  Heat fluxes in a district heating pipeline systems need to be controlled on
the scale from minutes to an hour to adjust to evolving demand. There are two
principal ways to control the heat flux - keep temperature fixed but adjust
velocity of the carrier (typically water) or keep the velocity flow steady but
then adjust temperature at the heat producing source (heat plant). We study the
latter scenario, commonly used for operations in Russia and Nordic countries,
and analyze dynamics of the heat front as it propagates through the system.
Steady velocity flows in the district heating pipelines are typically turbulent
and incompressible. Changes in the heat, on either consumption or production
sides, lead to slow transients which last from tens of minutes to hours. We
classify relevant physical phenomena in a single pipe, e.g. turbulent spread of
the turbulent front. We then explain how to describe dynamics of temperature
and heat flux evolution over a network efficiently and illustrate the network
solution on a simple example involving one producer and one consumer of heat
connected by "hot" and "cold" pipes. We conclude the manuscript motivating
future research directions.
