Circular Sector Ducts Research Articles

Escoamento laminar em dutos de setor circular

The fluid flow inside ducts is of great importance in engineering, because it is present in most domestic, commercial, and industrial application equipments. In this work was presented a hybrid analytical-numerical solution to hydrodynamic problem of fully developed laminar flow inside circular sector ducts. In order to facilitate the analytical treatment and the application of the boundary conditions, a Conformal Transform was used. Thereafter, the Generalized Integral Transform Technique was applied on the momentum equation to obtain the velocity field. Numerical results were obtained for quantities of practical interest, such as maximum and minimum velocity, Fanning friction factor, Poiseuille number, Hagenbach factor, and hydrodynamic entry length. The results were compared, as much as possible, with the parameter values available in the literature and they presented a great agreement, with a difference less than 1.5%. Keywords: Integral Transform, Conformal Transform, Laminar Flow, Newtonian Fluid, Circular Sector.

Unsteady flow in a circular sector duct

Analytic solutions for the unsteady flow in a circular sector duct are found using series sums of Bessel integrals. For starting flow due to a step pressure gradient, the velocity profile is initially flat, then approaches the rounded steady state shape in a time scale proportional to the square of opening angle of the sector. For oscillatory flow, the velocity is quasi-steady for low frequencies, but shows “annular effect” at large frequencies. Increased opening angle increases the amplitude and the phase lag. In all cases, the shear stress at the apex is zero for acute sector angles but becomes infinite for obtuse sector angles.

NUMERICAL INVESTIGATION OF FLOW AND HEAT TRANSFER IN TWISTED CIRCULAR-SECTOR DUCTS

Flow and heat transfer in a twisted circular-sector duct are analyzed numerically for steady, fully developed, and incompressible laminar flow with a uniform-wall-temperature boundary condition. A rotating coordinate system is employed to account for the duct twist. The friction factors and Nusselt numbers are predicted for duct sector angles ranging from 15° to 90°, Reynolds numbers ranging from 1 to 1,000, and Prandtl numbers ranging from 1 to 100. Results show significant influence of duct twist on both friction factors and Nusselt numbers, particularly at large values of Reynolds and Prandtl numbers. Accurate correlations are developed to predict the friction factors and Nusselt numbers for the entire range of geometric and operating conditions studied.

Nonlinear parameter estimation in laminar forced convection within a circular sector tube

In this article we examine an inverse heat convection problem of estimating unknown parameters of a parameterized variable boundary heat flux. The physical problem is a hydrodynamically developed, thermally developing, three-dimensional steady state laminar flow of a Newtonian fluid inside a circular sector duct, insulated in the flat walls and subject to unknown wall heat flux at the curved wall. Results are presented for polynomial and sinusoidal trial functions, and the unknown parameters as well as surface heat fluxes are determined. Depending on the nature of the flow, on the position of experimental points the inverse problem sometimes could not be solved. Therefore, an identification condition is defined to specify a condition under which the inverse problem can be solved. Once the parameters have been computed it is possible to obtain the statistical significance of the inverse problem solution. Therefore, approximate confidence bounds based on standard statistical linear procedure, for the estimated parameters, are analyzed and presented.

95/04318 Laminar flow developing heat transfer in circular sector ducts with Hl a and H2 a boundary conditions

95/04318 Laminar flow developing heat transfer in circular sector ducts with Hl a and H2 a boundary conditions

Laminar Flow Developing Heat Transfer in Circular Sector Ducts with H1aand H2aBoundary Conditions

Hydrodynamically developed and thermally developing laminar incompressible forced-connective flow in ducts containing twisted-tape inserts is analyzed. The flow is subjected to either uniform temperature or uniform heat flux on the curved duct surface, and the straight duct surfaces are insulated. The heat input into the fluid is only from the curved duel surface and is uniform axially. The thermal properties are assumed constant; the axial conduction and viscous dissipation are negligibly small. Numerical calculations of the temperature field and Nusselt number march forward axially in the thermal entrance region. The solutions of die developing temperature field as well as the heat transfer coefficient are presented as functions of axial distance for different opening angles of sector. Comparisons are made between computed results and some analytical and numerical findings reported in the literature. In all cases, satisfactory comparisons are attained.

Forced convection of thermally developing laminar flow in circular sector ducts

Numerical solutions are presented for laminar, forced convection heat transfer in the thermal entrance region of circular sector ducts using the H1 and H2 thermal boundary conditions. With fully developed hydrodynamics, results are given for duct apex angles of 20°, 45°, 90°, 130°, 180°, 270°, and 360°. For the H1 condition, decreasing apex angle increases the duct corner effects, hence enhancing local and fully developed Nusselt numbers and shortening thermal entrance sections. For the H2 condition, the apex angle influences the thermal quantities differently. The data presented are compared with the limited available solutions and good agreement is found.

Further Analyses of Laminar Flow Heat Transfer in Circular Sector Ducts

Heat transfer in circular sector ducts is often encountered in multipassage tubes. Certain flow characteristics of circular sector ducts for apex angles up to {pi} have been determined as documented by Shah and London (1978). Recently, Lei and Trupp (1989) have more completely analyzed the flow characteristics of fully developed laminar flow for apex angles up to 2{pi}, including the location of the maximum velocity. Heat transfer results of fully developed laminar flow in circular sector ducts are also available for certain boundary conditions. Trupp and Lau (1984) numerically determined the average Nusselt number (Nu{sub T}) for isothermal walls. Eckert et al. (1958) initially derived an analytical expression for the temperature profile for the case of H1. Sparrow and Haji-angles up to {pi}. However, the above work required numerical integration (or equivalent) to obtain a value for Nu{sub H1}. Regarding the H1{sub ad} boundary condition, Date (1974) numerically obtained a limiting value of Nu{sub H1}{sub ad} for the semicircular duct from the prediction of circular tubes containing a twisted tape (straight and nonconducting tape). Hong and Bergles (1976) also reported an asymptotic value of Nu{sub H1}{sub ad} for the semicircular duct from their entrance region solution. Otherwise it appears thatmore » there are no published analytical results of Nu{sub H1}{sub ad} for circular sector ducts. The purpose of this technical note is to communicate these results. In addition, a novel series expression for Nu{sub H1} is presented together with results for apex angles up to 2{pi}.« less

Maximum Velocity Location and Pressure Drop of Fully Developed Laminar Flow in Circular Sector Ducts

Circular sector ducts have become increasingly important as they continue to appear as flow passages in multipassage tubes. They also represent the limiting cases of internally finned tubes have equispaced, full tapered fins. There are no published data for the maximum velocity u{sub max} and its location (r*). For developing laminar flow, this information is very useful in determining hydrodynamic entrance length based on the velocity at r* attaining a particular percentage of the fully developed value. Unlike that of symmetric ducts such as the circular tube and rectangular ducts, the maximum velocity of the circular sector duct occurs away from the centroid on the axis of symmetry. The purpose of this note is to present the results of u{sub max} and r* and to extend the value for fanning friction factor and incremental pressure drop for apex angles up to 2{pi}.

Further Results for Laminar Heat Transfer in Annular Sector and Circular Sector Ducts

Calcul numerique par la methode des differences finies de Nu et du coefficient de friction pour des flux de chaleur uniformes aux frontieres avec des conditions aux limites isothermes

LAMINAR FLOW HEAT TRANSFER IN CIRCULAR SECTOR DUCTS WITH UNIFORM HEAT FLUX

This paper involves theoretical analyses of the heat transfer characteristics for fully developed laminar flow in circular sector ducts with uniform heat flux in both the axial and peripheral directions. With uniform heat input axially, the peripheral condition of uniform heat flux is first imposed only on the curved surface, with the flat surface insulated, and the corresponding Nusselt numbers are computed. Next, results are presented for the present series solution for a uniform peripheral heat flux on all surfaces. The results of these exact solutions provide a complete and accurate pattern of the Nusselt number variations for all apex angles.

ANALYSIS OF FLUID FLOW AND HEAT TRANSFER IN TWISTED CIRCULAR-SECTOR DUCTS

The flow in a twisted circular-sector duct is solved numerically for a steady, incompressible, hydrodynamically and thermally fully developed laminar flow. The wall of the duct is subjected to uniform heat flux per unit axial length with peripherally uniform temperature. A rotating cylindrical coordinate system is introduced to simplify the governing equations to two independent variables. The stream function and vorticity are adopted instead of the primitive variables of velocity and pressure. Friction factor and Nusselt number are presented for values of the duct angle from 11.25 to 90°, dimensionless twist ratio up to 0.7, and Prandtl number from 1 to 100. The results show that the influence of twist on friction and heat transfer is significant at high Reynolds numbers and high Prandtl numbers.

Analysis of Fluid Flow and Heat Transfer in Twisted Circular-Sector Ducts

Analysis of Fluid Flow and Heat Transfer in Twisted Circular-Sector Ducts

Laminar Flow in the Entrance Region of Circular Sector Ducts

Laminar Flow in the Entrance Region of Circular Sector Ducts

Laminar Heat Transfer and Pressure Drop in Isosceles Triangular, Right Triangular, and Circular Sector Ducts

Laminar Heat Transfer and Pressure Drop in Isosceles Triangular, Right Triangular, and Circular Sector Ducts