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 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.     

Prediction of onset of boundary layer transition in film condensation on a horizontal elliptical cylinder

This article is devoted to a numerical study of prediction of the onset of the boundary layer transition in film condensation of pure saturated vapor on a horizontal elliptical tube, under the simultaneous effects of gravity, shear stress, and the imposed pressure gradients, caused by the vapor flow and curvature, on the condensate film. The inertia and convection terms are retained in the analysis. The hypothesis of Shekriladze and Gomelauri is used at the liquid-vapor interface. Outside the boundary layer, the vapor phase velocity is obtained from potential flow. Temperature, velocity distribution, and dimensionless apparent turbulent stress of the fully developed flow are carried out using the implicit Keller method. The effects of pressure gradients characterized by Froude number, ellipticity, and Bond number on the transition position have been evaluated. The transition criterion has been given in terms of the critical film Reynolds number ( {\bf Re}_{\bGamma} ) C .     

Entropy generation minimization of free convection film condensation on an elliptical cylinder

This paper aims to perform thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical cylinder. This analysis provides us how the geometric parameter-ellipticity affects entropy generation during film-wise condensation heat transfer process. The results observe that local condensate film thickness decreases with an increase in ellipticity of a cylinder. From the first law point of view, the local heat transfer coefficient enhances as ellipticity increases. Meanwhile, from the second law point of view, entropy generation increases with increasing the value of ellipticity. We derive an expression for entropy generation, which accounts for the combined action of the specified irreversibilities. The result demonstrates that thermal irreversibility dominates over film flow friction irreversibility. Finally, an expression of minimizing entropy generation in laminar film condensation heat transfer is obtained.     

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.     

Effect of non-uniform slot injection (suction) on a forced flow over a slender cylinder

An analysis is performed to obtain the non-similar solution of a steady laminar forced convection boundary layer flow over a horizontal slender cylinder including the effect of non-uniform slot injection (suction). The effects of transverse curvature and viscous dissipation are also included in the analysis. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form using suitable transformations and the resulting system of nonlinear coupled partial differential equations is then solved by an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results for the effect of non-uniform slot injection (suction) on skin friction coefficient and heat transfer rate are presented. The effects of transverse curvature, viscous dissipation and Prandtl number on velocity and temperature profiles and skin friction and heat transfer coefficients are also reported.     

Heat Transfer from Pulsating Laminar Impingement Slot Jet on a Flat Surface with Inlet Velocity: Sinusoidal and Square Wave

Heat transfer from a pulsating laminar impingement slot jet on a flat surface was investigated numerically and experimentally. Inlet velocity was considered sinusoidal velocity and square wave velocity. Experimental studies were done only for the sinusoidal velocity state. An inverse heat conduction method, conjugated gradient method with adjoint equation, was used for the experimental estimation of the local heat transfer coefficient along the target surface. Effect of the square wave velocity of the laminar impingement slot jet was studied numerically. The results show pulsations in flow change flow patterns and the thermal boundary layer thickness because of the newly forming thermal boundary layer is extremely small each time the flow is resumed. Heat transfer rate in this state enhances due to pulsating inlet velocity in comparison with steady state. Heat transfer increases with increasing pulsation amplitude. Enhancement in mean heat transfer on the target plate for sinusoidal velocity is rather than square wave velocity.     

Effects of uniform suction and surface tension on laminar filmwise condensation on a horizontal elliptical tube in a porous medium

This study performs a theoretical investigation into the problem of steady filmwise condensation flow over the external surface of a horizontal elliptical tube embedded in a porous medium with suction at the tube surface. The combined effects of the surface tension force and the gravitational force in driving the flow of the liquid film within the porous medium are modeled using Darcy's law. An effective suction function, f, is introduced to model the effect of the suction force at the wall on the thickness of the condensate film. The theoretical results presented in this study show that the heat transfer performance can be enhanced by applying a suction effect at the wall. Furthermore, it is shown that the surface tension force has a negligible effect on the mean Nusselt number.     

Mixed free and forced convection in the incompressible boundary layer along a rotating vertical cylinder with fluid injection

We examine the steady incompressible laminar boundary layer flow along a vertical cylinder with isothermal walls. The mixed free and forced convection regime is studied while injection/suction of fluid can take place through the cylinder surface. The two-dimensional boundary layer equations are solved using an efficient finite difference scheme, and velocity and temperature profiles, as well as skin friction, heat transfer and pressure coefficients, are calculated. It is proved that fluid injection can considerably reduce the skin friction and heat transfer at the wall. Also, significant differences are reported when the present results are compared with published results for the zero mass transfer case.     

Interface Shape and Marangoni Effect Around aBubble Within the Thermal Boundary Layer

INTRoDUCTIoNDuetohighheattransferperformancecharacter-izedbysmalltemPeraturedifferencesandhighheatfluxes,transportprocesseswithphasechange,espe-ciallyboilingandcondensationprocessesarewidelyemployedinnumerousenergyconversionandtrans-portsystems,heatingand/orcoolingdevices,andaerospaceaPplications.Priortotheutilizationofboil-ingprocessesinspaceapplications,suchasspacecraftthermalcontrol,additionalunderstandingofboilingheattransferbehaviorisneeded.Becauselargedmer-encesekistinthefiuiddensiti…     

Condensate drop movement in Marangoni condensation by applying bulk temperature gradient on heat transfer surface

The spontaneous movement of condensate drops by application of a bulk temperature gradient on the heat transfer surface in Marangoni condensation was investigated, with consideration for applications to heat transfer devices. In the Marangoni condensation process, the removal of condensate on the heat transfer surface is important to maintain good heat transfer. A heat transfer device, in which the liquid movement occurs without external forces such as gravity and vapor shear force, may be useful in various applications. As a result of experiments using a water–ethanol vapor mixture, the movement of droplets from the low‐temperature side to high‐temperature side could be observed on a horizontally arranged heat transfer surface. The relation between the velocity of drop movement and the gradient of surface tension was studied for different concentrations. Furthermore, the effect of inclination of the condensing surface was examined. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(7): 387–397, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20218     

Turbulent film condensation on a half oval body

The paper is an investigation of turbulent film condensation on a half oval body. The high tangential velocity of the vapor flow at the boundary layer is determined from potential flow theory. The Colburn analogy is used to define the local liquid-vapor interfacial shear which occurs when the high velocity vapor flows across the body surface. The paper then presents a discussion of the results obtained for the local dimensionless film thickness and heat transfer characteristics. Furthermore, the present paper discusses the influence of Froude number, sub-cooling temperature and system pressure on mean Nusselt number.     

Non-uniform double slot injection (suction) on a forced flow over a slender cylinder

A general analysis has been developed to investigate the influence of non-uniform double slot injection (suction) on the steady non-similar incompressible laminar boundary layer flow over a slender cylinder, where the slender cylinder is inline with the flow. Non-similar solutions are obtained starting from the origin of the stream-wise coordinate along the stream-wise direction by using an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results are reported to display the effects of non-uniform double slot injection/suction on skin friction coefficient and heat transfer rate at the wall. Further, the effects of viscous dissipation and Prandtl number on velocity and temperature profile, and skin friction and heat transfer co-efficients are also presented in this paper.     

Characteristics of condensate drop movement with application of bulk surface temperature gradient in Marangoni dropwise condensation

The characteristics of the spontaneous movement of condensate drops when a bulk temperature gradient is applied to a horizontal condensing surface in Marangoni dropwise condensation of a water?ethanol vapor mixture were experimentally investigated over a wide range of bulk temperature gradients and for various mass fractions. Drops were observed to move from the low-temperature side to the high-temperature side of the heat transfer surface. When the initial drop distance was adopted as a parameter for the Marangoni force acting on the condensate drop together with the surface tension gradient corresponding to the surface temperature of the condensing surface, the drop velocity was highly correlated with both the surface tension gradient and the initial drop distance over a wide range of parameters. At relatively large initial drop distances, the condensate drop velocity increases as the initial drop distance is reduced and it subsequently decreases after the velocity reaches its maximum value under an almost constant bulk surface tension gradient. The drop velocity increases linearly with increasing bulk surface tension gradient for a constant initial drop distance.     

Spectral relaxation method analysis of Casson nanofluid flow over stretching cylinder with variable thermal conductivity and Cattaneo–Christov heat flux model

This article deals with non‐Newtonian Casson nanofluid flow and heat transfer over stretching cylinder in a porous medium. The mode of heat transfer is presented considering temperature‐dependent thermal conductivity by integrating the Cattaneo–Christov heat flux and mass flux models. Boundary layer theory is applied to develop the governing partial differential equations from the physical problem. Employing proper similarity transformation, the governing boundary layer equations are transformed into dimensionless system of nonlinear ordinary differential equations. Then, the resulting problem is numerically solved by means of spectral relaxation method. The convergence analysis of the proposed numerical scheme is presented via a table, which confirms almost the 10th order of approximation is enough for the convergence of the skin friction coefficient, local heat transfer, and mass transfer rates. The effects of various embedded parameters on velocity, temperature, and concentration profiles as well as skin friction coefficient, surface heat and mass transfer rates are examined through graphs and tables. The findings reveal that the growth of permeability and velocity slip parameters appears to decelerate the velocity distributions of fluid. Thermal boundary layer thickness tends to develop with greater values of permeability and Brownian motion parameters. Also, the local heat transfer rate is less with Fourier's law of heat conduction than Cattaneo–Christov heat flux model. Furthermore, the validity and accuracy of the present result is checked with the available literature, and very sound agreement has been obtained.     

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.     

Influence mechanism of rotation on the convective heat transfer and fluid-flow characteristics from a large diameter rotating isothermal cylinder

A micro-thermocouple is specially designed and employed to measure the temperature distribution in the boundary layer around a cylinder surface, and the influence mechanism of rotation on the convective heat transfer characteristics from a large diameter rotating isothermal cylinder has been experimentally investigated. The effect of rotation on the trailing vortex is observed and analyzed by using a schlieren apparatus. The results show that rotation has an obvious effect on the air flow and temperature distribution characteristics around the cylinder surface. There exists a worst convective heat transfer region which does not coincide with the trailing vortex region as previously reported.     

Buoyancy-Aided Mixed Convection Between Shear-Thinning Non-Newtonian Nanofluids and Unbounded Elliptic Cylinders in a Vertical Channel

Abstract

This work presents buoyancy-driven mixed convective flow and heat transfer phenomena of an isothermally heated horizontal elliptic cylinder in vertically upward unbounded flow of power-law type non-Newtonian nanofluids using ANSYS Fluent. The governing continuity, momentum and energy equations for the shear-thinning power-law nanofluids along with suitable boundary conditions are simultaneously solved within the limitations of Boussinesq approximation. The semi implicit method for pressure-linked equations algorithm along with the quadratic upstream interpolation for convective kinematics scheme for discretizing the convective terms in both momentum and energy equations are adopted. The ranges of parameters considered for this study are: volume fraction of nanoparticles, 0.005–0.045; aspect ratio of elliptic cylinder, 0.5–2.5; and Richardson number, 0–40; and a representative Reynolds number of 20. The streamline patterns, surface pressure coefficient distributions, total drag coefficients, isotherm contours, and Nusselt numbers are presented for better understanding of heat transfer and flow phenomena around elliptic cylinders. Briefly results indicate that the total drag coefficient is found to increase with the increasing Richardson number whereas it decreases with the increasing volume fraction of nanoparticles. The average Nusselt numbers are found to increase with increasing Richardson number and increasing volume fraction of nanoparticles.     

Unsteady mixed convection from a rotating vertical slender cylinder in an axial flow

Unsteady mixed convection flow over a rotating vertical slender cylinder under the combined effects of buoyancy force and thermal diffusion with injection/suction has been studied where the slender cylinder is inline with the flow. The effect of surface curvature is also taken into account, especially for the applications such as wire and fiber drawing, where accurate predictions are desired. The governing boundary layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled nonlinear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. The effects of various parameters on velocity and temperature profiles and on skin friction coefficients and heat transfer rate at the wall are reported in the present study.