Convection and instability of thermocapillary flow in a liquid bridge subject to a non-uniform rotating magnetic field

A three-dimensional liquid bridge is considered in this study to numerically investigate the effects of an external non-uniform rotating magnetic field (RMF) on the thermocapillary flow in semiconductor melt under microgravity. Simulations are carried out to examine the convection and instability features of the thermocapillary flow over a range of Marangoni numbers (Ma = 15–50) under a non-uniform RMF. The present results show that applying an external non-uniform RMF enhances the maximum tangential velocity and depresses the maximum axial velocity. As a consequence, an approximately axisymmetric flow is maintained in the melt under the effect of the non-uniform RMF, which is beneficial for growing high quality crystal. Further investigation of the thermocapillary flow subject to different non-uniform RMFs (corresponding to Taylor numbers Ta = 3.8 × 10²–1.86 × 10⁴ and Rotating Reynolds number Re_ω = 2.2 × 10⁴) reveals that the thermocapillary convection may undergo a transition from the approximately axisymmetric steady flow to a periodically oscillatory flow for Ma above a critical value. The critical Ma generally increases with the intensity of the non-uniform RMF.     

Dispersion of a buoyant plume in a turbulent pressure-driven channel flow

Direct numerical simulations of the turbulent dispersion of a buoyant line of hot fluid released at the inlet of a plane channel flow are reported (Re_τ = 180, Gr = 10⁷ and Pr = 0.7). Results of turbulent dispersion of a neutrally buoyant scalar and mixed convection flow are also included. The buoyancy force induces a vertical movement that, although small in mean, exhibits a significant fluctuation in the vertical velocity component and deflects the plume with the consequent loss of symmetry found in the neutrally buoyant results. The modification of the budgets for the time averaged momentum and heat transport equations reflects the rearranging of the different contributions induced by the buoyancy force.     

Numerical investigation for natural convection of a nanofluid in an inclined L-shaped cavity in the presence of an inclined magnetic field

The problem of natural convection in an inclined L-shaped enclosure filled with Cu/water nanofluid that operates under differentially heated walls in the presence of an inclined magnetic field is presented in this paper. The fully implicit finite difference method is used to solve the governing equations. A comparison with previously published results in special case of the present study is performed and a very good agreement is found. Heat transfer and fluid flow are examined for parameters of the Hartmann number (0 ≤ Ha ≤ 100), the nanoparticles volume fraction (0% ≤ ϕ ≤ 20%), the cavity inclination angle (0° ≤ ϑ ≤ 300°), the magnetic field inclination angle (0° ≤ γ ≤ 270°), the cavity aspect ratio (0.25 ≤ AR ≤ 0.6) and the Rayleigh number (10³ ≤ Ra ≤ 10⁶). It is found that, the presence of the magnetic field in the fluid region causes a significant reduction in the fluid flow and heat transfer characteristics. Also, a good enhancement in the heat transfer rate can be obtained by adding the copper nanoparticles to the base fluid.     

Numerical thermal analysis and optimization of a water jet impingement cooling with VOF two-phase approach

The fluid flow and heat transfer characteristics of a free-surface liquid jet impingement cooling have been investigated numerically. The slot jet with water impinging normally on a flat plate is employed. To describe the turbulent structure, the turbulent governing equations are solved by a control-volume-based finite-difference method with a power-law scheme and the well-known turbulence model, which are associated with wall function. Numerical computations have been conducted with variations of jet exit Reynolds number (11,000 ≤ Re_d ≤ 17,000), dimensionless jet-to-surface distance (3 ≤ H/d₀ ≤ 12), dimensionless jet width (1 ≤ B/d₀ ≤ 2), and the heat flux (140 kW/m² ≤ q″ ≤ 280 kW/m²). The theoretical model developed is validated by comparing the numerical predictions with available experimental data in the literature. Under the studied ranges, the variations of local Nusselt numbers by hydraulic diameter Nu_d of the dimensionless jet-to-surface distance 3 ≤ H/d₀ ≤ 12 along the flat plate decrease monotonically from its maximum value at the stagnation point. In addition, the shape of the inlet area and jet-to-surface distance are optimized by using the response surface methodology (RSM) and the genetic algorithm (GA) method after solutions are carefully validated with available experimental results in the literature. Based on the optimal results, the optimum condition is in H/d₀ = 7.86 and B/d₀ = 2 for this physical model.     

Effects of moving lid direction on MHD mixed convection in a linearly heated cavity

Effects of moving lid-direction on MHD mixed convection in a cavity with the bottom wall being linearly heated are analyzed using a numerical technique. Vertical walls of the enclosure are adiabatic and the sliding wall at the top has constant temperature. The lid moves in the negative and positive x-direction. Finite volume method has been used to solve the governing equations. Results are presented for different values of Hartmann number (0 ? Ha ? 30), Reynolds number (100 ? Re ? 1000) and Grashof number (10⁴ ? Gr ? 10⁶). It is found that direction of lid is more effective on heat transfer and fluid flow in the case of mixed convection than it is the case in forced convection. Heat transfer is also decreased with increasing of magnetic field for all studied parameters.     

Boundary layer instability of the natural convection flow on a uniformly heated vertical plate

Direct numerical simulation is employed to investigate the two-dimensional boundary layer instability of a natural convection flow on a uniformly heated vertical plate submerged in a homogeneous quiescent environment. A Boussinesq fluid with Prandtl numbers of Pr = 0.733 (air) and 6.7 (water), in the local Rayleigh number range 0 ? Ra_x ? 2.4 × 10¹⁰, is studied. Controlled low amplitude numerical disturbances introduced into the base flow excite unstable travelling waves, with the resulting waves tracked and analyzed as they travel up the boundary layer. The numerical simulation readily reproduced what is predicted by the parallel linear stability theory for the two dimensional mode relatively short wave spectrum, but not for some parts of the long wave spectrum. Critical Rayleigh numbers have been obtained separately for both the temperature and velocity signals using the numerical results, and shown to be in good agreement with each other provided the data is renormalized using the boundary layer scalings of Sparrow and Greg [1]. It has been shown that the disturbance behavior depends on the Prandtl and Rayleigh numbers, the excitation frequency and to a lesser extent the prescribed thermal coupling at the plate.     

Some considerations on frictional losses evaluation of a water flow in microtubes

In the present paper numerical modeling of a water flow through microtubes was made in order to analyze the behavior of the Poiseuille constant for the case of heating fluid flow inside the microtube. The microtube from the experimental research presented in [D. Lelea, S. Nishio, K. Takano, International Journal of Heat and Mass Transfer 47, pp. 2817–2830 (2004). (Journal Article)] [5] was used as a model. The length to diameter ratio of the tube was very large (L/D_i = 1200), and a tube diameter was D_i = 0.5 mm. Only a portion of the tube was heated with a Joule heating and the heating length was L_h = 250 mm. The working fluid was distilled water and a laminar regime is considered Re < 800. The input power was 2 W.     

Analysis of combined thermal and magnetic convection ferrofluid flow in a cavity

A numerical analysis of the magnetic gradient and thermal buoyancy induced cavity ferrofluid flow is conducted by a semi-implicit finite element method. The physical model for a square cavity containing two different temperature side walls and a magnet near bottom wall is described by mass, momentum and energy equations. Conditions for the fixed Prandtl number, Rayleigh number and different ferro-hydrodynamic interaction parameter are studied for 5 × 10⁸ ≤ β ≤ 1.6 × 10¹⁰. Results show the flow strength increases with the strengthening magnetic field. However, the side-wall heat transfer rate presents a decrease trend with the increase in magnetic field strength, for the magnet located near the bottom central area evokes the circulation to move toward the central portion. In summary, a proper choice of magnet strength and location can adjust the flow field and local heat transfer rate to fit the practical application.     

Numerical analysis of natural convection heat transfer in a horizontal annulus partially filled with a fluid-saturated porous substrate

The current study centers around a numerical investigation of natural convection heat transfer within a two-dimensional, horizontal annulus that is partially filled with a fluid-saturated porous medium. In addition, the porous sleeve is considered to be press fitted to the inner surface of the outer cylinder. Both cylinders are maintained at constant and uniform temperatures with the inner cylinder being subjected to a relatively higher temperature than the outer one. Moreover, the Forchheimer and Brinkman effects are taken into consideration when simulating the fluid motion inside the porous sleeve. Furthermore, the local thermal equilibrium condition is assumed to be applicable for the current investigation. The working fluid is air while copper is used to represent the solid phase. The porosity is considered to be uniform and constant with ε = 0.9. The main objective of this study is to examine the effect of the porous sleeve on the buoyancy induced flow motion under steady-state condition. Such an effect is studied using the following dimensionless parameters: Pr = 0.05–50, Ra = 10²–10⁶ and Da = 10^?4–10^?6. Also, the study highlights the effect of the dimensionless porous sleeve thickness (b) and thermal conductivity ratio (k_s/k_f) in the range between 1.1–1.9 and 1–150, respectively.     

Simulation of turbulent natural convection in a porous cylindrical annulus using a macroscopic two-equation model

This work presents numerical computations for laminar and turbulent natural convection within a horizontal cylindrical annulus filled with a fluid saturated porous medium. Computations covered the range 25 < Ra_m < 500 and 3.2 × 10⁻⁴ > Da > 3.2 × 10⁻⁶ and made use of the finite volume method. The inner and outer walls are maintained at constant but different temperatures. The macroscopic k–ε turbulence model with wall function is used to handle turbulent flows in porous media. First, the turbulence model is switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra_m. Subsequently, the turbulence model is included and calculations start at high Ra_m, merging to the laminar branch for a reducing Ra_m. This convergence of results as Ra_m decreases can be seen as an estimate of the so-called laminarization phenomenon. Here, a critical Rayleigh number was not identified and results indicated that when the porosity, Prandtl number, conductivity ratio between the fluid and the solid matrix and Ra_m are kept fixed, the lower the Darcy number, the higher is the difference of the average Nusselt number given by the laminar and turbulent models.     

Numerical study of assisting and opposing mixed convective nanofluid flows in an inclined circular pipe

A numerical investigation of mixed convection is carried out to study the heat transfer and fluid flow characteristics in an inclined circular pipe using the finite volume method. The pipe has L/D of 500 and it was subjected to a uniform heat flux boundary condition. Four types of nanofluids (Al₂O₃, CuO, SiO₂, and TiO₂ with H₂O) with nanoparticles concentration in the range of 0 ≤ φ ≤ 5% and nanoparticles diameter in the range of 20 ≤ dp ≤ 60 nm were used. The pipe inclination angle was in the range of 30^∘ ≤ θ ≤ 75^∘ using assisting and opposing flow. The influences of Reynolds number in the range of 100 ≤ Re ≤ 2000, and Grashof numbers in the range of 6.3 × 10² ≤ Gr ≤ 8.37 × 10³ were examined. It is found that the velocity and wall shear stress are increased as Re number increases, while the surface temperature decreases. There is no significant effect of increasing Gr number on thermal and flow fields. The velocity and wall shear stress are increased and the surface temperature is decreased as φ and dp are decreased. It is concluded that the surface temperature is increased as the pipe inclination angle increases from the horizontal position (θ = 0^°) to the inclined position (θ = 75^°). In addition, it is inferred that the heat transfer is enhanced using SiO₂ nanofluid compared with other nanofluids types. Furtheremore, it is enhanced using assisting flow compared to opposing flow.     

Fully developed flow and heat transfer characteristics in a wavy passage: Effect of amplitude of waviness and Reynolds number

The present study deals with numerical simulation of fully developed flow and heat transfer through a wavy surface described by the function y = 2a sin²(πx/L). Finite volume method on collocated grid is used to solve incompressible, time-dependent Navier–Stokes and energy equation in primitive variable form. Effect of geometry, generated by varying H_min/H_max ratio from 0.1 to 0.5 and keeping L/a ratio fixed to 8, on fluid flow and heat transfer characteristics has been elaborated at a Reynolds number of 600. The critical Reynolds number of unsteadiness is found to depend on the geometrical parameters. At Re = 600, one model shows the flow with multiple frequencies while the others reveal single frequency. It is established that geometry with H_min/H_max ratio 0.2 produces the highest Nusselt number and spawns the best thermal performance factor (TPF). With increase in Reynolds number, the steady flow shows a decrease in TPF while an increase in TPF is noticed when the flow is unsteady.     

Convection heat and mass transfer along a vertical heated plate with film evaporation in a non-Darcian porous medium

A numerical analysis has been carried about to study the heat and mass transfer of forced convection flow with liquid film evaporation in a saturated non-Darcian porous medium. Parametric analyses were conducted concerning the effects of the porosity ε, inlet liquid Reynolds number Re_l, inlet air Reynolds number Re_a on the heat and mass transfer performance. The results conclude that better heat and mass transfer performances are noticed for the system having a higher Re_a, a lower Re_l, and a higher ε. Re_l plays a more important role on the heat and mass transfer performance than Re_a and ε. For the case of ε = 0.4 and Re_a = 10,000, the increases of Nu and Sh for Re_l = 50 are about by 33.9% and 35.3% relative to the values for Re_l = 250.     

Taylor dispersion coefficients for laminar,longitudinal flow past arrays of circular tubes

The problem of determining shell-side Taylor dispersion coefficients for a shell-and-tube configuration is examined in detail for both ordered as well as disordered arrangement of tubes. The latter is modeled by randomly placing N tubes within a unit cell of a periodic array. It is shown that shell-side Taylor dispersion coefficient D_T is expressed by D_T = D_M(1 + λPe²) and the coefficient λ is divergent with N, where D_M is the molecular diffusivity of solute on the shell side and Pe is the Peclet number given by aU/D_M with a and U being the radius of tube and the mean fluid velocity on the shell side, respectively. The coefficient λ depends on the spatial average and the fluid velocity weighted average of the concentration of solute on the shell side. The behavior of the coefficient λ with N arises due to logarithmically divergent nature of concentration disturbances caused by each tube in the plane normal to the axes of the tubes. An effective-medium theory is developed for determining conditionally-averaged velocity and concentration fields and hence the shell-side Taylor dispersion coefficients. Its predictions are compared with the results of rigorous numerical computations. The present study also presents formulas for determining the shell-side Taylor dispersion coefficients for square and hexagonal arrays of tubes with cell theory approximations.     

Numerical simulation of natural convection heat transfer in a porous cavity heated from below using a non-Darcian and thermal non-equilibrium model

The present paper investigates the numerical simulation of steady laminar incompressible natural convection heat transfer in an enclosed cavity that is filled with a fluid-saturated porous medium. The bottom wall is subjected to a relatively higher temperature than the top wall while the vertical walls are considered to be insulated. The flow field is modeled upon incorporating different non-Darcian effects, such as the convective term, Brinkman effect and Forchhiemer quadratic inertial effect. Moreover the two-equation model is used to separately account for the local fluid and solid temperatures. The numerical solution is obtained through the application of the finite volume method. The appraisals of the sought objectives are performed upon identifying key dimensionless groups of parameters. These dimensionless groups along with their operating domains are: Rayleigh number 1 ⩽ Ra ⩽ 400, Darcy number 10⁻⁴ ⩽ Da ⩽ 10⁻³, effective fluid-to-solid thermal conductivity ratio 0.1 ⩽ κ ⩽ 1.0, and the modified Biot number 1 ⩽ χ ⩽ 100. The non-Darcian effects are first examined over a broad range of Rayleigh number. Next, the implications of the group of parameters on the flow circulation intensity, local thermal non-equilibrium (LTNE) and average Nusselt number are highlighted and pertinent observations are documented.     

Time evolution of double-diffusive convection in a vertical cylinder with radial temperature and axial solutal gradients

The characteristics of transient double-diffusive convection in a vertical cylinder are numerically simulated using a finite element method. Initially the fluid in the cavity is at uniform temperature and solute concentration, then constant temperature and solute concentration, which are lower than their initial values, are imposed along the sidewall and bottom wall, respectively. The time evolution of the double-diffusive convection is investigated for specific parameters, which are the Prandtl number, Pr = 7, the Lewis number, Le = 5, the thermal Grashof number, Gr_T = 10⁷, and the aspect ratio, A = 2, of the enclosure. The objective of the work is to identify the effect of the buoyancy ratio (the ratio of solutal Grashof to thermal Grashof numbers: N = Gr_S/Gr_T) on the evolution of the flow field, temperature and solute field in the cavity. It is found that initially the fluid near the bottom wall is squeezed by the cold flow from the sidewall, a crest of the solute field forms and then pushed to the symmetry line. In the case of N > 0, a domain with higher temperature and weak flow (dead region) forms on the bottom wall near the symmetry line, and the area of dead region increases when N varies from 0.5 to 1.5. More crests of the solute field are formed and the flow near the bottom wall fluctuates continuously for N < 0. The frequency of the fluctuation increases when N varies from −0.5 to −1.5. Corresponding to the variety of the thermal and solutal boundary layers, the average rates of heat transfer (Nu) at the sidewall remain almost unchanged while the average rates of mass transfer (Sh) at the bottom wall change much in the cases of N = 1, 0, −1.     

CFD analysis of convective heat transfer at the surfaces of a cube immersed in a turbulent boundary layer

Steady Reynolds-Averaged Navier–Stokes (RANS) CFD is used to evaluate the forced convective heat transfer at the surfaces of a cube immersed in a turbulent boundary layer, for applications in atmospheric boundary layer (ABL) wind flow around surface-mounted obstacles such as buildings. Two specific configurations are analysed. First, a cube placed in turbulent channel flow at a Reynolds number of 4.6 × 10³ is considered to validate the numerical predictions by comparison with wind-tunnel measurements. The results obtained with low-Reynolds number modelling (LRNM) show a satisfactory agreement with the experimental data for the windward surface. Secondly, a cube exposed to high-Reynolds number ABL flow is considered. The heat transfer in the boundary layer is analysed in detail. The dimensionless parameter y¹, which takes into account turbulence, is found to be more appropriate for evaluating heat transfer than the commonly used y⁺ value. Standard wall functions, which are frequently used for high-Reynolds number flows, overestimate the convective heat transfer coefficient (CHTC) significantly (±50%) compared to LRNM. The distribution of the CHTC–U₁₀ correlation over the windward surface is reported for Reynolds numbers of 3.5 × 10⁴ to 3.5 × 10⁶ based on the cube height and U₁₀, where U₁₀ is the wind speed in the undisturbed flow at a height of 10 m.     

Effects of inlet geometry on heat transfer and fluid flow of tangential micro-heat sink

The paper presents the geometric optimization of the micro-heat sink with straight circular microchannels with inner diameter of D_i = 900 μm. The inlet cross-section has a rectangular shape and positioned tangentially to the tube axis with the four different geometries. The fluid flow regime is laminar and water with variable fluid properties is used as a working fluid. The heat flux spread through the bottom sink surface is q = 100 W/cm². Thermal and hydrodynamic performances of the heat sink are compared with results obtained for conventional channel configuration with lateral inlet/outlet cross-section. Besides, the results are compared with the tangential micro-heat sink with D_i = 300 μm. For all the cases, the thermal and hydrodynamic results are compared on a fixed pumping power basis.     

Experimental investigation of mixed convection heat transfer from longitudinal fins in a horizontal rectangular channel

Mixed convection heat transfer from longitudinal fins inside a horizontal channel has been investigated for a wide range of modified Rayleigh numbers and different fin heights and spacings. An experimental parametric study was made to investigate effects of fin spacing, fin height and magnitude of heat flux on mixed convection heat transfer from rectangular fin arrays heated from below in a horizontal channel. The optimum fin spacing to obtain maximum heat transfer has also been investigated. During the experiments constant heat flux boundary condition was realized and air was used as the working fluid. The velocity of fluid entering channel was kept nearly constant (0.15 ? w_in ? 0.16 m/s) using a flow rate control valve so that Reynolds number was always about Re = 1500. Experiments were conducted for modified Rayleigh numbers 3 × 10⁷ < Ra¹ < 8 × 10⁸ and Richardson number 0.4 < Ri < 5. Dimensionless fin spacing was varied from S/H = 0.04 to S/H = 0.018 and fin height was varied from H_f/H = 0.25 to H_f/H = 0.80. For mixed convection heat transfer, the results obtained from experimental study show that the optimum fin spacing which yields the maximum heat transfer is S = 8–9 mm and optimum fin spacing depends on the value of Ra¹.     

Unsteady-state mass transfer from a binary gas bubble with changing volume

Numerical methods are used to investigate the transient mass transfer from a binary gas bubble to an incompressible liquid. The bubble has two components: A – soluble and B – insoluble in the surrounding fluid. The concentration of A inside the bubble is considered spatially uniform but not constant in time. The maximum value of the initial volumetric fraction of A is 0.3. The mathematical model equations were solved numerically in spherical coordinates system. Creeping flow, moderate Re number flow, 10 ? Re ? 100, and potential flow around the bubble were assumed. The computations focused on the influence of the initial fraction of A and Henry number on the mass transfer rate for Pe ? 10⁴.