Abstract—Developing mixed convection in circular and annular sector ducts is investigated numerically for steady laminar flow of an incompressible Newtonian fluid with Pr = 0.7 and a wide range of Grashof number (0  Gr  10 7 ). Investigation is limited to the case of heating in circular and annular sector ducts with apex angle of 2ϕ = π/4 for the thermal boundary condition of uniform wall temperature axially and peripherally. A numerical, finite control volume approach based on the SIMPLER algorithm is employed to solve the 3D governing equations. Numerical analysis is conducted using marching technique in the axial direction with axial conduction, axial mass diffusion, and viscous dissipation within the fluid are assumed negligible. The results include developing secondary flow patterns, developing temperature and axial velocity fields, local Nusselt number, local friction factor, and local apparent friction factor. Comparisons are made with the literature and satisfactory agreement is obtained. It is found that free convection enhances the local heat transfer in some cases by up to 2.5 times from predictions which account for forced convection only and the enhancement increases as Grashof number increases. Duct geometry and Grashof number strongly influence the heat transfer and pressure drop characteristics. Keywords—Mixed convection, annular and circular sector ducts, heat transfer enhancement, pressure drop. I. INTRODUCTION HE importance of convective heat transfer in annular and circular sector ducts in many industrial and engineering applications has motivated a significant amount of research. These ducts are encountered for example in multi passage internally finned tubes used in compact heat exchanger applications. Compact heat exchangers frequently involve short passages and hence the flow over the whole or a major part of the heat exchanger is in developing stage [1]. Furthermore, if the flow is laminar, free and forced convection effects are of comparable order of magnitude [2]. Consequently, natural convection and entrance region effects should be considered for better prediction of heat transfer and pressure drop in annular and circular sector duct. The theme of convective heat transfer in smooth pipe has been extensively studied both theoretically and experimentally for the three limiting thermal boundary conditions; uniform heat flux axially and uniform wall temperature peripherally A. A. Abdalla is with the Department of Mechanical Engineering, University of Benghazi, Benghazi, Libya (corresponding author, phone: +218922192935; e-mail: Ayad.abdalla@uob.edu.ly). H. A. Elfergani and E. I. Elhadi are with the Department of Mechanical Engineering, University of Benghazi, Benghazi, Libya (e-mail: Hisham.elfergani@uob.edu.ly, Elhdi_elhdi@yahoo.com). (H1-thermal boundary condition); uniform heat flux axially and peripherally (H2-thermal boundary condition) and uniform wall temperature axially and peripherally (T-thermal boundary condition). Different theoretical approaches were used to tackle the problem: assuming large Prandtl number, [3]-[5]; using numerical methods [6]-[8]. Experimental studies have also been used to investigate this flow configuration [9]- [13]. Prakash and Liu [14] numerically investigated developing forced convection in internally finned tubes. Annular and circular sector ducts have received less attention compared to their smooth pipes counterpart. Closed form analytical solutions are rare and can only be obtained in a small number of cases. For flow in semicircular ducts, several studies have been conducted for different flow conditions; developing forced convection [15], fully developed forced convection [16], [17], fully developed mixed convection [18]- [20], fully developed mixed convection in inclined ducts [21], [22] and developing mixed convection for the H1 boundary condition [23]. Experimental and numerical studies on the H1 boundary condition in circular sector ducts of different apex angles have also been reported [24], [25]. Annular sector ducts have also attracted some research interest; forced convection for the friction factor [26] and heat transfer characteristics [27], and fully developed flow for both the Hl and H2 boundary analytically [28] and numerically [29]. Radiation- affected laminar natural convection in the cylindrical annuli [30] and developing mixed convection in horizontal concentric annulus [31] have been investigated as well. Some studies focused on the influence of other physics on heat transfer and pressure drop in annular and circular such as the presence of porous medium, [32]-[39]; nanofluids, [40]-[42] and non- Newtonian effects [43], [44]. The objective of this study is to investigate the developing steady laminar mixed convection in horizontal annular and circular sector ducts with constant wall temperature. The effect of duct geometry on heat transfer and pressure drop will be studied at different values of Grashof number using the SIMPLER algorithm which is a control volume finite difference based method for solving coupled partial differential equations. II. MATHEMATICAL FORMULATION The current focus is the developing mixed convection in isothermal annular and circular sector ducts. The flow is steady and laminar with negligible axial conduction and viscous dissipation. The fluid is Newtonian and Ayad A. Abdalla, Elhadi I. Elhadi, Hisham A. Elfergani Numerical Investigation of Developing Mixed Convection in Isothermal Circular and Annular Sector Ducts T World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering Vol:15, No:3, 2021 158 International Scholarly and Scientific Research & Innovation 15(3) 2021 ISNI:0000000091950263 Open Science Index, Mechanical and Mechatronics Engineering Vol:15, No:3, 2021 publications.waset.org/10011918/pdf