4. Unsteady Laminar Heat Transfer of a Free Rotating Disk

Transient heat transfer investigations are a matter of great importance both from the fundamental and applied points of view, primarily, in turbomachinery. One of the most widely used applications comprises various transient experimental techniques of determining surface heat transfer of a body in stationary hydrodynamic conditions. Such techniques, currently employing thermochromic liquid crystals, are based on the known fact that after a certain period of time from the beginning of the cooling process, the surface heat transfer coefficient becomes a time-independent function equal to its value for steady-state heat transfer under the same boundary conditions. The heat flux in this situation can be computed from more or less simple analytical solutions for unsteady heat conduction inside solid bodies for known surface temperatures. Experimentally measured dependencies of the surface temperature on time are substituted into the mentioned analytical solutions, and the resultant algebraic equations are further solved to find the heat transfer coefficients [91, 112, 121, 154–156, 176, 215].