What does the colon (:) mean in the following equation pertaining to conservation of energy?
$$p\frac{\partial E}{\partial t}-\nabla \cdot q -\tau \color{red}{:} \nabla v - ph = 0$$
The term $\tau : \nabla v$ is supposed to describe thermal power caused by movement of gas.
$p\frac{\partial E}{\partial t}$ is change in internal energy.
$\nabla \cdot q$ is heat flux.
$\tau : \nabla v$ is thermal power caused by movement.
$ph$ is heat sources.
$p$ is density.
$E$ is internal energy.
$\vec{q}$ is "flow of heat through the boundary".
$\tau$ is a stress tensor.
$v$ is velocity.
$h$ is internal heat sources.
As mentioned in numerous comments: the colon most likely stands for double contraction between two rank-2 tensors or equivalently the Frobenius inner product.