Effect of Flow Regimes on The Heat Transfer in An Annular  Cavity with Two Internal Blocks

Anas El Amraoui; Abdelkhalek Cheddadi; Mohammed Touhami Ouazzani

Authors

Anas El Amraoui Modeling of Energy Systems, Materials and Mechanical Structures, and Industrial Processes, MOSEM2PI, Mohammadia School of Engineers, Mohammed V University in Rabat, Ibn Sina Str., P.O.Box 765 Agdal, Rabat, Morocco
Abdelkhalek Cheddadi Modeling of Energy Systems, Materials and Mechanical Structures, and Industrial Processes, MOSEM2PI, Mohammadia School of Engineers, Mohammed V University in Rabat, Ibn Sina Str., P.O.Box 765 Agdal, Rabat, Morocco
Mohammed Touhami Ouazzani Modeling of Energy Systems, Materials and Mechanical Structures, and Industrial Processes, MOSEM2PI, Mohammadia School of Engineers, Mohammed V University in Rabat, Ibn Sina Str., P.O.Box 765 Agdal, Rabat, Morocco

Keywords:

Annular cylindrical cavity, blocks, bicellular flow, heat transfer, secondary cell size

Abstract

The present paper analyses numerically the flow fields in an annular cylindrical cavity provided with two isothermal blocks of different heights for Rayleigh numbers ranging from 103 to 104 . The steady-state solutions have been obtained using the discretization of the governing equations with the Centered Finite Difference method based on the Alternating Direction Implicit (ADI) scheme. The two blocks are arranged in the upper part of the annular cavity at φm = 0.82π. The radii ratio and the thickness of the blocks are kept fixed at the respective values of R = 2 and w = 0.203. For low block heights between 0.015 and 0.078, only the unicellular flow regime (UCR) is observed regardless of the Rayleigh number. The heights ranging from 0.093 to 0.953 give rise to flows that are more complex. The results are illustrated in the form of streamlines, isotherms, average Nusselt number and the size of the secondary cell located in the upper part of the cavity. For given Rayleigh numbers, the critical heights hc,app, which characterize the appearance of the bicellular flow regime (BCR) and those describing the development of this regime, hc,inc, are determined. Similarly, for given heights, the critical Rayleigh numbers, Rac,app and Rac,inc, which respectively determine the appearance of the BCR regime and the increase of the size and intensity of the secondary cell, are specified. The influence of these parameters on the heat transfer is studied.