Let ec denote the thermodynamic internal energy per unit mass of a material. Then the principle of balance of total energy of a material region can be expressed as The first two terms on the...

Let ec denote the thermodynamic internal energy per unit mass of a material. Then the principle of balance of total energy of a material region can be expressed as

The first two terms on the right-hand side describe the rate of work done on the material region by the surface stresses and the body forces. The third integral describes the net outflow of heat from the region, causing a decrease of energy inside the region. The heat-flux vector q describes the magnitude and direction of the flow of heat energy per unit time and per unit area. By suitable operations, obtain the differential form of the energy equation