The macroscopic picture of diffusive heat flow at low energy

Models of conduction (diffusion of heat-energy through materials) originated with Fourier, who devised the relevant partial differential equations by assuming heat-energy was independently conserved and that the heat transferred depended linearly on the temperature difference. This chapter discusses his model and problems arising in certain applications. Inappropriate analogies with electrical currents have yielded descriptions of parallel heat transport which do not conserve energy, but this problem can be remedied by applying the adiabatic approximation. The extremely important role of heat capacity is emphasized. Thermodynamic requirements have been insufficiently incorporated into boundary conditions, which Fourier recognized as important. The focus on steady-state behavior has led to some misconceptions regarding the physics of heat diffusion, which involves progressive steps toward equilibrium. This chapter therefore focuses on the time dependence of heat transfer and requirements of the second law.