Symmetry Methods of Flow and Heat Transfer between Slowly Expanding or Contracting Walls

摘要

An analysis has been carried out for the flow and heat transfer of an incompressible laminar and viscous fluid in a rectangular domain bounded by two moving porous walls which enable the fluid to enter or exit during successive expansions or contractions. The basic equations governing the flow are reduced to the ordinary differential equations using Lie-group analysis. Effects of the permeation Reynolds number R_e, porosity R, and the dimensionless wall dilation rate α on the self-axial velocity are studied both analytically and numerically. The solutions are represented graphically. The analytical procedure is based on double perturbation in the permeation Reynolds number R_e and the wall expansion ratio a, whereas the numerical solution is obtained using Runge-Kutta method with shooting technique. Results are correlated and compared for some values of the physical parameters. Lastly, we look at the temperature distribution.