Uniform Thermal Boundary Condition Research Articles

Numerical simulation of natural convection of nanofluids in an inclined square porous enclosure by lattice Boltzmann method

In this work, numerical simulation of nature convection of Al<sub>2</sub>O<sub>3</sub>-H<sub>2</sub>O nanofluid in an inclined square porous enclosure is investigated to analyze the influence of different physical parameters on fluid flow and heat transfer via the lattice Boltzmann method. Due to stable chemical properties and low price in the dispersion system, Al<sub>2</sub>O<sub>3</sub>-H<sub>2</sub>O nanofluid is widely used in the field of industrial heat transfer enhancement, which is the focus of present work. When the nanofluid is transport in a porous media, the Darcy-Brinkman-Forchheimer model is usually used to describe the porous media effects on nanofluid flow. Compared with uniform thermal boundary condition, the natural convection of nanofluids with non-uniform thermal boundary condition has not received much attention. In this paper, the sinusoidal boundary condition is applied to the left side wall to analyze the heat transfer mechanism of Al<sub>2</sub>O<sub>3</sub>-H<sub>2</sub>O nanofluid in the inclined square porous enclosure. The effect of porosity (0.3 ≤ <inline-formula><tex-math id="Z-20200813202835">\begin{document}$\epsilon $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202835.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202835.png"/></alternatives></inline-formula> ≤ 0.9), Rayleigh number (10<sup>3</sup> ≤ <i>Ra</i> ≤ 10<sup>6</sup>), volume fraction of nanoparticle (0 ≤ <i>ϕ</i> ≤ 0.04), tilt angle (0° ≤ <i>γ</i> ≤ 120°) on the heat transfer performance are systematically investigated. Numerical results show that the non-uniform boundary condition can affect the heat transfer performance on Al<sub>2</sub>O<sub>3</sub>-H<sub>2</sub>O nanofluid with different physical quantities, which is different from the uniform boundary condition. When <i>γ</i> = 0° and <i>Ra</i> is fixed, the <i>Nu</i><sub>ave</sub> number (average Nusselt number) at the heated wall increases with porosity. When <i>γ</i> = 40°, 80° or 120°, the <i>Nu</i><sub>ave</sub> reaches its maximum value at <inline-formula><tex-math id="Z-20200813202844">\begin{document}$\epsilon $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202844.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202844.png"/></alternatives></inline-formula> = 0.7. In addition, if <inline-formula><tex-math id="Z-20200813202907">\begin{document}$\epsilon $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202907.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202907.png"/></alternatives></inline-formula> and <i>Ra</i> are fixed, the results show that the heat transfer performance is most efficient at <i>γ</i> = 40° whereas it is weakened at <i>γ</i> = 80°. Moreover, when different inclination angles are applied to the square cavity, the <i>Nu</i><sub>ave</sub> increases slightly with an augmentation of <i>ϕ</i>. In all, compared with the uniform temperature boundary condition, the effect of volume fraction of nanoparticles on the enhanced heat transfer is not significant, therefore, to improve the heat transfer performance of nanofluids with given <i>ϕ</i> and <i>Ra</i>, it is necessary to take advantage of the improvement of effective thermal conductivity for the nanofluids in porous media and the perturbation influence of inclination angles on the system together with using appropriate porosity and square cavity tilt angle to intervene the flow.

Experimental study of natural convection heat transfer from a nonuniformly heated flat plate simulating PV panel

In view of the characteristic of Photovoltaic (PV) conversion, an experimental study has been conducted to investigate the natural convection heat transfer from a flat plate. In order to simulate the real PV cells, three electrical heating circuits were employed to achieve a linear nonuniform heat flux boundary condition. The major parameters, such as the gradient parameter of heat flux k, tilt angle θ and heat flux qw were introduced to analyze their influence on heat transfer ability. Both the local temperature distribution and the overall trend of Nusselt number have been presented. Comparing with the uniform thermal boundary condition, the results show that the local convection heat transfer coefficient is fluctuated at the positions where heat flux has changed. When gradient parameter of heat flux increases, the difference of local convection heat transfer coefficient at the top of the plate between tilt angle θ = 0° and 90° becomes smaller. Moreover, it is observed that the gradient parameter of heat flux has a promotion effect on average convection Nusselt number at larger tilt angle, but the effect becomes complex as tilt angle is smaller. Finally, a correlation combining all significant factors has been put forward to estimate the natural convection heat transfer.

Aspect ratio effect on natural convection in a square enclosure with a sinusoidal active thermal wall using a thermal non-equilibrium model

ABSTRACTA numerical investigation of the aspect ratio effect on natural convection in a square enclosure is carried out by adopting the local thermal non-equilibrium model. The top and bottom walls of the enclosure are adiabatic, the left vertical wall is partially heated and cooled by the sinusoidal thermal boundary condition, and the right vertical wall is maintained at uniform thermal boundary condition. The results show the value of periodicity parameter increasing. The streamlines vary in different patterns, rotating clockwise and counterclockwise simultaneously when N > 1, and the number of clockwise and counterclockwise rotating cells increases with the increase of N and equals the value of N. The sinusoidal local Nusselt number profiles are observed and the wave amplitude of local Nusselt number decreases with the increase of aspect ratio, and the absolute values of average Nusselt number at left wall of porous cavity reach maximum when Ar = 1. The absolute value of solid-to-fluid temperature differences decreases as the inter-phase heat transfer coefficient (H) increases and it increases as the value of aspect ratio increases. The total heat transfer of porous cavity can be enhanced by increasing the aspect ratio and the thermal conductivity ratio.

Numerical analysis of natural convection in a porous cavity with the sinusoidal thermal boundary condition using a thermal nonequilibrium model

ABSTRACTSteady non-Darcy natural convection in a porous cavity with sinusoidal thermal boundary condition is studied numerically by adopting the local thermal non-equilibrium (LTNE) model in this paper. The top and bottom walls of the enclosure are adiabatic, whereas the left vertical wall is partially heated and cooled by a sinusoidal temperature profile and the right vertical wall is cooled by the uniform thermal boundary condition. The results show that, compared with the uniform boundary conditions, the sinusoidal boundary conditions can enhance the heat transfer rate of a porous cavity. The values of local Nusselt numbers at the left sidewall can be enhanced by sinusoidal thermal boundary condition and the maximum absolute value of the local Nusselt number appears near the top and bottom walls of the cavity. The thermal nonequilibrium effect on natural convection in the porous cavity can be enhanced by the sinusoidal thermal boundary condition, and the absolute value of the dimensionless solid-to-fluid temperature differences decreases as the thermal conductivity ratio (γ) increases and approaches zero when γ = 10. The periodicity parameter (N) has a significant effect on the heat transfer rate of the porous cavity and the effect of periodicity parameter on heat transfer in porous cavity reduces gradually with the increase of H.

Buoyancy induced convection in a porous cavity with sinusoidally and partially thermally active sidewalls under local thermal non-equilibrium condition

Steady non-Darcy natural convection in a porous cavity with non-uniform thermal boundary condition is studied numerically by adopting the local thermal non-equilibrium (LTNE) model in this paper. The top and bottom walls of the cavity are adiabatic. The left vertical wall is partially heated and cooled by sinusoidal temperature profile and the right side wall of the cavity is partially cooled by uniform thermal boundary condition. The results show that, the oscillation amplitude of the local Nusselt number profiles (Nufy, Nusy) along the Y coordinate decreases with the increase of H. The difference of the local Nusselt numbers between different cases of partial cooling (case A–case D) can be reduced by increasing of N. The difference of solid-to-fluid temperature differences between different cases of partial cooling can be reduced by increasing of H and γ. Positive values of the average Nusselt number appear at the left side wall of the porous cavity, which indicates that there exists heat transfer along the positive direction of the X axis in the porous cavity. Compared with the left wall of the cavity, it is faster for the right wall to reach the thermal equilibrium state, which approaches a constant value for low values of H (H=3000).

Forced convective heat transfer from spheres to Newtonian fluids in steady axisymmetric flow regime with velocity slip at fluid–solid interface

The heat transfer phenomenon of spherical particles in Newtonian fluids with velocity slip and uniform thermal boundary condition at the fluid–solid interface has been numerically investigated using a computational fluid dynamics (CFD) based in-house solver. At the interface linear slip velocity boundary condition has been adopted. The dimensionless continuity, momentum and energy equations along with the appropriate non-dimensional boundary conditions are solved by a segregated approach. This numerical procedure is a finite difference method based CFD solver implemented on a staggered grid arrangement in spherical coordinates. The convective and diffusive terms are discretized using the quadratic upstream interpolation for convective kinematics and a second order central differencing scheme respectively. Prior to obtaining new results, the present numerical solver is extensively validated by comparing the present values of the average Nusselt numbers with the existing literature values for either extreme values of the slip conditions, i.e., for fully slip and no-slip conditions. Further new results are obtained over the range of conditions as the Reynolds number, Re = 0.1–200; the Prandtl number, Pr = 1–100; and dimensionless slip parameter, λ = 0.01–100. The effects of these parameters on the isotherm contours and the local and average Nusselt numbers are thoroughly discussed and finally on the basis of present numerical results (196 data points), an empirical correlation is proposed for the average Nusselt numbers of single spheres with velocity slip at the interface as function of Re, Pe, and λ.

Natural convection in a porous rectangular enclosure with sinusoidal temperature distributions on both side walls using a thermal non-equilibrium model

This study reports a numerical investigation of the natural convective flow and heat transfer in a rectangular cavity filled with a heat-generating porous medium by adopting the local thermal non-equilibrium model. The top and bottom walls of the enclosure are adiabatic and the left and right walls are partially heated and partially cooled by sinusoidal temperature profile. The results show that periodic variations with positive and negative values appear in the isotherms for fluid phase and solid phase, and the periodicity increases with the increase of N. The phase deviation has significant influence on fluid flow and heat transfer in the porous cavity. When N is large enough (N=32), patterns of streamlines, isotherms for fluid phase and solid phase display like that of uniform thermal boundary condition case, and the total heat transfer rate through the whole cavity is close to that resulted by uniform thermal boundary condition. The heat transfer of porous cavity can be enhanced by sinusoidal thermal boundary condition and the phase deviation has tiny effect on the heat transfer of cavity when N is large enough (N=32). The increase of inter-phase heat transfer coefficient leads to faster reduction of Q with the increase of periodicity parameter.

The Effects of Nonuniform Thermal Boundary Condition on Thermal Stress Calculation of Water-Cooled W/Cu Divertors

The thermal boundary condition has very important effects on the accuracy of thermal stress calculation of a water-cooled W/Cu divertor. In this paper, phase-change heat transfer was simulated based on the Euler homogeneous phase model, and local differences of liquid physical properties were considered under one-sided high heating conditions. The steady-state temperature field and thermal stress field under nonuniform thermal boundary conditions were obtained through numerical calculation. By comparison with the case of traditional uniform thermal boundary conditions, the results show that the distribution of thermal stress under nonuniform thermal boundary conditions exhibits the same trend as that under uniform thermal boundary conditions, but is larger in value. The maximum difference of maximum von Mises stress is up to 42% under the highest heating conditions. These results provide a valuable reference for the thermal stress calculation of water-cooled W/Cu divertors.

Analysis of MHD natural convection in a nanofluid-filled open cavity with non uniform boundary condition in the presence of uniform heat generation/absorption

This paper examines the natural convection in an open cavity with non uniform thermal boundary condition. The cavity is filled with a water-Al2O3 nanofluid and subjected to a magnetic field in the presence of heat generation or absorption. Lattice Boltzmann method (LBM) is applied to solve the coupled equations of flow and temperature fields. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number of the base fluid, Ra=103–106, Hartmann number varied from Ha=0–60, heat generation/absorption coefficient (q=−10, −5, 0, 5 and 10) and the solid volume fraction of nanoparticles between ϕ=0 and 6%. Results show that the heat transfer rate decreases with the rise of the Hartmann number and increases with the augmentation of the Rayleigh number. The nanoparticles effect is more important at a high Rayleigh number. Also, the nanoparticles effect is more important for heat generation condition (q>0) than absorption generation condition (q<0).

Manifold microchannel heat sink design using optimization under uncertainty

A three-dimensional numerical model is developed and validated to study the effect of geometric parameters such as microchannel depth and width, manifold depth, and manifold inlet and outlet lengths on the performance of a manifold microchannel (MMC) heat sink. The manifold arrangement used to distribute the flow through alternating inlet and outlet pairs greatly reduces the pressure drop incurred in conventional fluid supply arrangements due to its shorter flow paths, while simultaneously enhancing the heat transfer coefficient by limiting the growth of thermal boundary layers. The computational analysis is performed on a simple unit-cell model to obtain an optimized design for uniform thermal boundary conditions, as well as on a porous-medium model to obtain a complete system-level analysis of multiple microchannels across one manifold. The porous-medium approach can be further modified to analyze the performance under asymmetrical heating conditions. Along with conventional deterministic optimization, a probabilistic optimization study is performed to identify the optimal geometric design parameters that maximize heat transfer coefficient while minimizing pressure drop for an MMC heat sink. In the presence of uncertainties in the geometric and operating parameters of the system, this probabilistic optimization approach yields a design that is robust and reliable, in addition to being optimal. Such an optimization analysis provides a quantitative estimate of the allowable uncertainty in input parameters for acceptable uncertainties in the relevant output parameters. The approach also yields information such as the local and global sensitivities which are used to identify microchannel width and manifold inlet length as the critical input parameters to which the outputs are most sensitive. The deterministic analysis shows that the heat transfer performance of the MMC heat sink is optimal at a manifold inlet to outlet length ratio of 3. A comparison between the deterministic and probabilistic optimization approaches is presented for the unit-cell model. A probabilistic optimization study is performed for the porous-medium model and the results thus obtained are compared with those of the unit-cell model for a uniform heat flux distribution.

Analysis of Temperature Oscillations in Parallel Evaporators of a Carbon Dioxide Two-Phase Loop

The tracker thermal control system (TTCS) is an active-pumped two-phase carbon dioxide cooling loop, which is developed for the Alpha Magnetic Spectrometer (AMS) tracker front-end electronics. The evaporators in parallel, gathering waste heat from, and providing stable and uniform thermal boundary condition to the electronics, are the key components of the loop. Any abnormities to the parallel evaporators is unacceptable. In this paper, we observed self-sustained temperature oscillations at the outlet of the evaporators when the cooling loop is operated at low temperature with the pump rotation speed lower than 3,300 rpm. Analysis shows that the oscillation could be of density-wave origin, and the flow rate redistribution between the two parallel evaporators may result in the self-sustained temperature oscillations.

A Numerical Study of the Thermal Entrance Effect in Miniature Thermal Conductivity Detectors

The microchannel flow in miniature TCDs (thermal conductivity detectors) is investigated numerically. Solutions based on the boundary-layer approximation are not very accurate near the channel inlet for low Reynolds numbers. As a result the full Navier-Stokes equations were solved to analyze the gas flow in a miniature TCD. The effects of channel size and inlet and boundary conditions on the heat transfer rate were examined. When the gas stream is not preheated, the distance for a miniature TCD to reach the conduction-dominant region is approximately two to three times the thermal entry length of a constant property pipe flow subject to a uniform thermal boundary condition. If the gas inlet temperature is in the vicinity of the mean gas temperature in the conduction-dominant region, the entrance length is much shorter and very close to that of a constant property pipe flow with uniform surface temperature or heat flux.

Turbulent heat transfer in annuli with uniform thermal boundary condition of second kind

Die Warmeubertragungseigenschaften der voll ausgebildeten turbulenten Stromung in konzentrischen Ringspaltkanalen wurden fur den Fall konstanter thermischer Randbedingungen zweiter Art theoretisch untersucht. Die Energiegleichung wurde durch die Trennung der Variablen analytisch gelost. Ergebnisse fur den Warmeubergang im thermischen Einlauf, in der thermisch ausgebildeten Stromung und fur die thermischen Einlauflangen werden uber einen weiten Bereich der Reynolds-Zahl (104⩽Re⩽106) und der Prandtl-Zahl (0⩽Pr⩽100) angegeben und mit verfugbaren Mesergebnissen verglichen.

An Analysis of Laminar Free and Forced Convection between Finite Vertical Parallel Plates

Approximate analytical solutions are presented for constant-property laminar free- and forced-convection flows between finite vertical parallel plates. For free convection, the thermal boundary conditions considered include the thermally symmetric channel with uniform wall temperature or step change in wall temperature and the unsymmetric channel with uniform but unequal wall temperatures. For forced convection and combined free and forced convection, the thermally symmetric and uniform thermal boundary condition is considered. Where possible, results are compared with available numerical and experimental results. Particular attention is given to heat-transfer results, which cover a wide range of Rayleigh and Prandtl numbers. For combined convection the heat-transfer results are related to the impressed pressure difference and flow rate.