Heating rate in the model of the diffusion accretion-decretion disk

The evolution of circumstellar disks is commonly prescribed with the viscous disk model where turbulence is assumed to be the main factor of angular momentum transfer and is treated alike molecular viscosity. Previously, we have presented the model of diffusion accretion-decretion disk where turbulence is prescribed as mass exchange which preserves angular momentum. In the current paper, to progress with the diffusion model, we present the derivation of the heating rate associated with the release of gravitational energy.