K. V. Gubareva, E. Yu. Prosviryakov, A. V. Eremin

EXACT ANALYTICAL SOLUTION FOR THE PROBLEM OF UNSTEADY CONVECTION IN THE BOUSSINESQ APPROXIMATION WITH ACCOUNT FOR VISCOUS DISSIPATION

An exact analytical solution is derived for the system of equations describing an unsteady convective flow of a viscous incompressible fluid in a plane layer, taking into account the buoyancy force and viscous dissipation of energy. A class of shear flows with isothermal boundaries is considered, for which the temperature depends only on the transverse coordinate and time. The solution is constructed in the form of series in eigenfunctions, allowing one to describe the time evolution of velocity, temperature, and pressure fields. The flow characteristics are analyzed with water as an example for various time scales. The solution can be used to study transient processes in microfluidic systems and heat exchangers.

Article reference