Modulated gravity effects on nonlinear convection in viscoelastic ferromagnetic fluids between two horizontal parallel plates

In this study, the analysis of nonlinear stability with viscoelastic ferromagnetic fluids as working media is performed by finite-amplitude perturbations. The solution of the resulting nonautonomous system of the Lorenz model (generalized Khayat–Lorenz model of four modes) is obtained numerically to measure the amount of heat transport. The effects of elastic parameters, Prandtl number, modulation parameters, buoyancy magnetic parameter, and nonbuoyancy magnetic parameter on heat transport are studied. Heat transport is quantified through the average Nusselt number, which is determined by solving the scaled Lorenz model. As limiting cases of the study, the results of Newtonian, Maxwell, Rivlin–Ericksen fluids are determined. The results obtained have been presented graphically.     

Inhomogeneous flow model of natural convection,entropy generation,and heatlines visualization in wavy I-shaped enclosure with rectangular heater

The present investigation is on examination of the natural convection and entropy generation considering the heatlines visualization of nanofluid I-shaped enclosure with two corrugated walls considering inner rectangular heater of three different heights. The influence of Brownian motion along with thermophoresis had been implemented using Inhomogeneous two-phase model of nanofluid. The governing equations were solved numerically using COMSOL software. Influence of Rayleigh number $$, Buoyancy ratio number $$, Lewis number $$, heater length $$. The results indicate that the influence of Lewis number on heat transfer bettering is stronger at high Rayleigh number $$ while its impact is negligible at a lower value of Rayleigh number (conduction mode). In addition, the total entropy generation gets its highest value at Lewis number $$. Bejan number, fluid flow strength and heat rate increase as the rectangular heater height increases. Also, higher heat transfer augmentation is taken when the heater height is $$ while increasing the heater height to $$ leads to more total entropy generation. The impact of heater height on total entropy generation is highly affected by Rayleigh number as increasing the heater height from $$ into $$, total entropy generation increases by $$ at $$ while it increases by $$ at $$.     

轴向通流旋转盘腔内类Rayleigh-Benard对流稳定性研究

利用数值模拟的方法对冷气轴向通流旋转盘腔的流动过程进行了研究。研究发现。对应一进口冷气的冒诺教，存在一临界瑞利敷(Rαc)，高于该瑞利教(Rα)。流动出现不稳定现象。且Rα越大，不稳定行为越严重。对于特例，盘腔内的流动可以看成是由类Rayleigh—Benard对流和强迫对流两个区域构成，两个区域通过能量和质量交换相互影响。流动随着Rα的增加从稳态发展为非稳态；采用频谱图分析的方法对数值解的不稳定性进行定性分析。结果显示随着Rα的增大。教值解经历了从稳定解到分贫的周期性不稳定和准周期不稳定的发展过程，离心浮升力引起的类Rayleigh—Benard对流是造成流动从稳定到不稳定发展的重要原因，哥氏力的存在恶化了不稳定过程。     

Natural convection heat transfer from upward-facing plates in saline water

Saltwater or brackish water is used as a coolant in most industries. Therefore, understanding the heat transfer processes and hydrodynamics during the natural convection in saline water is crucial for enhancing the efficiency of a heat exchanger. This study elaborates on the natural convection heat transfer in saline water under atmospheric conditions. A DC power supply is used to regulate the power given to the heater in a liquid pool for thermal analysis. The pool liquid comprises solutions with varying salinity from 0%, 0.2%, 0.5%, and 2%. The effect of varying salinity on the heat transfer coefficient and the thermal aspects encountered during the desalination process is analyzed. The temperature distribution across the surface of the heater is monitored using an infrared camera. It is studied for the solution of different salinities. The heat transfer coefficient and Nusselt number are investigated during natural convection for normal water and salt solution of different concentrations. It is inferred from the study that in the regime of natural convection, there is no significant difference in the Nusselt number for normal water and saltwater for the lower value of temperature difference between the plate and pool. The heat transfer coefficient in 0.2% saline water is higher as compared to the other solutions.     

Two dimensional numerical simulation of transient natural convection in freezer

A two dimensional model of the transient natural convection in a freezer is studied numerically by finite volume approach. The temperatures of the freezer outside surfaces and the evaporator vary in specified manners, which were taken from an experimental work. The fluid in the freezer is of the Bousinnesq type and the flow is assumed laminar. The transient heat conduction in the insulating layers and the temperature and velocity fields of the fluid are solved conjugately. The radiation heat transfer between the freezer inner surfaces is taken into account by using the additional source term method. The distributions of the local Nusselt number along the upper and lower surfaces of the evaporator and their average values in the period of periodically unsteady operation are calculated. Comparisons are made between the results with and without consideration of inner surface radiative heat transfer. It is found that the radiative heat transfer between the inner surfaces has a profound effect on the evaporator heat transfer characteristics.     

Natural convection heat transfer of high temperature gas in an annulus between two vertical concentric cylinders

Water cooling panels have been adopted as the vessel cooling system of the High Temperature Engineering Test Reactor (HTTR) to cool the reactor core indirectly by natural convection and thermal radiation. In order to investigate the heat transfer characteristics of high temperature gas in a vertical annular space between the reactor pressure vessel and cooling panels of the HTTR, we carried out experiments and numerical analyses on natural convection heat transfer coupled with thermal radiation heat transfer in an annulus between two vertical concentric cylinders with the inner cylinder heated and the outer cylinder cooled. In the present experiments, Rayleigh number based on the height of the annulus ranged from 2.0 × 10⁷ to 5.4 × 10⁷ for helium gas and from 1.2 × 10⁹ to 3.5 × 10⁹ for nitrogen gas. The numerical results were in good agreement with the experimental ones regarding the surface temperatures of the heating and cooling walls. As a result of the experiments and the numerical analyses, the heat transfer coefficient of natural convection coupled with thermal radiation was obtained as functions of Rayleigh number, radius ratio, and the temperatures and emissivities of the heating and cooling wall surfaces. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(5): 293–308, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20070     

Forced—Flow Convection for Liquid Methanol Flowing through Microchannels

Experiments were conducted to investigate the single phase forced-flow convection of methanol flowing through microchannels with rectangular cross-section. The fully-developed turbulent convection regime was found to be initiated at aboutRe=1000 ∼ 1500. The fully developed turbulent heat transfer can be predicted by the well-known Dittus-Boelter correlation with mere modification of the original empirical constant coefficient 0.023 to 0.00805. The transition and laminar heat transfer behaviors in microchannels are highly peculiar and complicated, and heavily affected by liquid temperature, velocity and microchannel size.     

Nonlinear analysis of the effect of viscoelasticity on ferroconvection

This paper concerns a nonlinear analysis of the effects of viscoelasticity on convection in ferroliquids. We consider the Oldroyd model for the constitutive equation of the liquid. The linear stability analysis yields the critical value of the Rayleigh number for the onset of oscillatory convection in Maxwell and Jeffrey ferroliquids. The use of a minimal mode double Fourier series in the nonlinear perturbation equations yields a Khayat–Lorenz model for the ferromagnetic liquid, and that is scaled further to get the classical Lorenz model as a limiting case. The scaled Khayat–Lorenz model thus obtained is solved numerically and the solution is used to compute the time-dependent Nusselt number, which quantifies the heat transport. The results are analyzed for the dependence of the time-averaged Nusselt number on different parameters.     

Effect of rotation and internal heat generation on Darcy–Brinkman convection in Oldroyd-B liquid

Convection in an Oldroyd-B liquid saturated highly permeable porous medium is studied via both linear and nonlinear theories. Estimating a convection threshold is the objective of linear-stability analysis whereas convection amplitudes and heat transfer are elucidated by performing nonlinear-stability analysis. The eigenvalue problem is solved by the Galerkin method of weighted residuals. The oscillatory mode becomes dominant over the stationary mode. This is because of the race among diffusivity, viscoelasticity, internal-heat generation, and rotation. The increasing permeability, internal heat generation coefficient, and stress-relaxation parameter are liable to subcritical motions while the rotation, viscosities ratio, heat capacities ratio, and strain retardation parameter are responsible for the system attaining a supercritical state. The Runge–Kutta–Gill method presents the mechanism to evaluate the amount of heat transfer. The increasing Rayleigh number, internal Rayleigh number, Darcy number, Deborah number, Prandtl number, and the heat capacities ratio enhance the heat transfer. This offers a convenient mechanism for regulating convection. The results obtained in the present paper are expected to play a decisive role in some of the real-life applications such as oil-reservoir modeling, crude oil extraction, crystal growth, medicine industries, geothermal-energy utilization, and so on.     

Numerical study of mixed convective heat transfer in a lid‐driven enclosure with rotating cylinders

A numerical simulation is performed to characterize the mixed convective transport in a three‐dimensional square lid‐driven enclosure with two rotating cylinders. The top wall is moving in the positive x‐direction, and the bottom wall is at a higher fixed temperature compared with all other isothermal walls. Both cylinders are rotating in its own plane about their centroidal axis. On the basis of rotation of both cylinders in clockwise or counter‐clockwise directions, four rotational models are studied. Various controlling parameters considered in the present study are Grashof number (10 ³ < Gr < 10 ⁵), rotating speed of the cylinder (5 < ω < 50), and the Reynolds number based on top wall movement is fixed to 100. The effect of cylinder rotation on the heat transfer of bottom wall is reported with the help of streamlines, contour plots of z‐component of vorticity, averaged and local Nusselt number, ratios of secondary flow and drag coefficient. It is observed that the heat transfer at the bottom wall is substantially dependent on the rotational model and rotational speed of the cylinder.     

An improved model for natural convection heat loss from modified cavity receiver of solar dish concentrator

A 2-D model has been proposed to investigate the approximate estimation of the natural convection heat loss from modified cavity receiver of without insulation (WOI) and with insulation (WI) at the bottom of the aperture plane in our previous article. In this paper, a 3-D numerical model is presented to investigate the accurate estimation of natural convection heat loss from modified cavity receiver (WOI) of fuzzy focal solar dish concentrator. A comparison of 2-D and 3-D natural convection heat loss from a modified cavity receiver is carried out. A parametric study is carried out to develop separate Nusselt number correlations for 2-D and 3-D geometries of modified cavity receiver for estimation of convective heat loss from the receiver. The results show that the 2-D and 3-D are comparable only at higher angle of inclinations (60° ? β ? 90°) of the receiver. The present 3-D numerical model is compared with other well known cavity receiver models. The 3-D model can be used for accurate estimation of heat losses from solar dish collector, when compared with other well known models.     

Effect of heat source on Rayleigh–Bénard convection in rotating viscoelastic liquids

The influence of heat sources on instability in rotating viscoelastic liquids is studied. Linear stability analysis is done using normal modes. Computations are done for 10 boundary combinations and the results reveal that convection manifests via the oscillatory mode in this case. The critical values of the oscillatory and stationary instability have been studied. The results indicate individual stabilizing influences of rotation and strain retardation along with heat source in the case of free isothermal boundary conditions. It has quite unpredictable influences on the system stability in all the other boundary conditions for the chosen parameters. By suitable limiting processes, results pertaining to Oldroyd liquid B will lead to those of Maxwell, Newtonian, and Rivlin–Ericksen liquids. The problem finds applications in a working media consisting of viscoelastic liquids with nonisothermal systems.     

自然对流温度场节能改造

本文通过热流理论分析和传热计算,指出了某一运行多年的自然对流温度场的不足,为了节能增效,采取了快捷的改造措施。工程竣工后试运转表明节能率可达50%,对所有自然对流温度场的改造具有普遍指导意义和重要参考借鉴作用。     

Evaporation of a thin binary liquid film by forced convection into air and superheated steam

<正>This paper deals with a numerical analysis of the evaporation of a thin binary liquid film by forced convection inside a channel constituted by two plates.The first plate is externally insulated and wetted by a thin water ethylene glycol film while the second is dry and isothermal.The first part is concerned with the effects of inlet ambiance conditions and the liquid concentration of ethylene glycol on the distribution of the velocity,temperature,concentrations profiles and the axial variation of the evaporation rate.The second part is focused on the inversion temperature point of the evaporation of binary liquid film.Results show that the inversion temperature phenomenon for the evaporation of binary liquid mixture is observed for high liquid concentration of ethylene glycol.The present results show that in the inlet temperature range considered here,the inversion temperature does not exit for the evaporation of pure ethylene glycol.     

Effects of pressure work and radiation on natural convection flow around a sphere with heat generation

The effects of pressure work and radiation on natural convection flow around a sphere in presence of heat generation have been investigated in this paper. The governing equations are transformed into dimensionless non-similar equations by using set of suitable transformations and solved numerically by the finite difference method along with Newton's linearization approximation. Attention has been focused on the evaluation of shear stress in terms of local skin friction and rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles. Numerical results have been shown graphically and also in tabular form for some selected values of parameter set consisting of heat generation parameter Q, radiation parameter Rd, pressure work parameter Ge and the Prandtl number Pr.     

Multiobjective optimization of free convection through a nonuniform cabinet filled with porous media

In the current study, multiobjective optimization and numerical simulation were used to evaluate free convection through a nonuniform cabinet, which has several technical applications, such as cooling techniques, solar air collectors, and heat sinks. The new aspect of the current study is to compute the maximum free convection within an irregular L-shaped cavity filled with porous media using both computational analysis and response surface methodology (RSM). Moreover, the impacts of constant coefficients, such as aspect ratios of the horizontal (AR_h), vertical (AR_v), and Darcy numbers (Da) on the Nusselt number (Nu_ave), Nusselt number maximization (NNM), the temperature of the surface (Ts), and entropy (S) are studied and discussed to evaluate their effect on the thermal performance. The results showed that when Da, AR_h, and AR_v increase, Nu_ave improves while the Ts and S decline and the largest desirability is achieved at AR_h = 0.9, AR_v = 0.9, and Da = 10⁻¹. Additionally, when compared with the subpar design data, the largest gain in NNM was 26.7 times, while the biggest decreases in surface temperature and entropy were 59% and 97%, respectively. As a result, the combination of the numerical simulation and RSM study produces a novel strategy and insightful suggestions for the ideal cooling L-shaped cabinet design.     

Melting of a vertical ice cylinder inside a rotating cylindrical cavity filled with binary aqueous solution

The melting of a vertical ice cylinder into a homogeneous calcium chloride aqueous solution inside a rotating cylindrical cavity with several rotating speeds is considered experimentally. The melting mass and temperature are measured on four initial conditions of the solution and four rotating speeds of the cavity. The temperature of the liquid layer becomes uniform by the mixing effect resulting from cavity rotation and it enhances the melting rate of the ice cylinder. As the cavity‐rotating speed increases, the melting rate increases. The dimensionless melting mass is related to the Fourier number and the rotating Reynolds number in each initial condition, therefore an experimental equation that is able to quantitatively calculate the dimensionless melting mass is presented. It is seen that the melting Nusselt numbers increase again in the middle of the melting process. The ice cylinder continues to melt in spite of the small temperature difference between the ice cylinder and the solution. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 359–373, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20211     

Modified stability analysis of double-diffusive convection in viscoelastic fluid layer saturating porous media

The present analysis mathematically investigates the thermohaline convection problem in viscoelastic fluid layer saturating porous media by utilizing the modified Boussinesq approximation. By performing linear stability analysis, the Darcy–Rayleigh numbers for stationary and oscillatory modes of convection are derived. The effects of different parameters describing the problem are studied numerically. In nonlinear stability analysis, the heat and mass transfer rates in the form of Nusselt and Sherwood numbers, respectively, are obtained for oscillatory convection using the derived Ginzburg–Landau equation. From the results, it is observed that overstability is the preferred mode of instability in linear stability. It is found that in linear double-diffusive convection problems, the stress relaxation imparts a destabilizing effect whereas the strain retardation time, the coefficient of specific heat variation due to temperature, and the concentration gradient have a stabilizing effect on the system's stability. The numerical values of heat and mass transfer rates varied with the coefficient of specific heat showing that the heat transport decreases while the mass transport increases. Also, the stress relaxation time, the concentration gradient, and the gravity modulation's amplitude increase while the strain retardation time decreases the heat and mass transfer rates. The wavelength of oscillations remains unaltered with the variation of specific heat variation due to temperature. The modulation frequency does not affect the heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency.     

Limitations of the lumped model for in‐tube laminar forced convection interacting with cross forced convection flows

The short communication addresses forced convection heat transfer of a viscous fluid flowing in a tube with fully developed laminar velocity and uniform entrance temperature that exchanges heat convection with a surrounding fluid. The idea is to implement the lumped model following the footsteps of the potent lumped model within unsteady heat conduction, instead of the differential model. The computed mean bulk temperatures of the viscous fluid expressed by a simple exponential function agrees well with the baseline numerical mean bulk temperatures when the internal fluid is air, water or crude oil and the external fluid is air for small values of the modified Biot numbers and maximum Reynolds numbers are satisfied.     

Forced turbulent heat convection in a square duct with non-uniform wall temperature

In the present work, the numerical simulation to calculate the problem of the turbulent convection with non-uniform wall temperature in a square cross-section duct was adopted. To solve this problem some assumptions for the flow, such as: the condition of fully developed turbulence and incompressible flow have been assumed. The methodology of the dimensionless energy equation was used to calculate the fluid temperature field in the square cross-section in function of the non-uniform wall temperatures prescribed. Numerical simulations were done using two different turbulent models to resolve the momentum equations and two more models to resolve the energy equation. The models of turbulence k-ε Nonlinear Eddy Viscosity Model (NLEVM) and the Reynolds Stress Model (RSM) were used to determine the turbulent intensities as well as the profiles of axial and secondary mean velocities. The turbulence model RSM was simulated using a commercial software. The thermal field was determined from other two models: Simple Eddy Diffusivity (SED), based in the hypothesis of the constant turbulent Prandtl number; and Generalized Gradient Diffusion Hypothesis (GGDH). In this last model, as the turbulent heat transfer depends on the shear tensions, the anisotropy is considered. These two last equation models of the energy equation of the fluid have been implemented in FORTRAN, a code of programming. The performances of the models were evaluated by validating them based in the experimental and numerical results published in the literature. Two important parameters of great interest in engineering are presented: the friction factor and the Nusselt number. The results of this investigation allow the evaluation of the behavior of the turbulent flow and convective heat fluxes for different square cross-sectional sections throughout the direction of the main flow, which is mainly influenced by the temperature distribution in the wall.