Conservation of Energy in Solids

The conservation of energy equation is,

ρsCp,sTstxi(ksTsxi)q˙s=0 \rho_sC_{p,s}\frac{\partial T_s}{\partial t}-\frac{\partial}{\partial x_i}\left(k_s\frac{\partial T_s}{\partial x_i}\right)-\dot{q}_s=0(1)

where TsT_s is the solid temperature, ρs\rho_s is the solid density, Cp,sC_{p,s} is the solid isobaric specific heat capacity, ksk_s is the solid thermal conductivity, and q˙s\dot{q}_s is a solid volumetric heat source.