approx 500$ nm (visible). The Earth ($288$ K) peaks at $\approx 10\,\mu$m (infrared).

Common pitfall: "Cold" does not flow into you. Heat always flows out from hot to cold; reversing this direction causes sign errors.