The purpose of this paper is to compare the numerical laminar two‐dimensional unsteady natural convection in a partial sector‐shaped enclosure submitted respectively to a constant heat flux density q1 and a uniform temperature T1 on the inner cylindrical wall. The numerical model performed in this paper is applied more particularly for high Grashof numbers, in order to point out the advent and the development of pre‐turbulent flows. Results of numerical runs are presented. The mean Nusselt number on active walls is represented as a function of the Grashof number Gr and the aspect ratio Fr. The results may be correlated very well with an expression of the form \overlineNu = k1 Gr1k2, for technical calculations.
If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. AbstractPurpose -The purpose of this paper is to study the transient natural convection of a Newtonian fluid which develops in a closed spherical annulus delimited by two vertically eccentric spheres by using a bispherical coordinates system. The inner sphere is heated by a heat flux of constant density and the outer one is maintained isothermal. Design/methodology/approach -The transfer equations are written by using a bispherical coordinates system. The Navier-Stokes equations are solved and coupled with the energy equation by using the alternating direction implicit (ADI) and the successive over relaxation (SOR) methods. Findings -The study of the stream function and the Nusselt number shows that the convection motion is reinforced for the geometries characterized by positive values of the eccentricity with heat exchange increasing. The Nusselt number increases with the modified Rayleigh number. The heat exchange increases with the radius ratio. The results show that the steady state is reached faster when the modified Rayleigh number increases and the influence of the eccentricity is very low on the establishment of the steady state. The fluids flow depends strongly on the eccentricity and the modified Rayleigh number. Research limitations/implications -Simulations are performed for modified Rayleigh numbers ranging from 10 3 to 10 6 , for eccentricities varying between -0.6 and þ0.6 and for radius ratio between 1.5 and 2. Originality/value -The results of eccentricity and modified Rayleigh number effects in transient natural convection between vertically eccentric spheres have been displayed. NomenclatureLatin letters a ¼ parameter of torus pole [m] D ¼ hydraulic diameter, D ¼ r i À r e [m] e ¼ eccentricity, e ¼ O i O e D g ¼ gravitational acceleration[m s À2 ] G 1 and G 2 ¼ coefficients, G 1 ¼ G 1 ð; Þ ¼ 1 À cos uchh chh À cos u and G 2 ¼ G 2 ðh; uÞ ¼ À sin ushh chh À cos u
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