Cong Tam Nguyen

Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension

Purpose – To study the hydrodynamic and thermal behaviors of a turbulent flow of nanofluids, which are composed of saturated water and Al2O3 nanoparticles at various concentrations, flowing inside a tube submitted to a uniform wall heat flux boundary condition.Design/methodology/approach – A numerical method based on the “control‐volume” approach was used to solve the system of non‐linear and coupled governing equations. The classical κ‐e model was employed in order to model the turbulence, together with staggered non‐uniform grid system. The computer model, satisfactorily validated, was used to perform an extended parametric study covering wide ranges of the governing parameters. Information regarding the hydrodynamic and thermal behaviors of nanofluid flow are presented.Findings – Numerical results show that the inclusion of nanoparticles into the base fluid has produced an augmentation of the heat transfer coefficient, which has been found to increase appreciably with an increase of particles volume co...

Effects of axial diffusion on laminar heat transfer with low Peclet numbers in the entrance region of thin vertical tubes

Laminar upward and downward flows with mixed convection in a thin vertical tube with a short uniformly heated section were investigated numerically. Calculations were performed by solving the elliptic Navier-Stokes and energy equations for slow flows of air (Pr = 0.7) corresponding to low Reynolds numbers from 20 to 500 and a wide range of Grashof numbers. Results reveal that axial diffusion plays a significant role in preheating the fluid upstream from the entrance of the heat transfer region for both aiding and opposing buoyancy, with a stronger effect for the latter, and can lead to flow reversal. By mapping the conditions that correspond to significant preheating and flow reversal on a Grashof-Reynolds plane, it has become possible to establish criteria that determine (1) when the upstream boundary conditions can be applied at the entrance of the heated section and (2) when the elliptical formulation is necessary to describe the flow field accurately. Applications in which this regime of mixed convection occur include shell-tube heat exchangers, and nuclear reactors.

Developing laminar mixed convection of nanofluids in an inclined tube with uniform wall heat flux

Purpose – The aim is to study the conjugate problem of developing laminar mixed convection flow and heat transfer of water‐Al2O3 nanofluid inside an inclined tube submitted to a uniform wall heat flux.Design/methodology/approach – The set of non‐linear, coupled and fully elliptic governing equations has been solved using a “finite‐control‐volume” numerical method, the classical power‐law scheme for computing heat and momentum fluxes staggered and non uniform grids for spatial discretization of various regions of the tube.Findings – Numerical results have shown that the presence of nanoparticles slightly intensifies the secondary flow due to buoyancy, in particular in the developing region. It also increases the average Nusselt number and decreases slightly the product ReCf with respect to those of water. For the horizontal inclination, two new correlations have been proposed to calculate these two variables in the fully developed region, for Grashof number ranging from 103 to 105 and particle volume conce...

Developing mixed convection with aiding buoyancy in vertical tubes: a numerical investigation of different flow regimes

Abstract Laminar upward flows with mixed convection in a vertical tube with a uniformly heated zone preceded and followed by adiabatic zones were investigated numerically. Calculations were performed by solving the elliptic Navier–Stokes and energy equations for air and a wide range of heating lengths, Reynolds and Richardson numbers. Different combinations of these parameters establish the existence of five types of flow fields: developing with or without flow reversal, developing followed by a fully developed region both without flow reversal, and developing with flow reversal followed by a fully developed region with or without flow reversal. The conditions leading to flow reversal as well as significant upstream diffusion of heat and momentum have been mapped on the Peclet–Richardson plane for different lengths of the heated zone.

Bifurcation in steady laminar mixed convection flow in uniformly heated inclined tubes

The fully developed laminar mixed convection flow in inclined tubes subject to axially and circumferentially uniform heat flux has been studied numerically for a Boussinesq fluid. Dual solutions characterized by a two‐ and a four‐vortex secondary flow structure in a cross‐section normal to the tube’s longitudinal axis have been found for different combinations of the Grashof number Gr and of the tube inclination α for all Prandtl numbers between 0.7 and 7. In the two‐parameter space defined by Gr and α dual solutions occur: at a given α, if the Grashof number exceeds a critical value Grl (for horizontal tubes Grl is approximately 5.5 × 105, 1.7 × 105 and 1.7 × 104 respectively for Pr = 0.7, 7 and 70); at a given Gr, if the tube inclination is below a critical value αc (for Gr = 106 this critical angle is approximately 62.5° and 83.5° respectively for Pr = 0.7 and 7). Numerical experiments carried out for developing flows indicate that the two‐vortex solution is the only stable flow structure.

Numerical study of the unstable thermocapillary flow in a silicon float zone under μ–g condition

Abstract In this work, the problem of the hydrodynamic instabilities of the thermocapillary flow inside a Silicon ( Pr =0.016) float zone supported by a pair of coaxial disks and operating under μ – g conditions has been investigated. The system of the conservation equations corresponding to a three-dimensional transient model was directly solved by employing a finite control volumes method fully-implicit in time and a staggered spatial mesh in the cylindrical coordinates system. Results have shown that for a low Marangoni number or a low temperature difference between the disks, the flow remains steady and consists of a perfectly axisymmetrical toroidal structure with the vortex center located beneath the free surface near the cold disk. Beyond the first critical Marangoni number, say Ma cr 1 ≈48, the transition from the axisymmetrical to the steady three-dimensional state has been observed. The flow structure consists of a drastically distorted torus with its vortex centers displaced both radially and axially and is located along a ‘saddle-like’ curve. At the second critical Marangoni number, say Ma cr 2 ≈80, the transition from this three-dimensional-steady-state to the three-dimensional-oscillatory state occurs. Under the effects of some azimuthally travelling instabilities, the entire velocity and temperature fields rotate around the main axis; and a dependent variable varies periodically both in time and space. The flow instabilities, which appear similar to those of the theoretical ‘unstable vortex ring’, are believed to be of the hydrodynamic origin. A detailed description of the internal flow structure and its dynamic behavior as well as a comparison with the previous numerical and experimental data have been given.

VARIABLE-PROPERTY EFFECTS IN LAMINAR AIDING AND OPPOSING MIXED CONVECTION OF AIR IN VERTICAL TUBES

Abstract A numerical investigation has been conducted in order to determine the effects of variable properties on the flow pattern and neat transfer performances in laminar developing ascending flow with mixed convection for two cases: in case J the fluid is heated, and in case II it is cooled. Calculations are performed for air at various Grashof numbers with a fixed entrance Reynolds number of 500 using both the Boussinesq approximation (constant-property model) and a variable-property model. In the latter case, the fluid viscosity and thermal conductivity are allowed to vary with absolute temperature according to simple power laws, while the density varies linearly with the temperature, and the heat capacity is assumed to be constant. The comparison between constant- and variable-property models shows a substantial difference in the temperature and velocity fields when the Grashof number \Gr\ is increased. The friction factor is seen to be underpredicted by the Boussinesq approximation when the fluid i...

Développement simultané hydrodynamique et thermique d'un écoulement laminaire dans un tube incliné en régime de convection mixte

Abstract In this work, we study numerically the heat transfer and fluid flow inside a circular inclined tube. The thermal boundary condition is that of a constant and uniform (axially and circumferentially) heat flux on the tube wall. A finite volume method is used to solve, in dimensionless form, the parabolic equations of mixed convection. The results, obtained for water with different combinations of the Grashof number and the tube inclination, show that the average heat transfer is improved and the wall shear stress is increased compared to those of pure forced flow.

TRANSIENT BEHAVIOR OF A NaNO3 FLOAT ZONE OPERATING AT HIGH MARANGONI NUMBER UNDER μg CONDITIONS

This work is concerned with the problem of transient behavior of the ansymmetric thermocapillary laminar flow that occurs inside a NaNO3 cylindrical float zone subject to variable surface tension. The molten liquid is assumed to be incompressible, with constant properties, except for the fluid density, which appears in buoyancy forces. It has been shown that the problem under study can be characterized by a set of five dimensionless parameters. The system of governing equations subject to appropriate hydrodynamic and thermal boundary and initial conditions has been solved by employing the modified SIMPLE method. Numerical results have allowed investigation of the rather complex flow structure and the thermal field as well as the temporal behavior for the case of a half-tone operating under μ-g conditions. It has been clearly confirmed in this study that the Marangoni number could not be the unique relevant parameter that dictates the onset of oscillatory flow. Numerical results have also allowed establish...

Numerical simulation of oscillatory Marangoni convective flow inside a cylindrical liquid zone

Abstract The problem of the oscillatory thermocapillary convection flow inside a NaNO 3 float zone which is suspended between a pair of coaxial disks with prescribed time-dependent temperature profiles and bounded by a cylindrical free surface, has been investigated. The system of governing equations corresponding to a three-dimensional transient model was directly solved by employing a finite control volume method, fully-implicit in time, and a staggered spatial mesh in cylindrical coordinates. It has been clearly shown that for a sufficiently low temperature difference between the disks, the flow consists of a steady and perfectly axisymmetrical toroidal structure with a purely axial moyement of the fluid on the free surface and the vortex center located near that surface. Beyond the critical Marangoni number, Ma cr U ≈ 12 500, a transition from the axisymmetrical to the three-dimensional oscillatory state occurs. Under the effects of the time-dependent thermal disturbances on the free surface, the entire velocity and temperature fields rotate around the main axis following the second mode, i.e. the symmetrical mode of instability. A complete description of the flow structure and its dynamical behavior as well as a comparison with previous numerical and experimental data is given. The phenomenon of hysteresis has also been studied. It has been observed that there is a certain range of the Marangoni number where both the axisymmetrical and the oscillatory states may exist depending on whether the zone is heated up or cooled down. It has been found that the second critical Marangoni number i.e. the one corresponding to the reverse transition from the oscillatory to the axisymmetrical state, depends strongly on the temperature time-rate at which the zone is cooled.