Lattice Boltzmann simulation of MHD mixed convection in a two‐sided lid‐driven square cavity

In this paper the effects of a magnetic field on mixed convection flow in a two‐sided lid‐driven cavity have been analyzed by the lattice Boltzmann method (LBM). The Hartmann number varied from Ha = 0 to 100. The study has been conducted for different Richardson numbers (Ri) from 0.01 to 100 while the direction of the magnetic field was investigated in the x‐direction. Consequences demonstrate that the heat transfer augments with an increment of the Richardson number for different Hartmann numbers for two cases. The heat transfer declines with the growth of the magnetic field for various Richardson numbers for two cases. The difference between the values of heat transfer for the two cases at variant parameters is negligible but the trend of fluid flow for the two cases is multifarious. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20402     

Free convention heat transfer from an isothermal horizontal thin strip: The influence of the Prandtl number

Simultaneous free convection above and below a uniformly heated horizontal plate has been widely investigated,both in the case of an isothermal surface,and of a uniformly heated surface,but always assuming only air as fluid（Pr=0.7）.Nevertheless,there are works dealing with horizontal plates whose results show that the Nu dependence on Pr may not be simply expressed by a power law with the same exponent of the Gr one.So it was considered useful to study the Prandtl number influence in the case of the isothermal horizontal strip.Results show that,while for the lower surface of the strip the Nu dependence in Gr can be expressed by a power law with an exponent close to the Gr one,for the upper surface the exponent is sensibly different.Correlating equations related to the investigated situations are proposed.     

Role of Prandtl number in the interaction phenomenon of surface radiation with an opposing mixed convection within a differential heated cavity

A numerical analysis has been done for opposing mixed convection resulting due to wall movement and buoyancy induced by a clockwise fluid motion in a differentially heated cavity. The effect of Prandtl number (Pr) and wall surface emissivity (?) has been investigated for different values of Richardson number. The net radiation method has been employed to simulate the effect of surface radiation. The energy equation along with its nonlinear boundary condition is treated with the Newton‐Raphson scheme. As momentum and energy equations are coupled with each other through their source terms, an iterative solution procedure is employed. A vorticity‐stream function formulation of the momentum equation has been adopted and solved by using an underrelaxation parameter of 0.45. The effect of Prandtl number with respect to the transformation of a multi‐cellular structure of streamline into a unicellular structure has been analyzed. For the same Richardson number (Ri) with an increase in Prandtl number, the flow and heat transfer phenomena changes from a buoyancy‐induced dominated flow to a shear‐induced dominated flow, which leads to some exciting results with respect to wall movement as well. Furthermore, the role of surface radiation in this respect has been emphasized. Nusselt number variation with the Prandtl number and surface emissivity has also been presented. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21003     

Effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls

We examined the effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls numerically. Non‐dimensional governing equations were solved for Re = 100, Pr = 0.1–10, and Ri = 36.44 by the SIMPLE method. The numerical results show that the swirl flow was generated along the flow direction, and its pitch lengthened with the increase of Pr. We also examined the strength of swirl flow using the swirl number, S, and we discuss heat transfer behavior as it corresponded to the flow. Heat transfer was promoted by the swirl flow with all Pr, and the optimum value existed within these Pr. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20319     

Wall Shape Effects on Convection Heat Transfer Over a Corrugated Channel

This study investigates the effects of the wall waviness on forced convection and its fluid flow in a channel bound by two wavy walls. The lattice Boltzmann method based on the boundary fitting method is used to simulate flow and thermal fields in the corrugated channel. The problem is investigated for different Reynolds numbers (50 to 150), wall amplitudes (0 to 0.35), number of wall wavelength (2 to 8), and phase difference of the walls (0 to 270) when the Prandtl number is equal to 0.71 for air flow. The study represents the significant effects of wavy walls on flow and thermal fields in a two‐dimensional channel. It is found when the phase difference between the channel walls has a value equal to 90°; the best heat transfer rate can be achieved in comparison with other geometrical conditions and the flow is likely to be periodically unsteady at lower Reynolds numbers.     

Simulating magnetohydrodynamic natural convection flow in a horizontal cylindrical annulus using the lattice Boltzmann method

A numerical study is presented about the effect of a uniform magnetic field on free convection in a horizontal cylindrical annulus using the lattice Boltzmann method. The inner and outer cylinders are maintained at uniform temperatures and it is assumed the walls are insulating with a magnetic field. Detailed numerical results of heat transfer rate, temperature, and velocity fields have been presented for Pr=0.7, Ra=10³ to 5 × 10⁴, and Ha=0 to 100. The computational results show that in a horizontal cylindrical annulus the flow and heat transfer are suppressed more effectively by a radial magnetic field. It is also found that the flow oscillations can be suppressed effectively by imposing an external radial magnetic field. The average Nusselt number increases by increasing the radius ratio while it decreases by increasing the Hartmann number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21008     

Lattice Boltzmann Simulation of Natural Convection in a Differentially Heated Square Enclosure Containing Heat Generating Low‐Prandtl Number Fluid

Lattice Boltzmann simulations were conducted for the free convective flow of a low‐Prandtl number (Pr = 0.0321) fluid with internal heat generation in a square enclosure having adiabatic top and bottom walls and isothermal side walls. The problem of free convection with volumetric heat source has represented itself in connection with advanced engineering applications, such as water‐cooled lithium–lead breeder blankets for nuclear fusion reactors and liquid metal sources of spallation neutrons for subcritical fission systems. A single relaxation time (SRT) thermal lattice Boltzmann method (LBM) was employed. While applying SRT, a D2Q9 model was used to simulate the flow field and temperature field. Results have been obtained for various Rayleigh numbers characterizing internal and external heating from 10³ to 10⁶. Flow and temperature fields in terms of stream function and isotherms in the enclosure were predicted for these cases. The temperature of the fluid in the enclosure was found higher than the heated wall temperature at high values of internal Rayleigh numbers. The internal heat generation affected the rate of heat transfer significantly as two convection loops are observed in the enclosure. The average Nusselt number at the heated and cold wall was determined for all the cases.     

Local Convective Heat Transfer from Small Heaters to Impinging Submerged Axisymmetric Jets of Seven Coolants with Prandtl Number Ranging from 0.7 to 348

INTRODUCTIoNJetimpingementhasbeenextensivelyemployedintechnicalprocessestoproducerelativelyhighheat/massfluxes.Incomparisonwiththeheat/masstransferratesprovidedbyconventionaltechniqueswithfluidfiowsparalleltotheheat/masstransfersur-face,aremarkableincreaseintransfercoefficientscanbeobtainedinthisfashion.Inmostcasesairisusedastheworkingmedium.Examplesofairjetapp1icationsincludecoolingofturbinebladesandelectroniccom-ponents,annealingofmetallicandplasticsheets,dry-ingoftextilesandpaper,andtem…     

Numerical Simulation of Fluid Flow and Heat Transfer on the Lubricating Surface with Micro‐Groove

The effect of the lubricant flow in the micro‐grooves which resulted from the machining can be expressed in the flow fluid and heat transfer during the mechanical lubrication process. In this paper, a thermal lattice Boltzmann model (LBM), which consists of the heat viscous dissipation term, was proposed to investigate on the lubricants flow and heat transfer in the micro‐grooves. The heat, generated in the lubricating flowing process, was equivalent to a heat source R (x, t) within the fluid and added to the internal energy distribution function. The effect of the heat generated by the fluid on the flow and temperature field can be derived by comparing these two models. The results showed that the fluid temperature rises slower than the mainstream area on account of the vortex motion in the grooves. When the heat source is added to the function, the vortex became larger and the solid boundary was heated by the fluid. Thus, the improved thermal lattice Boltzmann method can accurately simulate the flow of lubricants.     

Lattice Boltzmann Simulation of Natural Convection in a Square Cavity with Linearly Heated Wall(s)

In this study, the lattice Boltzmann method is used in order to investigate the natural convection in a cavity with linearly heated wall(s). The bottom wall is heated uniformly and the vertical wall(s) are heated linearly, whereas the top wall is insulated. Investigation has been conducted for Rayleigh numbers of 10³ to 10⁵, while Prandtl number is varied from 0.7 to 10. The effects of an increase in Rayleigh number and Prandtl number on streamlines, isotherm counters, local Nusselt number and average Nusselt number are depicted. It has been observed that the average Nusselt number at the bottom wall augments with an increase in Prandtl number.     

Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid

Natural convection in enclosures using water/SiO₂ nanofluid is simulated with Lattice Boltzmann method (LBM). This investigation compared with other numerical methods and found to be in excellent agreement. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³-10⁵, the volumetric fraction of nanoparticles between 0 and 4% and aspect ratio (A) of the enclosure between 0.5 and 2. The thermal conductivity of nanofluids is obtained on basis of experimental data. The comparisons show that the average Nusselt number increases with volume fraction for the whole range of Rayleigh numbers and aspect ratios. Also the effect of nanoparticles on heat transfer augments as the enclosure aspect ratio increases.     

The effects of Prandtl number on natural convection in triangular enclosures with localized heating from below

The effect of Prandtl number on natural convection heat transfer and fluid flow in triangular enclosures with localized heating has been analyzed by solving governing equations of natural convection in streamfunction–vorticity form with finite-difference technique. Solution of linear algebraic equations was made by Successive Under Relaxation (SUR) method. Bottom wall of triangle is heated partially while inclined wall is maintained at a lower uniform temperature than heated wall while remaining walls are insulated. Computations were carried out for dimensionless heater locations (0.15 ≤ s ≤ 0.95), dimensionless heater length (0.1 ≤ w ≤ 0.9), Prandtl number (0.01 ≤ Pr ≤ 15) and Rayleigh number (10³ ≤ Ra ≤ 10⁶). Aspect ratio of triangle was chosen as unity. It is observed that both flow and temperature fields are affected with the changing of Prandtl number, location of heater and length of heater as well as Rayleigh number.     

MHD Turbulent and Laminar Natural Convection in a Square Cavity utilizing Lattice Boltzmann Method

In this study, the lattice Boltzmann method was used to solve the turbulent and laminar natural convection in a square cavity. In this paper a fluid with Pr = 6.2 and different Rayleigh numbers (Ra = 10³, 10⁴,10⁵ for laminar flow and Ra = 10⁷, 10⁸,10⁹ for turbulent flow) in the presence of a magnetic field (Ha = 0, 25, 50, and 100) was investigated. (Results show that the magnetic field drops the heat transfer in the laminar flow as the heat transfer behaves erratically toward the presence of a magnetic field in a turbulent flow. Moreover, the effect of the magnetic field is marginal for a turbulent flow in contrast with a laminar flow.The greatest influence of the magnetic field is observed at Ra = 10⁵ from Ha = 0 to 100 as the heat transfer decreases significantly.