On the discontinuity of the dissipation rate associated with the temperature variance at the fluid-solid interface for cases with conjugate heat transfer

•Discontinuity of the dissipation rate at the fluid-solid interface is established.•A novel compatibility condition governing that discontinuity is exhibited.•Direct Numerical Simulations performed confirm this analysis.•Database publicly available online. In the case of conjugate heat transfer, the dissipation rate associated with the temperature variance is discontinuous at the fluid-solid interface. The discontinuity satisfies a compatibility condition involving the fluid-solid thermal diffusivity and conductivity ratios and the relative contribution to the dissipation rate of its wall-normal part. The present analysis is supported by the Direct Numerical Simulations of an incompressible channel flow at a Reynolds number, based on the friction velocity, of 150, a Prandtl number of 0.71 and several values of fluid-solid thermal diffusivity and conductivity ratios.