General equation of heat transfer

In fluid dynamics, the general equation of heat transfer is a nonlinear partial differential equation describing specific entropy production in a Newtonian fluid subject to thermal conduction and viscous forces:where s {\displaystyle s} is the specific entropy, ρ {\displaystyle \rho } is the fluid's density, T {\displaystyle T} is the fluid's temperature, D / D t {\displaystyle D/Dt} is the material derivative, κ {\displaystyle \kappa } is the thermal conductivity, μ {\displaystyle \mu } is the dynamic viscosity, ζ {\displaystyle \zeta } is the second Lamé parameter, v {\displaystyle {\bf {v}}} is the flow velocity, ∇ {\displaystyle \nabla } is the del operator used to characterize the gradient and divergence, and δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. If the flow velocity is negligible, the general equation of heat transfer reduces to the standard heat equation.

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