Laminar Mixed Convection Research Articles

Numerical investigation of mixed convection of Bingham fluids in cylindrical enclosures with heated rotating top wall

The steady-state laminar mixed convection of yield stress fluids obeying the Bingham model in a cylindrical enclosure with a heated rotating top cover has been numerically analysed based on axisymmetric incompressible flow simulations. Yield stress effects on heat and momentum transport have been investigated for an aspect ratio (height/radius) of unity (i.e. AR=1) for a range of different values of nominal Prandtl, Richardson and Reynolds numbers given by 10⩽Pr⩽500, 0⩽Ri⩽1 and 100⩽Re⩽3000. The mean Nusselt number Nu‾ has been found to decrease sharply with increasing Bingham number Bn, but subsequently Nu‾ approaches asymptotically to a value of unity, which is indicative of conduction-driven transport. It has also been found that Nu‾ increases with increasing values of Prandtl and Reynolds numbers for both Newtonian (i.e. Bn=0) and Bingham fluids. In contrast, Nu‾ decreases with increasing Ri for both Newtonian and Bingham fluids for small values of Bingham number, whereas Nu‾ remains insensitive to the variation of Ri for large values of Bingham number. The variation of torque coefficient CT, which gives a quantitative measure of power consumption, has also been investigated. The torque coefficient CT has been found to increase with increasing Bn whereas it decreases with increasing Re. It has also been found that CT decreases slightly with increasing Ri for small values of Bn, whereas it becomes insensitive to the variation of Ri for large Bingham numbers. For the fully forced convection (Ri=0) case, Pr does not have a significant influence on CT. However, in the case of mixed convection CT increases with increasing Pr. The simulation data has been used in conjunction with a detailed scaling analysis to propose a correlation for Nu‾ for the range of Re,Ri and Pr considered here.

Combined Effect of Mixed Convection and Surface Radiation Heat Transfer for Thermally Developing Flow in Vertical Channels

ABSTRACTCombined effect of laminar flow mixed convection and surface radiation heat transfer for thermally developing airflow in a vertical channel heated from a side has been experimentally examined with different thermal and geometric parameters. The channel boundary is made of two isothermal walls and two adiabatic walls, the isothermal parallel wall is heated uniformly and the opposite cold wall temperature is maintained equal to the inlet conditions. The heated wall temperature ranged from 55 to 100°C, Reynolds number ranged from 800 to 2900 and the heat flux was varied from 250 to 870 W/m2. To cover the wide range of Reynolds numbers, two aspect ratios of square and rectangular section were used. Surface radiation from the internal walls is considered through two emissivities i.e. 0.05 and 0.85, to represent weak and strong radiation effects, respectively. From the experiments, surface temperature and Nusselt number distributions of convection and radiation heat transfer are obtained for different heat flux values. Flow structure inside the channel is visualized to observe the flow pattern. The results show the combined effect of laminar flow mixed convection and surface radiation on the total heat transfer rate within the channel. The accumulating buoyancy force and airflow moves together vertically in the upward direction to give significant heat transfer enhancement in the vertical orientation of the channel.

Viscous dissipation effects on entropy generation in heated vertical parallel-plate channels for mixed convection

In this study, effect of viscous dissipation on entropy generation for fully developed incompressible laminar flow mixed convection in vertical parallel-plate channels with asymmetric and symmetric uniform heat fluxes was parametrically analysed. Analytical equations were derived by using continuum approach and perturbation method. A specific MATLAB code was created to solve the governing equations. The effects of Gr/Re, the Brinkman number, and the ratio of wall heat flux on the entropy generation are presented and discussed. It is concluded that viscous dissipation has a significant effect on the entropy generation for mixed convection in heated vertical parallel-plate channels. Entropy generation resulting from fluid friction goes up, however, entropy generation due to heat transfer decreases by increasing of viscous dissipation. Consequently, it can be said that, this study will contribute to literature in optimising the systems that operates under mixed convection conditions in the vertical parallel-plate configuration.

Numerical Analysis of the Parameters Governing 3D Laminar Mixed Convection Flow in a Rectangular Channel with Imposed Wall Flux Density

Numerical Analysis of the Parameters Governing 3D Laminar Mixed Convection Flow in a Rectangular Channel with Imposed Wall Flux Density

Mixed convection in a rotating eccentric annulus containing nanofluid using bi-orthogonal grid types: A finite volume simulation

In this paper, the steady state and laminar mixed convection of nanofluid in horizontal eccentric annulus with rotating inner cylinder has been investigated numerically. The inner and outer cylinders are considered at constant temperature Ti and To respectively, where Ti>To. The annular space is filled with Alumina-water nanofluid. The nonlinear governing equations and the associated boundary conditions in the polar coordinate are solved numerically using the finite volume method and SIMPLER algorithm. In order to perform the numerical simulations, a code has been written to model the problem using bipolar orthogonal co-ordinates as well as non-orthogonal co-ordinates grid types. It is worth mentioning that in non-orthogonal co-ordinates grid types the code is able to model the problem with or without the effects of non-orthogonality. Due to the inconsiderable non-orthogonality of the grid, difference between the results of three schemes is <3%. Considering the computational cost, the code developed for non-orthogonal co-ordinates grid types without effects of non-orthogonality has been used for this study. The effects of the eccentricity and the nanoparticle volume fraction on the heat transfer inside the annuli have been investigated. According to the results, the average Nusselt number increases by increasing the downward eccentricity of the inner cylinder. Furthermore, the maximum average Nusselt number occurs for an optimal nanoparticle volume fraction.

Density maximum effects on mixed convection in a square lid-driven enclosure filled with Cu-water nanofluids

In this paper, the authors investigate the laminar mixed convection flow of Cu-water nanofluid near density maximum of water in a lid-driven enclosure. The governing equations based on the Boussinesq and non-Boussinesq homogenous models are solved using a pressure-based finite volume method. Four different lid-driven cases are simulated when volume fractions of nanoparticles range from 0.0, 0.03 and 0.05 and the Richardson (Ri) number varies from 0.01, 0.1, 1, 10 and 100 under both the Boussinesq and non-Boussinesq approximations. Streamlines, isotherms, mid-plane velocities, mid-plane temperature and the average Nusselt (Nu) number in various boundary conditions have been analyzed. Results show that the flow pattern and thermal behavior of the nanofluid strongly depend on the density inversion of water and the presence of nanoparticles. Further, the findings indicate that the density inversion phenomenon leads to a lower average Nu number under the non-Boussinesq approximation compared to the Boussinesq approximation, suggesting that studies with the Boussinesq approximation may overestimate heat transfer performance. In addition, the average Nu number increases as the volume fractions of nanoparticles increase. Finally, the maximum value of the average Nu number can be achieved under the Boussinesq approximation when the shear-driven force is aligned with the buoyancy force.

Soret and Dufour effects on double diffusive mixed convection of Newtonian and shear-thinning fluids in a two sided lid-driven cavity

Purpose The thermal-diffusion (Soret) and the diffusion-thermo (Dufour) effects play a crucial role in double diffusive mixed convection in a lid-driven cavity; but they have not been studied properly by researchers. The purpose of this paper is to investigate effects of Soret and Dufour parameters on double diffusive laminar mixed convection of shear-thinning and Newtonian fluids in a two-sided lid-driven cavity. Design/methodology/approach Finite Difference Lattice Boltzmann method (FDLBM) has been applied to solve the complex problem. This study has been conducted for the certain pertinent parameters of Richardson number (Ri=0.00062-1), power-law index (n=0.2-1), Soret parameter (Sr=−5-5) as Dufour number effects have been investigated from Dr=−5 to 5 at Buoyancy ratio of N=1 and Lewis number of Le=5. Findings Results indicate that the augmentation of Richardson number causes heat and mass transfer to decrease. The fall of the power-law index declines heat and mass transfer at Ri=0.00062 and 0.01 in various Dufour and Soret parameters. At Ri=1, the heat and mass transfer rise with the increment of power-law index for Dr=0 and Sr=0. The least effect of power-law index on heat and mass transfer among the studied Richardson numbers was observed at Ri=1. The positive Dufour numbers augment the heat transfer gradually as the positive Soret numbers enhance the mass transfer. The Dr=−5 and Sr=−5 provokes the negative average Nusselt and Sherwood numbers, respectively, to be generated. The least magnitude of the average Nusselt and Sherwood numbers were obtained at Dr=−1 and Sr=−1, respectively. Originality/value Soret and Dufour effects in double diffusive mixed convection has not been studied in a lid-driven cavity. In addition. this study has been conducted also for shear-thinning fluids.

Investigating the effects of nanoparticles mean diameter on laminar mixed convection of a nanofluid through an inclined tube with circumferentially nonuniform heat flux

In this study, laminar mixed convection of a water-based nanofluid containing Al2O3 nanoparticles in an inclined copper tube, which is heated at the top half surface, is investigated numerically. A heat conduction mechanism through the tube wall was implemented. Three-dimensional equations using a two-phase mixture model were solved to investigate the hydrodynamic and thermal behaviors of the nanofluid over a wide range of nanoparticle volume fractions. To verify the model, the results were compared with previous works and a good agreement between the results was observed. The effect of nanoparticles diameter on the hydrodynamic and thermal parameters over a wide range of Grashof numbers is presented and discussed for a particle volume fraction and Reynolds number. It is shown that the diameter of nanoparticles affects the particle distribution in the cross section perpendicular to the tube axis, heat transfer coefficient, and shear stress.

Combined Mixed Convection and Radiation Heat Transfer in an Obstacle Wall Mounted Lid-driven Cavity

AbstractThis paper presents a numerical investigation for laminar mixed convection flow of a radiating gas in a lid-driven cavity with a rectangular-shaped obstacle attached on the bottom wall. The vertical walls of the square cavity are assumed to be adiabatic, while other walls of cavity and obstacle are kept at constant temperature. The fluid is treated as a gray, absorbing, emitting and scattering medium. The governing differential equations consisting the continuity, momentum and energy are solved numerically by the computational fluid dynamics techniques to obtain the velocity and temperature fields. Discretized forms of these equations are obtained by the finite volume method and solved using the SIMPLE algorithm. Since the gas is considered as a radiating medium, besides convection and conduction, radiative heat transfer also takes place in the gas flow. For computation of the radiative term in the gas energy equation, the radiative transfer equation is solved numerically by the discrete ordinate method. The streamline and isotherm plots and the distributions of convective, radiative and total Nusselt numbers along the bottom wall of cavity are presented. The effects of Richardson number, obstacle location, radiation–conduction parameter, optical thickness and albedo coefficient on the flow and temperature distributions are carried out. Comparison between the present numerical results with those obtained by other investigators in the cases of conduction–radiation and pure convection systems shows good consistencies.

Mixed convection nanofluid flow over microscale forward-facing step — Effect of inclination and step heights

A numerical study of nanofluid flow and heat transfer of laminar mixed convection flow over a three-dimensional, horizontal microscale forward-facing step (MFFS) is reported. The effects of different step heights and the duct inclination angle on the heat transfer and fluid flow are discussed in this study. The straight and downstream walls were heated to a constant temperature and uniform heat flux respectively. The numerical results were carried out for step heights of 350μm, 450μm, 550μm and 650μm. Different inclination angles were considered to determine their effects on the flow and heat transfer. Ethylene glycol-SiO2 nanofluid is considered with a 25nm particle diameter and 4% volume fraction. The results reveal that the Nusselt increases as the step heights increase. Additionally, no significant effect of the duct inclination angle is found on the heat transfer rate and the fluid flow.

Experimental study of laminar mixed convection in a rod bundle with mixing vane spacer grids

Heat transfer by mixed convection in a rod bundle occurs when convection is affected by both the buoyancy and inertial forces. Mixed convection can be assumed when the Richardson number (Ri=Gr/Re2) is on the order of unity, indicating that both forced and natural convection are important contributors to heat transfer. In the present study, data obtained from the Rod Bundle Heat Transfer (RBHT) facility was used to determine the heat transfer coefficient in the mixed convection regime, which was found to be significantly larger than those expected assuming purely forced convection based on the inlet flow rate. The inlet Reynolds (Re) number for the tests ranged from 500 to 1300, while the Grashof (Gr) number varied from 1.5×105 to 3.8×106 yielding 0.25<Ri<4.3. Using results from RBHT test along with the correlation from the FLECHT-SEASET test program for laminar forced convection, a new correlation ​is proposed for mixed convection in a rod bundle. The new correlation accounts for the enhancement of heat transfer relative to laminar forced convection.

Three-dimensional numerical study on fully-developed mixed laminar convection in parabolic trough solar receiver tube

In this paper, a numerical investigation is presented, aiming at the effect of the buoyancy force induced by the non-uniform heat flux on the laminar flow and heat transfer characteristics in the solar receiver tube of parabolic trough collector. The flow and heat transfer performances are analyzed for forced and mixed laminar convection in receiver tube heated by uniform and non-uniform heat fluxes with different Grashof numbers, Reynolds numbers and solar elevation angles. The results show that the natural convection can increase heat transfer rate of laminar forced convection by more than 10% when the Grashof number is greater than a threshold value. The mixed fluid flow and heat transfer characteristics vary with solar elevation angle. Heat transfer deterioration occurs when the Richardson number is greater than 12.8.

Combined Buoyancy Effects of Thermal and Mass Diffusion on Laminar Mixed Convection in Vertical and Horizontal Semicircular Ducts

The development of laminar mixed convection with heat and mass transfer in vertical and horizontal semicircular ducts has been investigated for the case of thermal boundary conditions of uniform heat input, concentration at the fluid–solid interface axially, and uniform peripheral wall temperature at any axial station. The governing equations were solved numerically over the following conditions: Pr = 0.7, Le = 1, Re = 500, Grt = 1.66 × 105, and Grc = 1.66 × 105. The combined effects of solutal and thermal Grashof numbers on the flow and thermal fields were observed in terms of the axial velocity, temperature, and concentration distributions, as well as, friction factor, Nusselt number, and Sherwood number. Further, the development of velocity, temperature, and concentration at different axial stations was found to be influenced by the solutal and thermal Grashof numbers. The results also showed that the forced-convection boundary layer development dominates very close to the duct inlet, while further downstream, the heat and mass transfer rates are enhanced due to the effect of solutal buoyancy.

Numerical Simulation of Nanofluid-Cooling Enhancement of Three Fins Mounted in a Horizontal Channel

This article presents a numerical study of two-dimensional laminar mixed convection in a horizontal channel. The upper horizontal wall of the channel is insulated. The governing equations were solved by using the finite volume method based on the simpler algorithm. Comparisons with previous results were performed and found to be in excellent agreement. The results were presented in terms of streamlines, isotherms, local and average Nusselt numbers for the Richardson number (0 ≤ Ri ≤ 10), Reynolds number (5 ≤ Re ≤ 100), solid volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.10), and the type of nanofluids (Cu, Ag, Al2O3, and TiO2). The results show that the previous parameters have considerable effects on the flow and thermal fields. It was found that the heat transfer increases with increasing of Ra, Re, and ϕ.

Numerical Analysis of Mixed Convection of Nanofluids Inside a Vertical Channel

Laminar mixed convection of an Al[Formula: see text]O[Formula: see text]/water nanofluid inside a vertical channel is investigated numerically. Single-phase and two-phase Eulerian models are employed to analyze flow and thermal fields of the nanofluid in conjunction with the suitable expressions for the particle viscosity and effective particle thermal conductivity. The results of two-phase Eulerian model are compared with the single-phase model and with the published experimental data. Effects of the solid volume fraction, Reynolds number and Grashof number on the heat transfer performance of the nanofluid are investigated and discussed in detail.

Numerical analysis of mixed convection at various walls speed ratios in two-sided lid-driven cavity partially heated and filled with nanofluid

In this study, the problem of laminar mixed convection in a two-sided lid-driven square cavity partially heated and filled with Cu/water nanofluid, is analyzed using a numerical procedure based on the finite volume method with the help of a full multigrid solver. Two heat sources of dimensionless length B maintained at high temperature (TH) are embedded in the center of the two side walls of the cavity. The top and bottom walls of the enclosure are considered with low temperature (TC), while the remaining boundary parts of the enclosure are thermally insulated. The top and bottom walls of the cavity can slide in the same or opposite direction with various speed ratios named λ. A parametric study is conducted and a set of graphical results is presented and discussed to illustrate the effects of λ (−2≤λ≤2), the Richardson number Ri (0.01≤Ri≤100) and the solid volume fraction ϕ (0≤ϕ≤0.1) on the flow and heat transfer characteristics. The results show that varying the speed ratio has significant effects on both the flow structure and the heat transfer. It is found that heat transfer enhancement can be provided by the presence of nanoparticles and that this is accentuated by decreasing the Richardson number. Special attention has been given to predict a characteristic Richardson number of equilibrium, namely Rie, leading to an equal heat transfer rate balance between the two opposite sources. Finally, multiple correlations in terms of Richardson number and volume fraction nanoparticles have been established at various speed ratios.

Effect of buoyancy-assisted flow on convection from an isothermal spheroid in power-law fluids

In this work, the coupled momentum and energy equations have been solved to elucidate the effect of aiding-buoyancy on the laminar mixed-convection from a spheroidal particle in power-law media over wide ranges of the pertinent parameters: Richardson number, 0≤Ri≤5; Reynolds number, 1≤Re≤100; Prandtl number, 1≤Pr≤100; power-law index, 0.3≤n≤1.8, and aspect ratio, 0.2≤e≤5 for the case of constant thermo-physical properties. New results for the velocity and temperature fields are discussed in terms of the streamline and isotherm contours, surface pressure and vorticity contours, drag coefficient, local and surface averaged Nusselt number. The effect of particle shape on the flow is seen to be more pronounced in the case of oblates (e 1). The propensity for wake formation reduces with the rising values of power-law index, Richardson number and slenderness of the body shape (e > 1). Also, the drag coefficient is seen to increase with the Richardson number and power-law index. All else being equal, the Nusselt number shows a positive dependence on the Richardson number and Reynolds number and an inverse dependence on the power-law index and aspect ratio of the spheroid. Limited results were also obtained by considering the exponential temperature dependence of the power-law consistency index. This factor can increase the values of the average Nusselt number by up to ~10-12% with reference to the corresponding values for the case of the constant thermo-physical properties under otherwise identical conditions. Finally, the present values of the Nusselt number have been consolidated in the form of Colburn j-factor as a function of the modified Reynolds and Prandtl numbers for each value of the aspect ratio (e). The effect of the temperature dependent viscosity is included in this correlation in terms of a multiplication factor.

Numerical study of laminar mixed convection in a square open cavity

The Lattice Boltzmann Method (LBM) is used to study steady and unsteady laminar flow in a channel with an open square cavity and a heated bottom wall in two dimensions, under mixed convection flow conditions. LBM is compared to results obtained by ANSYS-FLUENT for validation. Temperature, velocity and Nusselt number agree very well in the range of Reynolds and Richardson numbers studied, i.e. 50⩽Re⩽1000 and 0.01⩽Ri⩽10. Our observations indicate that the effect of the buoyancy force is negligible for Ri⩽0.1, for all values of the Reynolds number considered. For Ri=1, 10 buoyancy effects are important, which combined with a high enough Re (≳200 in our study), causes the development of the upstream secondary vortex and the stratification of the flow into two main recirculating cells. As previously observed in earlier studies, for high enough Ri the recirculation is no longer encapsulated, the flow becomes unsteady, and an oscillatory instability develops. This is observed in our simulations starting from Re=500, Ri=10. The analysis of the unsteady regime reveals a very rich phenomenology where the geometry of the problem couples with the oscillatory thermal instability. This regime is characterized by the periodic emission of pairs of vortices generated from the upper downstream vertex of the square cavity, and pseudoperiodic variations of the Nusselt number which persist at least up to Re=1500, while the two main vortices remain in the cavity. Our observations extend previous studies and shed a new light on the characteristics of the oscillatory instability and the role of the Reynolds and Richardson numbers.

Coupled Thermal Radiation and Mixed Convection Step Flow of Nongray Gas

The main goal of this paper is to analyze the thermal and hydrodynamic behaviors of laminar mixed convection flow of a nongray radiating gas over an inclined step in an inclined duct. The fluid is considered an air mixture with 10% CO2 and 20% H2O mole fractions, which is treated as homogeneous, absorbing, emitting, and nonscattering medium. The full-spectrum k-distribution (FSK) method is used to handle the nongray part of the problem, while the radiative transfer equation (RTE) is solved using the discrete ordinate method (DOM). In addition, the results are obtained for different medium assumptions such as pure mixed convection and gray medium to compare with the nongray calculations as a real case. The results show that in many cases, neglecting the radiation part in computations and also use of gray simulations are not acceptable and lead to considerable errors, especially at high values of the Grashof number in mixed convection flow.

MHD mixed convection flow and heat transfer in a porous medium

The effects of a steady two-dimensional laminar MHD mixed convection flow and heat transfer against a heated vertical semi-infinite permeable surface in a porous medium are discussed. The coupled nonlinear partial differential equations describing the conservation of mass, momentum, and energy are solved by a perturbation technique. The results are presented to illustrate the influence of Hartmann number (M), Prandtl number (Pr), permeability parameter (Kp), suction/blowing parameter (fw), heat generation/absorption coefficient (ϕ), and mixed convection or buoyancy parameter (γ). The effects of different parameters on the velocity and temperature as well as the skin friction and wall heat transfer are discussed with the help of figures.