Abstract: Firstly, by using differential inequality techniques, we gave  a prior estimate of the L⁴ norm  and solution of temperature for bidirectional flow media under the Newtonian cooling boundary conditions. Secondly, by using a prior estimate of the solution and setting an appropriate energy function, we proved that the solutions decayed algebraically with spatial variable in a semi-infinite pipe.

Key words: bidispersive flow, spatial property, energy analysis