Laminar natural convection of newtonian and non – newtonian fluids in a square enclosure

الملخص EN

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 none Newtonian fluids under consideration were assumed to obey the Prandtl–Eyring model.

The numerical results of the values of average Nussle number have been confirmed by comparing them to similar known yesses 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 Nussle 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 Nussle number is a strong function of modified Rayleigh number, modified Prandtl number, no dimensional parameter, and the boundary conditions.

Four different correlations have been made to show the dependence of the average Nussle number on the non-dimensional parameter, the modified Rayleigh and Prandtl numbers.