New methods for calculating the inlet hydrodynamic and thermal length in a laminar nanofluid flow by applying entropy generation theory

Abstract

Several ways have been suggested for obtaining the inlet hydrodynamic and thermal length (lhy and<br><br>lth). Studying on nanofluid inlet region is more complicated than fully developed region. Blasius,<br><br>Sparrow, Schlichting, Atkinson and Chen presented different equations due to Reynolds number<br><br>and diameter of channel to predict lhy. Another method is where maximum velocity reaches to 1.5<br><br>times of inlet velocity. In this research the new method due to hydrodynamic entropy generation is<br><br>presented. The difference between this method and Atkinson equation is 0.8%. Shah and Hanna<br><br>presented the relations due to Pecklet number and hydraulic diameter of channel to obtain the lth.<br><br>The other ways to find lth are according to difference of mean temperature and walls temperature,<br><br>dimensionless temperature and Nusselt number. The new method to predict the lth is due to thermal<br><br>entropy generation. When the entropy generation approaches to 0.94% of final value, lth value<br><br>equals to Shah solution.