Slender Orientation Research Articles

ZERO NANOPARTICLES FLUX EFFECT ON NATURAL CONVECTION ABOUT A CYLINDER OF ELLIPTIC CROSS SECTION IN POROUS MEDIA FILLED WITH A NANOFLUID

In this investigation, numerical analysis was performed on the zero nanoparticle flux (ZNF) effect on natural convection in a cylinder with an elliptical cross section embedded in Darcy porous media filled with a nanofluid. The boundary conditions of the cylinder with the elliptical cross section were maintained at uniform wall temperature and ZNF to ensure that the results obtained were realistic and useful. The model adopted for the nanofluid incorporated the effects of Brownian motion and thermophoresis. The non-similar governing equations were obtained by using an appropriate coordinate transformation, and then solved by the Keller box method. Comparisons with previously published work showed good agreement. Numerical data for the dimensionless temperature profiles and Nusselt numbers are presented in graphical and tabular forms for the eccentric angle (B), buoyancy ratio (Nr = 0.4), Brownian motion parameter (Nb = 0.3), thermophoresis parameter (Nt), and the Lewis number (Le). Increasing the thermophoresis parameter and the Lewis number decreased the Nusselt number. For blunt orientation, the Nusselt number first increased with increasing eccentric angle, reached a maximum, and then decreased to zero. For slender orientation, the Nusselt number decreased monotonically. The Nusselt number in the blunt configuration initially increased with an increase in the aspect ratio, attained a maximum, and then gradually decreased. For the slender configuration, the Nusselt number decreased. In this paper, the results of the investigated physical aspects of the problem are discussed in detail.

Mixed convection boundary-layer flow of a viscoelastic fluid due to horizontal elliptic cylinder with constant heat flux

This article presents numerical analysis of mixed convection laminar flow of a second grade viscoelastic fluid due to cylinder of elliptic cross-section with prescribed surface heat flux. Dimensionless non-linear analysis is computed employing Keller-box method. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed graphically to examine their behavior along the surface of cylinder. The flow and heat transfer rates are carefully judged while varying the important resulting parameters (mixed convection parameter, viscoelastic parameter aspect ratio, etc.) through sketched graphs keeping major axis of ellipse along and perpendicular to the horizontal. These two positions of major axis are termed as blunt and slender orientations, respectively. The values of skin friction and Nusselt number increase with rise in mixed convection parameter. On the other hand, these quantities lessen by increasing the value of viscoelastic parameter.

Effect of thermal radiation on unsteady mixed convection flow near forward stagnation point over a cylinder of elliptic cross section

The effect of thermal radiation on unsteady mixed convection flow near a forward stagnation point over a cylinder of elliptic cross section is investigated in this paper. The governing equations are transformed into dimensionless partial differential equations by using a suitable transformation and then are solved numerically by using an implicit finite difference scheme known as Keller Box method. The accuracy of the results is verified by comparing the obtained results with the previous studies available in the literature. It is shown that the results are highly accurate and are in good agreement. The separation times for both blunt and slender orientations in the presence of thermal radiation are shown in tabular forms. Moreover, the effects of pertinent parameters including Prandtl number Pr, mixed convection parameter ?, thermal radiation parameter Rd, surface temperature parameter qw and blunt/slender orientation parameter w on the velocity profile, the temperature profile and the Nusselt number are shown graphically. From the present study, it is observed that boundary layer separation occurs early due to thermal radiation and Nusselt number increases for both blunt and slender orientations.

Mixed convection boundary layer flow over a horizontal elliptic cylinder with constant heat flux

Mixed convection boundary layer flow of a viscous fluid over a horizontal elliptic cylinder with a constant heat flux is investigated numerically. The governing partial differential equations are transformed to non-dimensional form and then are solved by an efficient implicit finite different scheme known as Keller-box method. The solutions are expressed in the form of skin friction and Nusselt number, which are plotted against the eccentric angle. The effect of pertinent parameters such as mixed convection parameter, aspect ratio (ratio of lengths of minor axis to major axis), and Prandtl number on skin friction and Nusselt number are illustrated through graphs for both blunt and slender orientations. The increase in the value of mixed convection parameter results in increase in skin friction coefficient and Nusselt number for blunt as well as slender orientations.

Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Free convection from an isothermal elliptical cylinder in Bingham plastic fluids is studied numerically. This work spans a wide range of aspect ratios of the elliptical cylinder () to delineate the effect of shape on the flowfield close to the heated cylinder. The influence of the relevant parameters, namely, Rayleigh number (), Prandtl number (), and Bingham number (), on the momentum and heat transfer characteristics is studied in terms of the yielded/unyielded regions, streamline, isotherm contours, and local Nusselt number for an elliptical cylinder of constant surface area in blunt () and slender orientations (). The Nusselt number shows a positive dependence on the Rayleigh number, and it correlates negatively with Bingham and Prandtl numbers. The blunt orientations () enhance heat transfer as compared to that for a circular cylinder (of equal surface area) while slender orientations () impede it. Using the present numerical results, predictive correlations have been established in terms of the modified Rayleigh number () and Prandtl number (), thereby enabling the prediction of Nusselt number in a new application.

Effect of opposed eccentricity on free convective heat transfer through elliptical annulus enclosures in blunt and slender orientations

This paper presents an experimental investigation for the effect of opposed lateral and vertical eccentricities on free convective heat transfer through elliptical annulus enclosures in blunt and slender orientations. Three test specimens of elliptical cylinders having an equal radius ratio and an equal length were prepared. The surface area of the inner cylinder is the same for each specimen as well as the area of the outer cylinder. Different elliptical ratios of 0.662, 0.866 and 0.968 were investigated. Experimental tests were done by maintaining constant heat flux on the inner cylinder and the outer one was exposed to approximately constant temperature of the closed laboratory. Both annuals ends of the annular elliptical cylinders were closed by cork to form the annular enclosure space. The experimental tests monitored Rayleigh number (1.642 × 103 ≤ Ra* ≤ 3.849 × 106). The effects of both opposed vertical and lateral eccentricities for both blunt and slender orientations were investigated. The experimental results were fitted by correlations. Considerable agreement was found in the comparison among the results of present and previous works. Opposed eccentricity enhances free convective heat transfer by about 40 % from concentric. Slender orientation results in more enhancements in free convection than blunt one.

Unsteady Mixed Convection Flow over a Cylinder of Elliptic Cross Section near Forward Stagnation Point

The unsteady mixed convection flow over a cylinder of elliptic cross section when the major axis is horizontal (blunt orientation) or vertical (slender orientation) near forward stagnation point is studied. The unsteadiness is due to an impulsive motion on the free stream. The governing boundary layer equations are first reduced into a non-dimensional form, and then transformed into a set of non-similar boundary layer equations, which are solved numerically using an efficient implicit finite-difference method known as Keller-Box method. The numerical results are obtained for various values of the Prandtl number, Pr, the mixed convection parameter, and parameter for blunt and slender orientation, !. The effects of these parameters on velocity profiles, temperature profiles as well as Nusselt number are presented through graphs and tables. The results show that as the mixed convection parameter, is increased, the velocity of the fluid is increased but the temperature of the fluid is decreased, for both blunt and slender orientations. Furthermore, the slender orientation gives earlier separation times for opposing flow while there is no separation of flow detected for the assisting flow. Keywords: unsteady flow; mixed convection; cylinder of elliptic cross section; forward stagnation point. 2010 Mathematics Subject Classification: 76B99; 76R99.

Natural Convection of Water Near its Density Maximum around a Cylinder Inside an Elliptical Enclosure along Slender Orientation

A numerical investigation of natural convection of water near its density maximum around a cylinder inside the concentric elliptical enclosure along slender orientation was carried out. The effects of the aspect ratio, the elliptical ratio, the density inversion parameter, and the Rayleigh number were investigated. The typical flow and thermal fields were exhibited by means of streamlines and isotherms, respectively. Variations of the local and average Nusselt numbers were obtained and discussed with the details of both flow and thermal fields. The mechanism of oscillation was also analyzed when the stable flow transits to the unstable flow. Based on the simulation results, the heat transfer correlation has been proposed.

Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid

This work studies the free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar governing equations are then solved by the cubic spline collocation method. The effects of the Brownian motion parameter and thermophoresis parameter on the profiles of the temperature, nanoparticle volume fraction and velocity profiles are presented. The local Nusselt number is presented as a function of the thermophoresis parameter, Brownian parameter, Lewis number and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). Results show that the local Nusselt number is increased as the thermophoresis parameter or the Brownian parameter is decreased. The local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased. Moreover, the local Nusselt number of the elliptical cylinder with slender orientation is higher than those of the elliptical cylinder with blunt orientation over the lower half cylinder.

Double diffusion from a horizontal cylinder of elliptic cross section with uniform wall heat and mass fluxes in a porous medium

This work studies the double diffusion near a horizontal cylinder of elliptic cross section with uniform wall heat and mass fluxes in a fluid-saturated porous medium. A coordinate transformation is used to obtain the non-similar governing boundary layer equations. The transformed equations are solved numerically by an efficient cubic spline collocation method. Results for the local surface temperature and the local surface concentration are presented as functions of the Lewis number, the buoyancy ratio, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). As the Lewis number is increased, the local surface concentration decreases while the local surface temperature increases. Moreover, an increase in the buoyancy ratio tends to decrease both the local surface temperature and the local surface concentration.

Experimental study of free convection in an elliptical annular enclosure in blunt and slender orientations

In this paper, free convection heat transfer between two elliptical cylinders having different elliptical ratios in blunt and slender situations was studied experimentally. Three pairs of elliptical cylinders having the same radius ratio of 2.0, the same surface area and different elliptical ratios of 0.662, 0.866 and 0.968 were cut using the computed numerically controlled wire-cut machining. The tests were carried out by keeping a constant heat flux on the inner cylinder while cooling the outer one to be isothermal. The effects of vertical eccentricity, lateral eccentricity, angle of attack of the inner cylinder on natural convection for both blunt and slender situations of each pair were investigated. Empirical correlation was deduced within an acceptable uncertainty for the experimental results. Compatible and satisfactory to the conscience agreement was found in the comparison among the results of present and previous works. In the vision of the comparison, it was found that; the vertical eccentricity can enhance free convection by about 15% than the concentric case, the horizontal eccentricity can enhance natural convection by about 10% than concentric case and slender situation offers about 40% enhancement in free convection than the blunt situation for the same elliptical ratio.

Natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and internal heat generation

In this paper the natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and temperature dependent internal heat generation is investigated. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. An increase in the aspect ratio of the elliptical cylinder decreases the average surface temperature of the elliptical cylinder with blunt orientation, while it increases the average surface temperature of the elliptical cylinder with slender orientation. Moreover, an increase in the heat generation parameter for natural convection flow over a horizontal elliptic cylinder with constant heat flux leads to an increase in the average surface temperature of the elliptical cylinder.

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.

A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model

This work uses a thermal non-equilibrium model to study the free convection boundary layer flow driven by temperature gradients near a permeable horizontal cylinder of elliptic cross-section with constant wall temperature in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar boundary layer equations. The transformed boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt numbers are presented as functions of the porosity scaled thermal conductivity ratio, the heat transfer coefficient between solid and fluid phases, the transpiration parameter, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). An increase in the porosity scaled thermal conductivity ratio or the heat transfer coefficient between the solid and fluid phases increases the heat transfer rates. Moreover, the use of suction (positive transpiration parameter) tends to increase the heat transfer rates between the porous medium and the surface.

Natural Convection Heat and Mass Transfer From a Horizontal Cylinder of Elliptic Cross Section with Constant Wall Temperature and Concentration in Saturated Porous Media

AbstractThis work studies the natural convection heat and mass transfer near a horizontal cylinder of elliptic cross section with constant wall temperature and concentration in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar governing boundary layer equations. The transformed governing equations are then solved by the cubic spline collocation method. Results for the local Nusselt and Sherwood numbers are presented as functions of the Lewis number, the buoyancy ratio, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). The heat and mass transfer rates of the elliptical cylinder with slender orientation are higher than those with blunt orientation.

The effect of temperature-dependent viscosity on the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature-dependent viscosity. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of viscosity-variation parameter, aspect ratio, and Prandtl number. The total heat transfer rate and the total skin friction of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, increasing the viscosity-variation parameter tends to enhance the heat transfer rates from a horizontal elliptical cylinder.

Free convection heat and mass transfer from a horizontal cylinder of elliptic cross section in micropolar fluids

This work examines the natural convection heat and mass transfer near a horizontal cylinder of elliptic cross section with constant wall temperature and concentration in a micropolar fluid. The transformed governing equations are then solved by the cubic spline collocation method. Results for local Nusselt and Sherwood numbers are presented as functions of vortex viscosity parameter and aspect ratio. The heat and mass transfer rates of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, the heat and mass transfer rates from an elliptical cylinder in Newtonian fluids are higher than those in micropolar fluids.

Natural convection from a buried elliptic heat source

Numerical solutions are presented for the natural convection heat transfer from an elliptic heat source buried beneath a semi-infinite, saturated, porous medium. The surface of the medium is assumed to be permeable. The governing equations for Darcy flow are solved using finite differences. The complicated geometry is handled through the use of a body-fitted curvilinear coordinate system. Results are presented for Ra values ranging from 10 to 200 and ellipse aspect ratio values from 1.0 (circular cylinder) to 0.167. Two body orientations have been considered. The slender orientation yields much higher hear transfer rates (especially at low ellipse aspect ratio values) than the blunt orientation. The numerical simulations indicate that the boundary-layer approximations cannot be employed for low ellipse aspect ratios. In addition, the heat loss does not depend on the burial depth.