Visualizing energy flows through energy streamlines and pathlines

This paper describes the new technique of total energy flow visualization inside channels and enclosures for natural, mixed, and forced convection heat transfer problems. Specifically, the flow of the total energy is visualized by energy streamlines or pathlines. In 2-D, energy streamlines are obtained by solving a Poisson equation of type ∇ 2 Φ = ( ∇ × E ˙ ) · k ˆ where Φ is the energy streamfunction. E ˙ is the energy flux density vector and k ˆ is the unit vector. One of the objectives of this paper is to find expressions for E ˙ as a function of velocity, temperature, electric field, magnetic field, and fluid/flow properties. In 3-D, energy pathlines are used to visualize total energy flow. In concept, “total energy” includes all relevant forms of energy; for example, thermal, potential, kinetic, magnetic, electrical, and chemical. Steady-state convection heat transfer problems are selected from the available literature and energy streamlines are presented for these problems. For unsteady periodic problems, energy streamfunctions are calculated from the time averaged velocity, temperature, and other relevant properties. Finally, an energy pathline visualization technique is proposed for 3-D problems.