In this investigation, steady two – dimensional natural convection heat
transfer of Newtonian and non-Newtonian fluids inside square enclosure has been
analyzed numerically for a wide range of the modified Rayleigh number of (103 ≤
Ra ≤ 105), with non-dimensional parameter(NE) of Prandtl – Eyring model ranging
from (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 side
walls are heated at different uniform temperatures and the horizontal walls are
insulated. The second, when the bottom wall is heated by applying a uniform heat
flux while the other walls are at the constant cold temperature. Also, the non-
Newtonian fluids under consideration were assumed to obey the Prandtl – Eyring
model. The numerical results of the values of average Nusselt number have been
confirmed by comparing them to similar known yeslts of previous works using the
same boundary conditions. Good agreement was obtained. The results are
presented in terms of isotherms and streamlines to show the behavior of the fluid
flow and temperature fields. In addition, some graphics represent the relation
between average Nusselt number and the parameters that are mentioned
previously. The results show the effect of non – dimensional parameter (NE) on the
velocity and temperature profiles. It also shows that the average Nusselt number is
a strong function of modified Rayleigh number, modified Prandtl number, nondimensional
parameter, and the boundary conditions. Four different correlations
have been made to show the dependence of the average Nusselt number on the
non-dimensional parameter, the modified Rayleigh and Prandtl numbers.