Laminar Natural Convection of Newtonian and Non – Newtonian Fluids in a Square Enclosure

Abstract

In this investigation, steady two – dimensional natural convection heattransfer of Newtonian and non-Newtonian fluids inside square enclosure has beenanalyzed numerically for a wide range of the modified Rayleigh number of (103 ≤Ra ≤ 105), with non-dimensional parameter(NE) of Prandtl – Eyring model rangingfrom (0 to 10), and modified Prandtl number in the range (Pr* =1,10, and 100).Two types of boundary conditions have been considered. The first,is when the sidewalls are heated at different uniform temperatures and the horizontal walls areinsulated. The second, when the bottom wall is heated by applying a uniform heatflux while the other walls are at the constant cold temperature. Also, the non-Newtonian fluids under consideration were assumed to obey the Prandtl – Eyringmodel. The numerical results of the values of average Nusselt number have beenconfirmed by comparing them to similar known yeslts of previous works using thesame boundary conditions. Good agreement was obtained. The results arepresented in terms of isotherms and streamlines to show the behavior of the fluidflow and temperature fields. In addition, some graphics represent the relationbetween average Nusselt number and the parameters that are mentionedpreviously. The results show the effect of non – dimensional parameter (NE) on thevelocity and temperature profiles. It also shows that the average Nusselt number isa strong function of modified Rayleigh number, modified Prandtl number, nondimensionalparameter, and the boundary conditions. Four different correlationshave been made to show the dependence of the average Nusselt number on thenon-dimensional parameter, the modified Rayleigh and Prandtl numbers.