Fully developed mixed convection in horizontal and inclined tubes with uniform heat flux using nanofluid

Fully developed laminar mixed convection of a nanofluid consists of water and Al₂O₃ in horizontal and inclined tubes has been studied numerically. Three-dimensional elliptic governing equations have been solved to investigate the flow behaviors over a wide range of the Grashof and Reynolds numbers. Comparisons with previously published experimental and numerical works on mixed convection in a horizontal and inclined tube are performed and good agreements between the results are observed. Effects of nanoparticles concentration and tube inclinations on the hydrodynamics and thermal parameters are presented and discussed. It is shown that the nanoparticles concentration does not have significant effects on the hydrodynamics parameters. Heat transfer coefficient increases by 15% at 4 Vol.% Al₂O₃. Skin friction coefficient continually increases with the tube inclination, but the heat transfer coefficient reaches a maximum at the inclination angle of 45°.     

Shape analysis based critical Eotvos numbers for buoyancy induced partial detachment of oil drops from hydrophilic surfaces

Removal of oil drops from solid surfaces immersed in an aqueous medium is of interest in many applications. It has been shown that drop shape analysis can be used to predict conditions at which the stability limit of a lighter than water oil drop on a solid surface immersed in an aqueous bath is reached (Adv. Colloid Interface Sci. 98 (2002) 265). However the above analysis is restricted to cases where the contact angle made by the drop is below 90degrees and when the surface conditions result in a 'pinned' contact line. In this paper, it is shown that drop shape analysis can be used to predict the critical conditions at which drop stability limit is reached for drop contact angles of 90degrees and above, which is encountered with 'hydrophilic' surfaces. This critical condition can predict the occurrence of partial oil drop detachment, before complete removal due to 'roll-up', which occurs when the hydrophilic surface is adequately smooth which prevents 'pinning' of the contact line. The critical conditions at which partial drop detachment occurs can also be approximately predicted from simple force balances. It has been shown (Adv. Colloid Interface Sci. 98 (2002) 265) that for contact angles less than 90degrees, the critical limit based on shape analysis appears to resolve the differences that arise due to alternate expressions for capillary retention force. This paper shows that even for contact angles above 90degrees, the critical conditions predicted from the shape analysis resolves the differences in the predictions from the alternate force balances. Drop shape analysis used in this paper is based on the 'Arc-length' form of Young-Laplace or 'drop shape' equation, which is different from the 'Y vs X' form of the above equation that is used in Adv. Colloid Interface Sci. 98 (2002) 265. The above drop shape equation is solved by a fourth order Runge-Kutta technique and it is shown that for angles less than 90degrees, the two forms of the drop shape equation, predict almost identical values of the critical Eotvos number. This paper highlights the competing effects of interfacial tension lowering induced drop instability and 'roll-up', a term that is used to describe the retraction of the contact line of an oil drop on a surface, in being the primary c ause for drop detachment.     

A 3D numerical simulation of mixed convection of a magnetic nanofluid in the presence of non-uniform magnetic field in a vertical tube using two phase mixture model

In this paper, results of applying a non-uniform magnetic field on a ferrofluid (kerosene and 4 vol% Fe₃O₄ ) flow in a vertical tube have been reported. The hydrodynamics and thermal behavior of the flow are investigated numerically using the two phase mixture model and the control volume technique. Two positive and negative magnetic field gradients have been examined. Based on the obtained results the Nusselt number can be controlled externally using the magnetic field with different intensity and gradients. It is concluded that the magnetic field with negative gradient acts similar to Buoyancy force and augments the Nusselt number, while the magnetic field with positive gradient decreases it. Also with the negative gradient of the magnetic field, pumping power increases and vice versa for the positive gradient case.     

Buoyancy-driven convection of water near its density maximum with time periodic partially active vertical walls

The effect of density inversion on transient natural convection heat transfer of cold water in a square cavity with partially active vertical walls is studied numerically. The governing equations are solved by control volume method with power law scheme. In the hot location the temperature is varied sinusoidally and in the cold location uniform temperature is maintained. Nine different positions of the active zones are considered. Results are discussed for various values of the amplitude, period and different Grashof numbers and presented graphically in the form of isotherms, streamlines, mid-height velocity profile and average Nusselt number. It is found that density inversion of water affects natural convection flow and heat transfer. Heat transfer rate is enhanced upto 80% when the heating location is in the middle of the hot wall.     

Surface tension and buoyancy-driven flow in a non-isothermal liquid bridge

The Navier–Stokes–Boussinesq equations governing the transport of momentum, mass and heat in a non-isothermal liquid bridge with a temperature-dependent surface tension are solved using a vorticity-stream-function formulation together with a non-orthogonal co-ordinate transformation. The equations are discretized using a pseudo-unsteady semi-implicit finite difference scheme and are solved by the ADI method. A Picard-type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary-driven flow situations and mixed thermocapillary- and bouyancy-driven flow.     

Unsteady boundary layer and its separation over a heated circular cylinder

A numerical method is developed to solve the coupled unsteady laminar momentum and thermal boundary layers over a circular cylinder impulsively started from rest. The present non-iterative finite difference method, which requires relatively fewer grid points in the reversed flow region than any other method, can easily handle the separating boundary layer flows. The results indicate that the present method has accuracy comparable with the earlier methods, while consuming computer time approximately one order of magnitude less. The present numerical method allowed investigation of the effect of buoyancy parameter on the starting boundary layer. The time-dependent behaviour of the boundary layer is studied in terms of the appearance of the singularity, the distribution of skin friction and wall heat flux, and the wall position of the inflection point of the velocity profile. The transient as well as buoyancy-dependent patterns of the streamlines and isotherms are also studied.     

Numerical and analytical modelling of the MHD buoyancy-driven flow in a Bridgman crystal growth configuration

We present analytical and numerical models of magnetohydrodynamic(MHD) buoyancy-driven flow within the liquid pool of a horizontal Bridgman crystal growth furnace, under the influence of a uniform vertical magnetic field B₀. A horizontal differentially heated cylinder, whose aspect ratio (radius to length) is small enough for a fully developed regime to be established in the central core, is considered. With Hartmann layers remaining electrically inactive, a modified Rayleigh number Ra_G, which is the ration of the ordinary Rayleigh number to the square of the Hartmann number, is found to control the MHD reorganisation of the flow. This modified Rayleigh number is a measure of the importance of thermal convection relative to diffusion if velocity is estimated from the balance between the torques of buoyancy and the Laplace force. When Ra_G is much smaller than unity (quasi-diffusive regime), an analytical modelling of the flow, based on a power series of Ra_G, demonstrates that this balance requires secondary vortices within vertical mid-planes of the cylinder, both within the core flow and near the end walls. A 3-D numerical calculation of the flow provides evidence of the transition from a convective MHD flow (when Ra_G is still of the order of unity) to the quasi-diffusive flow, analytically studied. Indeed, this transition takes the form of a rather complex 3-D MHD organisation of the flow which is due to the nonuniformity of the axial temperature gradient along the cylinder.     

竖直细圆管中超临界氮的对流换热研究

在内径为2mm的竖直细圆管内进行了向上流动的超临界对流换热实验。通过实验发现,质量流量、进口温度对壁面温度分布以及压降有很大影响;并讨论了换热发生增强和恶化的原因;用浮升力和热加速准则解释了其中的一些热流体现象。并基于FLUENT软件进行了数值计算,与实验结果进行比较,分析表明,数值计算预测壁面温度分布和压降有一定的适用性。