Microfluidics: Modeling, Mechanics and Mathematics

Chapter 12

Conservation of Energy: The Energy Equation and the Thermodynamic Equation of State

12.1 Introduction

After discussing the conservation of momentum, we now turn to the last equation we need in order to calculate all six flow variables. This last equation is derived from the conservation of energy. For this equation, we need to sum up all energy contributions into and out of the control volume dV . Energy can be brought into and removed from the control volume

• in the form of energy flow by convection, i.e., in- and outflowing mass: Ė_convection

• in the form of heat flow by conduction, i.e., heat transfer across the boundary: ${\dot{Q}}_{\text{conduction}}$

• in the form of work performed by boundary forces, i.e., shear, normal forces as well as pressure ...