Heat Transfer: Conduction, Convection, Radiation

Touch a metal bench and a wooden one on the same cold morning: same temperature, wildly different feel. Your skin measures heat flow, not temperature — and conduction, convection and radiation are the three highways that flow can take. Engineering a thermos is just blocking all three at once.

There are three mechanisms of heat transfer.

Conduction — Heat flows through a material by molecular collisions:

$$\frac{dQ}{dt} = -kA\frac{dT}{dx} \qquad\text{(Fourier's law)}$$

where $k$ is thermal conductivity (W/(m K)).

Thermal resistance for a slab of thickness $L$:

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

Convection — Heat carried by fluid motion:

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

where $h$ is the convective heat transfer coefficient.

Radiation — All objects emit thermal radiation:

$$P = \varepsilon\sigma A T^4 \qquad\text{(Stefan-Boltzmann law)}$$

Wien's displacement law — Peak wavelength of blackbody radiation:

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

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

Common pitfall: "Cold" is not a thing that flows into you. There is only heat flowing out. Every heat-transfer analysis tracks energy moving from hot to cold; reversing the bookkeeping direction is the fastest way to sign errors.