Effect of Two Radial Fins on Heat Transfer and Flow Structure in a Horizontal Annulus

Authors: Anas El Amraoui, Abdelkhalek Cheddadi, Mohammed Touhami Ouazzani

Abstract:

Laminar natural convection in a cylindrical annular cavity filled with air and provided with two fins is studied numerically using the discretization of the governing equations with the Centered Finite Difference method based on the Alternating Direction Implicit (ADI) scheme. The fins are attached to the inner cylinder of radius r_i (hot wall of temperature T_i). The outer cylinder of radius r_o is maintained at a temperature T_o (T_o < T_i). Two values of the dimensionless thickness of the fins are considered: 0.015 and 0.203. We consider a low fin height equal to 0.078 and medium fin heights equal to 0.093 and 0.203. The position of the fin is 0.82π and the radius ratio is equal to 2. The effect of Rayleigh number, Ra, on the flow structure and heat transfer is analyzed for a range of Ra from 10³ to 10⁴. The results for established flow structures and heat transfer at low height indicate that the flow regime that occurs is unicellular for all Ra and fin thickness; in addition, the heat transfer rate increases with increasing Rayleigh number and is the same for both thicknesses. At median fin heights 0.093 and 0.203, the increase of Rayleigh number leads to transitions of flow structure which correspond to significant variations of the heat transfer. The critical Rayleigh numbers, Ra_c.app and Ra_c.disp corresponding to the appearance of the bicellular flow regime and its disappearance, are determined and their influence on the change of heat transfer rate is analyzed.

Keywords: Natural convection, fins, critical Rayleigh number, heat transfer, fluid flow regime, horizontal annulus.

References:

[1] S. Acharya, Sukanta K. Dash, Natural convection heat transfer from a hollow horizontal cylinder with external longitudinal fins: A numerical approach. Numerical Heat Transfer, Part A: Applications, 2018.
[2] T Bhattacharyya, R Anandalakshmi, K. Srinivasan, Heat Transfer Analysis on Finned Plate Air Heating Solar Collector for its Application in Paddy Drying. Energy Procedia, 2017.
[3] A. Nag, A. Sarkar, V. M. K. Sastri, Effect of Thick Horizontal Partial Partition Attached to One of the Active Walls of a Differentially Heated Square Cavity. Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology, 1994.
[4] A. Elatar, M. A. Teamah, M. A. Hassab, Numerical study of laminar natural convection inside square enclosure with single horizontal fin. International Journal of Thermal Sciences, 2016.
[5] Y. Taher, A. Cheddadi, M. T. Ouazzani, Heat transfer in an annular space provided with fins: numerical simulation of the effect of the fins width. Phys. Chem. News, 2006.
[6] A. Idrissi, A. Cheddadi, M.T. Ouazzani, Heat transfer in annular space containing heating blocks with moderate heights multicellular flows, Phys. Chem. News, 2015.
[7] A. El Amraoui, A. Cheddadi, M.T. Ouazzani, Effect of Flow Regimes on The Heat Transfer in An Annular Cavity with Two Internal Blocks, Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 2020.