The variations of heat transfer and slip velocity of FMWNT-water nano-fluid along the micro-channel in the lack and presence of a magnetic field

Simulation of forced convection of FMWNT-water (functionalized multi-walled carbon nano-tubes) nano-fluid in a micro-channel under a magnetic field in slip flow regime is performed. The micro-channel wall is divided into two portions. The micro-channel entrance is insulated while the rest of length of the micro-channel has constant temperature (T_C). Moreover, the micro-channel domain is exposed to a magnetic field with constant strength of B₀. High temperature nano-fluid (T_H) enters the micro-channel and exposed to its cold walls. Slip velocity boundary condition along the walls of the micro-channel is considered. Governing equations are numerically solved using FORTRAN computer code based on the SIMPLE algorithm. Results are presented as the velocity, temperature, and Nusselt number profiles. Greater Reynolds number, Hartmann number, and volume fraction related to more heat transfer rate; however, the effects of Ha and ϕ are more noteworthy at higher Re.     

Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.     

Surface radiation influence on the regimes of conjugate natural convection in an enclosure with local energy source

A numerical analysis of the unsteady regimes of the natural convection and thermal radiation in a square enclosure with heat-conducting walls has been carried out in the presence of a heat source of finite sizes located in the base zone under the conditions of convective exchange with the ambient medium. The mathematical model formulated in the dimensionless variables “stream function — vorticity — temperature” has been implemented numerically by a finite difference method. The influence of the reduced emissivity of internal surfaces of bounding walls on the local characteristics (the streamlines and temperature fields) and on the integral complex (the mean Nusselt number on typical boundaries) has been analyzed in detail for 0 ≤ ? < 1, the location of the heat source 0.1 ≤ l/L ≤ 0.4, and its length 0.2 ≤ l _hs /L ≤ 0.6 for Ra = 10⁶, Pr = 0.7. The approximation relations have been derived for the mean convective and radiation Nusselt numbers depending on the reduced emissivity of the internal surfaces of bounding walls and the energy source location relative to vertical walls.     

The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump

The forced convection of nanofluid flow in a long microchannel is studied numerically according to the finite volume approach and by using a developed computer code. Microchannel domain is under the influence of a magnetic field with uniform strength. The hot inlet nanofluid is cooled by the heat exchange with the cold microchannel walls. Different types of nanoparticles such as Al₂O₃ and Ag are examined while the base fluid is considered as water. Reynolds number are chosen as Re=10 and Re=100. Slip velocity and temperature jump boundary conditions are simulated along the microchannel walls at different values of slip coefficient for different amounts of Hartmann number. The investigation of magnetic field effect on slip velocity and temperature jump of nanofluid is presented for the first time. The results are shown as streamlines and isotherms; moreover the profiles of slip velocity and temperature jump are drawn. It is observed that more slip coefficient corresponds to less Nusselt number and more slip velocity especially at larger Hartmann number. It is recommended to use Al₂O₃-water nanofluid instead of Ag-water to increase the heat transfer rate from the microchannel walls at low values of Re. However at larger amounts of Re, the nanofluid composed of nanoparticles with higher thermal conductivity works better.     

Correlated process of phase separation and microstructure evolution of ternary Co-Cu-Pb alloy

The phase separation and rapid solidification of liquid ternary Co₄₅Cu₄₂Pb₁₃ immiscible alloy have been investigated under both bulk undercooling and containerless processing conditions. The undercooled bulk alloy is solidified as a vertical two-layer structure, whereas the containerlessly solidified alloy droplet is characterized by core-shell structures. The dendritic growth velocity of primary α(Co) phase shows a power-law relation to undercooling and achieves a maximum of 1.52 m/s at the undercooling of 112 K. The Pb content is always enriched in Cu-rich zone and depleted in Co-rich zone. Numerical analyses indicate that the Stokes motion, solutal Marangoni convection, thermal Marangoni convection, and interfacial energy play the main roles in the correlated process of macrosegregation evolution and microstructure formation.     

Numerical prediction of heat transfer by natural convection and radiation in an enclosure filled with an isotropic scattering medium

This paper deals with the numerical solution for natural convection and volumetric radiation in an isotropic scattering medium within a heated square cavity using a hybrid thermal lattice Boltzmann method (HTLBM). The multiple relaxation time lattice Boltzmann method (MRT-LBM) has been coupled to the finite difference method (FDM) to solve momentum and energy equations, while the discrete ordinates method (DOM) has been adopted to solve the radiative transfer equation (RTE) using the S8 quadrature. Based on these approaches, the effects of various influencing parameters such as the Rayleigh number (Ra), the wall emissivity (ε_ι), the Planck number (Pl), and the scattering albedo (ω), have been considered. The results presented in terms of isotherms, streamlines and averaged Nusselt number, show that in absence of radiation, the temperature and the flow fields are centro-symmetrics and the cavity core is thermally stratified. However, radiation causes an overall increase in the temperature and velocity gradients along both thermally active walls. The maximum heat transfer rate is obtained when the surfaces of the enclosure walls are regarded as blackbodies. It is also seen that the scattering medium can generate a multicellular flow.     

Numerical investigation of natural convection heat transfer of nanofluids in a Γ shaped cavity

This paper analyzes the heat transfer and fluid flow of natural convection in a Γ shaped enclosure filled with Al₂O₃/Water nanofluid that operates under differentially heated walls. The Navier–Stokes and energy equations are solved numerically. Heat transfer and fluid flow are examined for parameters of non-uniform nanoparticle size, mean nanoparticle diameter, nanoparticle volume fraction, Grashof number and different geometry of enclosure. Finite volume method is used for discretizating positional expressions, and the forth order Rung-Kuta is used for discretizating time expressions. Also an artificial compressibility technique was applied to couple continuity to momentum equations. Results indicate that using nanofluid causes an increase in the heat transfer and the Nusselt number so that for R = 0.001 in Gr = 10³, the Nusselt number 25%, in Gr = 10⁴ 26%, and in Gr = 10⁵ 28% increases. Furthermore; by decreasing the mean diameters of nanoparticles, Nusselt number increases. By increasing R parameter (d_p,min/d_p,max) and nano particle volume fraction, Nusselt number increases.     

Non-Darcy free convection of Fe3O4-water nanoliquid in a complex shaped enclosure under impact of uniform Lorentz force

Effect of Lorentz forces on natural convection in a complex shaped cavity filled with nanoliquid immersed in porous medium is investigated by means of Control volume based finite element method (CVFEM). Non Darcy model is taken into account for porous media. The working fluid is Fe₃O₄ –water and its viscosity considered as function of magnetic field. Figures are illustrated for different values of Darcy number (Da), Fe₃O₄ -water volume fraction (?), Rayleigh (Ra) and Hartmann (Ha) numbers. Results depict that enhancing in Lorentz forces results in reduce in nanofluid motion and increase the thickness of thermal boundary. Convective heat transfer enhances with rise of Darcy number.     

Effect of the morphology on the mechanisms of the magnetization reversal of multilayered thin Co/Pd films

A comparative study of the magnetization curves of continuous and porous multilayered Pd_10nm/[Co_0.3nm]/Pd_0.55nm]15/Pd_2nm films deposited on an anodized TiO₂ template was performed by magnetometry. Based on the comparison of the dependences of coercive field H_C on angle θ between the easy-magnetization axis and the direction of external magnetic field H with theoretical dependences H_C(θ) for the magnetization reversal by domain walls motion (according to the Kondorski model) and the rotation of magnetic moments (by the Stoner–Wohlfarth model), the differences in the mechanisms of magnetization reversal for two mentioned types of the films were revealed. The correlation between the difference in the morphologies of the continuous and porous films and revealed change in the mechanisms of the magnetization reversal, as well as the changes in values of H_C and calculated constants of the magnetic anisotropy, is discussed.     

Entropy generation and MHD natural convection of a nanofluid in an inclined square porous cavity: Effects of a heat sink and source size and location

The effects of a heat sink and the source size and location on the entropy generation, MHD natural convection flow and heat transfer in an inclined porous enclosure filled with a Cu-water nanofluid are investigated numerically. A uniform heat source is located in a part of the bottom wall, and a part of the upper wall of the enclosure is maintained at a cooled temperature, while the remaining parts of these two walls are thermally insulated. Both the left and right walls of the enclosure are considered to be adiabatic. The thermal conductivity and the dynamic viscosity of the nanofluid are represented by different verified experimental correlations that are suitable for each type of nanoparticle. The finite difference methodology is used to solve the dimensionless partial differential equations governing the problem. A comparison with previously published works is performed, and the results show a very good agreement. The results indicate that the Nusselt number decreases via increasing the nanofluid volume fraction as well as the Hartmann number. The best location and size of the heat sink and the heat source considering the thermal performance criteria and magnetic effects are found to be D?=?0.7 and B?=?0.2. The entropy generation, thermal performance criteria and the natural heat transfer of the nanofluid for different sizes and locations of the heat sink and source and for various volume fractions of nanoparticles are also investigated and discussed.     

EXPERIMENTAL STUDY OF MARANGONI-BENARD CONVECTION IN A LIQUID LAYER INDUCED BY EVAPORATION

Marangoni-Bénard instability and convection in evaporating liquid layers have been studied experimentally through flow visualization and temperature profile measurement. Bénard cells have been observed in an evaporating thin liquid layer whether it is heated, adiabatic, or cooled from below. This experimental study has revealed a different mechanism from the traditional Rayleigh-Bénard and Marangoni-Bénard instabilities and convections, which require a negative temperature gradient in the thin liquid layer. Evaporation rate and enthalpy of evaporation have been found to be important parameters of instability and convection in an evaporating liquid layer. A modified form of Marangoni number, Ma^*, is proposed and its critical values, Ma^* _c, for alcohol and Freon-113 evaporating layers are determined experimentally. A quantitative comparison between Ma^* and the traditional Marangoni number, Ma, shows that Ma^* is an adequate indicator of the stability status in evaporating liquid layers.     

Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

A model for penetrative ferroconvection via internal heat generation in a ferrofluid saturated porous layer is explored. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid- paramagnetic and insulated to temperature perturbations, while at upper stress-free boundary a general convective-radiative exchange condition on perturbed temperature is imposed. The resulting eigenvalue problem is solved numerically using the Galerkin method. It is found that increasing in the dimensionless heat source strength N_s, magnetic number M₁ Darcy number Da and the non-linearity of magnetization parameter M₃ is to hasten, while increase in the ratio of viscosities Λ, Biot number Bi and magnetic susceptibility χ is to delay the onset of ferroconvection. Further, increase in Bi, Da⁻¹ and N_s and decrease in Λ, M₁ and M₃ is to diminish the dimension of convection cells.     

Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium

This study has compared the convection heat transfer of Water-based fluid flow with that of Water-Copper oxide (CuO) nanofluid in a sinusoidal channel with a porous medium. The heat flux in the lower and upper walls has been assumed constant, and the flow has been assumed to be two-dimensional, steady, laminar, and incompressible. The governing equations include equations of continuity, momentum, and energy. The assumption of thermal equilibrium has been considered between the porous medium and the fluid. The effects of the parameters, Reynolds number and Darcy number on the thermal performance of the channel, have been investigated. The results of this study show that the presence of a porous medium in a channel, as well as adding nanoparticles to the base fluid, increases the Nusselt number and the convection heat transfer coefficient. Also the results show that As the Reynolds number increases, the temperature gradient increases. In addition, changes in this parameter are greater in the throat of the flow than in convex regions due to changes in the channel geometry. In addition, porous regions reduce the temperature difference, which in turn increases the convective heat transfer coefficient.     

Numerical simulations of electro-thermo-convection and heat transfer in 2D cavity

In this article the electro-thermo-convective phenomena in a dielectric liquid enclosed in a 2D cavity and subjected to the simultaneous action of an electric field and a thermal gradient is studied. We solved directly the full set of coupled equations of Electro-Hydro-Dynamic (EHD) and energy equation using a finite volume method. In order to characterize the influence of the electric field on heat transfer the liquid is first heated (from a lateral wall) till the thermal steady state is obtained and then the electric potential and injection of electric charge is applied. Two cases of injection are considered: from the lower electrode and from a lateral wall (left or right). The flow pattern and Nusselt number strongly depend on the non-dimensional characteristic parameters: electrical parameter, Rayleigh number, Prandtl number and mobility parameter M. The convective motion passing from a purely thermal convection to a purely electrical convection and the number of electro-thermo-convective rolls patterns are investigated.As a consequence of the analysis of the combined effect of electric and thermal fields on the flow structure and on Nusselt number, we have also evaluated the heat transfer enhancement due to electroconvection. It is shown that the injection of electric charge increases the heat transfer and Nusselt number is independent of Rayleigh number for high enough values of T.     

多孔介质方腔内混合对流格子Boltzmann模拟

采用格子Boltzmann方法,对多孔介质方腔内的混合对流现象进行研究.方腔内部中心有一发热圆,径宽比D/L=0.4,冷流体从方腔左下角入口流进,从方腔左上角出口流出,四周壁面绝热.在普朗特数Pr=0.71和格拉晓夫数Gr=1.4×10⁴时,分析理查德森数Ri和达西数Da对发热圆表面平均努赛尔数Nu的影响.结果表明：Ri数位于10^-3~10范围内,Nu随Ri的增大而减小.Da越大,Ri对Nu的影响越显著;Da数位于10^-5~10^-2范围内,强制对流占主导的情况下（Ri≤0.1）,Nu随着多孔介质的Da的增大而增大.自然对流占主导的情况下（Ri=10）,Nu对Da的变化不敏感.     

Marangoni effects on forced convection of power-law liquids in a thin film over a stretching surface

The effect of Marangoni convection on the flow and heat transfer within a power-law liquid film on an unsteady stretching sheet is examined. The governing equations are non-dimensionalized using suitable transformation variables and the resulting transformed PDEs are then solved numerically by an implicit finite-difference scheme. Results for the velocity and temperature distributions, the free-surface temperature, and the wall temperature gradient are presented for various values of the unsteadiness parameter S, the power-law index n, the thermo-capillarity number M, and the modified Prandtl number Pr. The velocity and temperature distributions in the film are affected significantly by the thermally-induced Marangoni convection adjacent to the free surface. A fluid with a smaller Pr is more sensitive to the Marangoni effect. For Pr less than a moderate value (e.g., at selected values of n and ξ  , Pr?1$\mathit{Pr}?1$ for S=0.8$S=0.8$ and Pr?10$\mathit{Pr}?10$ for S=1.2$S=1.2$), the Marangoni effect tends to increase the heat transfer rate; whereas this impact diminishes in the high Pr regime.     

Laminar Natural Convection in a Square Cavity with a Partition on the Heated Vertical Wall

Abstract

The laminar natural convection in an air-filled square cavity with a partition on the heated vertical wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number Gr _H of approximately 1.4 × 10⁸) and non dimensional top wall temperatures θ _T of 0.57 (insulated) to 2.3. Experiments were performed with an aluminum partition with non dimensional height H _P /H of 0.0625 and 0.125 attached to the heated vertical wall at y/H = 0.65 and 0.95. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields but were mainly limited to the vicinity of the partition. For the cases with the heated top wall, the change in the height of the partition at y/H = 0.95 resulted in changes to the ambient temperature outside the boundary layer due to the reduction of the size of the recirculating flow in the corner region. The changes in the partition height and the top wall temperature affected the blockage effect of the partition, resulting in the local Nusselt number near the corner region to be affected. The local Nusselt number over most of the heated vertical wall of the partitioned cavity (y/H < 0.7) was correlated to the local Rayleigh number in the form Nu = C · Ra ⁿ .     

Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer by hydromagnetic three-dimensional free convection over a permeable stretching surface with radiation

The thermal-diffusion and diffusion-thermo effects on the heat and mass transfer characteristics of free convection past a continuously stretching permeable surface in the presence of magnetic field, blowing/suction and radiation are studied. The fluid viscosity is assumed to vary with temperature. The resulting, governing three-dimensional equations are transformed using a similarity transformation and then solved numerically by the shooting method. Comparison with previously published work is performed and full agreement is obtained. A parametric study showing the effects of variable viscosity parameter β, magnetic parameter M, Dufour number Df, Soret number Sr, radiation parameter R and blowing/suction parameter f₀ on the velocity, temperature, and concentration field of a hydrogen-air mixture as a non-chemical reacting fluid pair, as well as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number is carried out. These are illustrated graphically and in tabular form to depict special features of the solutions.     

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 10⁴ ≤ RA ≤ 10⁷ and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.     

Natural Convection of Temperature-Sensitive Magnetic Fluids in Porous Media

In this article, natural convection of a temperature-sensitive magnetic fluid in a porous media is studied numerically by using lattice Boltzmann method. Results show that the heat transfer decreases when the ball numbers increase. When the magnetic field is increased, the heat transfer is enhanced; however, the average wall Nusselt number increases at small ball numbers but decreases at large ball numbers due to the induced flow being more likely confined near the bottom walls with a high number of obstacles.