What is Heat current density? — Physics

Definition 25.1 University Physics — Year 2 · Chapter 25 — Heat Conduction

The heat current density $\vect{j}_Q$ (in $\mathrm{W}/\mathrm{m}^{2}$ ) is the vector such that the energy transferred by conduction through an oriented surface element $\dd\vect S$ during $\dd t$ is $\vect{j}_Q\cdot\dd\vect S\,\dd t$ ; the thermal flux (a power, in watts) through a surface $S$ is $\Phi = \iint_S\vect{j}_Q\cdot\dd\vect S$ .

Examples

Example 25.3 (Conductivities)

Metals (electrons carry the heat as well as the current — conductivities track each other): copper $400\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ , aluminium $240\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ , steel $50\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ . Insulating solids: concrete $1.5\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ , glass $1\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ , brick $0.8\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ , wood $0.15\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ . Liquids: water $0.6\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ . Gases: air $0.026\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ — and the best insulators, glass wool or foam at $0.04\,\mathrm{W}/\mathrm{m}/\mathrm{K}$ , are mostly still air, trapped so that it cannot convect. Four orders of magnitude from copper to air.

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