# Numerical Study of Laminar Mixed Convection Heat Transfer of Power-Law Non-Newtonian Fluids in Square Enclosures by Finite Volume Method

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Numerical study of laminar mixed convection heat transfer of power-law non-Newtonian fluids in square enclosures by finite volume method Mohammad Reza Safaei1*, Behnam Rahmanian2 and Marjan Goodarzi3 1

Young Researchers Club and Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran. 2 Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran. 3 Department of Computer Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran. Accepted 23 October, 2011

In this study, we have numerically considered mixed convection heat transfer in a square enclosure with cold left and right walls, insulated moving upper wall and hot fixed lower wall. The governing flows of two reliable articles were initially modeled and after validating calculations, the given flow of the study was solved by finite volume method. To examine the effects of different factors, such as Prandtl, Reynolds and Rayleigh numbers on heat transfer in a square enclosure, the laminar flow of Newtonian fluids was approximated and then laminar flow of non-Newtonian fluids, such as carboxy methyl cellulose (CMC) and carboxy poly methylene (Carbopol) water solutions were studied for different Richardson numbers. It was found from the results obtained in the present study that when Ri is less than 1, governing heat transfer inside the enclosure is forced convection for non-Newtonian fluids similar to Newtonian ones. When Ri increases, the effect of forced convection is reduced and natural convection heat transfer increases. It was also found that in constant Grashof numbers, if n decreases, the dimensionless temperature increases. Also, if n is constant, any increase in Grashof number causes a higher dimensionless temperature. It may be related to the fact that in similar conditions, any increase in forced convection, makes shear stresses more. Key words: Richardson number, power-law non-Newtonian fluids, mixed convection heat transfer, square enclosure, finite volume method.

INTRODUCTION The process of heat transfer, in which the free convection and forced convection occur coincidentally, is called mixed convention heat transfer. Mixed convection heat transfer occurs when the buoyancy effect in a forced flow or the effect of forced flow in a buoyancy flow is significant (Safaei and Goshayeshi, 2010). In recent years, the practical applications of mixed convection heat transfer in various areas such as designing solar collectors, double-layer glasses, building insulation, cooling electronic parts, food drying, sterilization, etc., have motivated many scientists to study this phenomenon. Basak et al. (2009) have studied laminar mixed convection of airflow inside a square enclosure by using a finite element method. Using local Nusselt number, they showed that the rate of heat transfer on the corners of the lower wall is high and decreases on its center. Oztop and Dagtekin (2004) conducted a study on laminar mixed convection flow inside an enclosure with moving isothermal vertical and insulated horizontal walls. 4 They examined the flow of air (Pr = 0.7) in Gr = 10 and 0.01 < Ri < 100. The results of his study demonstrated that in low values of Richardson's number, if the moving

*Corresponding author. E-mail: CFD_Safaiy@yahoo.com. Tel: +98 9151022063.

Safaei et al.

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walls of the enclosure move inversely, the heat transfer from the enclosure is more than the state that walls slide on one direction. On the other hand, since a long time ago, the behavior of fluids and their characteristics have been focused. Considering the linear relation between the changes in shear stress and rate of shear strain, the behavior of many...

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