geometrization of heat flow on volumetrically isothermal manifolds via the ricci flow

the present article serves the purpose of pursuing geometrization of heat flow on volumetrically isothermal manifold by means of rf approach. in this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of riemannian manifold and fundamental properties of thermodynamic systems. by making use of the notions of various curvatures, we have discussed different types of heat diffusion equation for our volumetrically isothermal manifold and its isothermal surfaces. finally, we have delineated a heat diffusion model for such isothermal manifold and by decomposing it into isothermal surfaces we have developed equation for heat diffusion.