Analytic solution for convection dominant heat transport induced by buoyant jet entrainment inside hot fluid storage tanks.

• New analytic solution for convective heat transport. • Qualitative insight into the buoyant jet entrainment process. • Understanding some qualitative features of the charging process of hot fluid containers. • Investigation of the effectiveness of different modeling possibilities around the jet shear layer. • New test problem to verify the consistency and error estimate of numerical methods. Unsteady heat transfer process and the developed temperature field inside hot water storage tanks with a buoyant inflow jet can be described by a coupled first order partial and a first order ordinary differential equation system (PDE-ODE). Non-polynomial series solutions of this PDE-ODE system for an initial-boundary condition have been presented. The different solutions have been compared to the numerical solution of the PDE-ODE system and to the relevant measurement. The rate of the convergence of the analytic solutions is also investigated. Linear equation systems are constructed to calculate the constant coefficients of the series solution. Additionally the entire 3D flow and temperature field of the investigated thermo physical process have been calculated numerically and compared to the results of the analytic solution of the simplified model. Besides theoretical importance, the solutions can be benchmark solutions to develop the computational heat transfer. [ABSTRACT FROM AUTHOR]