Heat transfer

Remarks

Example: for conduction in an isotropic solid, Fourier's law gives $q = -k \nabla T$ with conductivity $k > 0$. Take a wall of thickness $L = 0.2$ m and conductivity $k = 1\ \mathrm{W/(m\,K)}$, with faces at $20\,^\circ\mathrm{C}$ and $0\,^\circ\mathrm{C}$. It carries the flux $\abs{q} = k \Delta T / L = 1 \cdot 20 / 0.2 = 100\ \mathrm{W/m^2}$, where $\Delta T = 20$ kelvin. Let $T_s$ be the temperature of a surface and $T_\infty$ that of its surroundings. For convection, Newton's law of cooling gives $q \cdot n = h (T_s - T_\infty)$, with heat transfer coefficient $h > 0$. For radiation from a grey surface to large surroundings, the Stefan–Boltzmann law gives $q \cdot n = \varepsilon \sigma (T_s^4 - T_\infty^4)$, with emissivity $\varepsilon$ and Stefan–Boltzmann constant $\sigma$. Non-example: work done by a piston on a gas is a transfer of energy, but it is not heat transfer, since it is not driven by a temperature difference.