Weakly non-linear stability of stratified natural convection in a vertical cavity with lateral temperature gradient

Stability of free convection is examined in a vertical cavity with a fixed lateral temperature difference on the walls, which is also heated from the bottom by a constant heat flux causing vertical stratification of the base flow. Weakly nonlinear stability equations are derived, under the assumption of fully developed flow conditions. Critical Rayleigh numbers and Landau coefficients are determined in terms of the Prandtl number and stratification parameter. It is found that critical disturbances are always two-dimensional, for stationary and oscillating instabilities as well. Alternatives are considered for the calculation of the Landau coefficient. Analysis reveals that unstationary instability is the preferred mode at the codimension point.     

Dual mixed convection flows in a vertical channel

The classical problem of the fully developed mixed convection flow with frictional heat generation in a vertical channel bounded by isothermal plane walls having the same temperature is revisited in this paper. The existence of dual solutions of the local balance equations is pointed out. They are either columnar upflows or cellular down–up–down flows. Below a maximum value Ξ_max of the governing parameter Ξ = Ge Pr Re (the product of the Gebhart, Prandtl and Reynolds numbers), for any given Ξ a pair of different solutions occurs. The value Ξ_max corresponds to a maximum value of the Reynolds number above which no laminar solution can be found. At this maximum value, the two solution branches bifurcate from each other. In the neighborhood of the bifurcation point Ξ_max even small perturbations can cause transitions from one flow regime to the other. In the paper, the mechanical and thermal characteristics of the dual flow regimes are discussed in detail both analytically and numerically.     

Three-dimensional convective cooling in a vertical channel with flush-mounted heat sources

Three-dimensional free convection in a vertical channel with spatially periodic, flush-mounted heat sources is investigated by a spectral element method. All numerical solutions are obtained using a time-accurate finite-difference integration scheme capable of capturing temporal instabilities that spontaneously appear at large values of Grashof number, Gr. In addition, the leading order approximation of the 3-D solution for small Gr is derived and compared with the numerical solutions. The agreement is excellent for sufficiently small Gr.Computations are carried out for a Boussinesq fluid, Prandtl number, Pr=0.71, non-dimensional reference temperature, and values of Grashof number in the range 0.1?Gr?5×10⁴. For given aspect ratios, and for sufficiently small values of Grashof number, the solution evolves to a unique, time-independent state that exhibits the maximum symmetry consistent with the boundary conditions. At Gr∗?28,000, self-sustained oscillations appear spontaneously in the flow and thermal fields. For time-dependent solutions (Gr?Gr∗) the symmetry of the flow and temperature fields breaks down.Temperature and velocity distributions as well as maximum temperature, maximum velocity and local Nusselt number distributions are presented for the values of Grashof number studied. For time-dependent flows, instantaneous as well as averaged-in-time solutions are discussed.     

Three-dimensional natural convection in an enclosure with a sphere at different vertical locations

Numerical calculations are carried out for the three-dimensional natural convection induced by a temperature difference between a cold outer cubic enclosure and a hot inner sphere. The immersed-boundary method (IBM) to model a sphere based on the finite volume method is used to study a three-dimensional natural convection for different Rayleigh numbers varying in the range of 10³–10⁶. This study investigates the effect of the inner sphere location on the heat transfer and fluid flow. The flow and thermal fields eventually reach the steady state for all Rayleigh numbers regardless of the sphere location. For Rayleigh numbers of 10⁵ and 10⁶, the variation of local Nusselt number of the sphere along the circumferential direction is large, showing the strong three dimensionality of the natural convection in the enclosure unlike to the cases of lower Rayleigh numbers of 10³ and 10⁴. For the highest Rayleigh number, the local peaks of the Nusselt number on the top wall of the enclosure shows the sinusoidal distribution along the circumferential direction. The flow and thermal fields, and the local and surface-averaged Nusselt numbers on the sphere and the enclosure are highlighted in detail.     

Thermal dispersion in vertical gas-liquid flows with foaming and non-foaming liquids

Heat transfer experiments have been performed in gas-liquid upwards flow in a vertical column with non-foaming (water) and foaming (kerosene) liquids. The main purpose of the experiments has been to characterize the degree of thermal mixing in the system. For the range of conditions employed, the non-foaming liquid exhibits complete mixing at low liquid superficial velocities. An increase in liquid velocity leads to incomplete mixing. In the latter case, the thermal dispersion coefficient at low gas superficial velocities is larger than what correlations in the literature predict. For the foaming liquid, when foaming and bubbling regions coexist in the bubble column, each region behaves as a completely-mixed subsystem.     

Experimental investigation of heterogeneous hydrolysis with Zn vapor under a temperature gradient

The hydrolysis step of the Zn/ZnO thermochemical cycle for hydrogen production is experimentally investigated in a laboratory-scale tube-reactor. The current work uses a new approach in which the heterogeneous oxidation of gaseous Zn with steam is carried out under a negative axial temperature gradient in order to improve cycle efficiency by reducing the proportion of steam and inert carrier gas used. It is shown that complete conversion of Zn to ZnO is possible at steam-to-Zn stoichiometries greater than 5.0. As the steam-to-Zn stoichiometry approaches unity at reduced inert gas fractions, condensation of Zn on the reactor walls becomes more likely. In addition, the observed gas-phase equilibrium shift toward increased production of ZnO at temperatures under 800 K is consistent with earlier theoretical predictions. While complete conversion with low inert gas and steam usage was not achieved, our approach shows great improvement over previous aerosol-based approaches when considering the total amounts of steam and inert gas used per unit of hydrogen produced. Therefore, the current temperature gradient approach is promising for the design of an efficient reactor for water splitting via Zn vapor.     

Mixed convection flow from a vertical flat plate with temperature dependent viscosity

A two-dimensional mixed convection flow of a viscous incompressible fluid of temperature dependent viscosity past a vertical impermeable fluid is considered. The governing equations for the flow are transformed for the regions appropriate to the forced convection, free convection and forced-free convection regimes. Solutions of the reduced equation appropriate in the forced convection and free convection regime are obtained using the perturbation technique treating ξ, the buoyancy parameter, as the perturbation parameter and those for the forced-free convection regime are obtained by the implicit finite difference method. Numerical results thus obtained are presented in terms of the local shear stress and local surface heat-flux. Effect of the viscosity variation parameter, ε, on the surface shear stress and the surface heat-flux for the fluid appropriate for Prandtl number ranging from 0.02 to 100 is shown. The perturbation solutions obtained for small and large values of ξ are found in excellent agreement with the finite difference solutions for the entire ξ regime.     

Heat Transfer to a Particle Exposed to a Rarefied Plasma with a Great Temperature Gradient

A kinetic-theory analysis is presented concerning the heat transfer from a rarefied plasma to a spherical particle for the extreme case of free-molecule regime and thin plasma sheath. A great temperature gradient is assumed to exist in the plasma, and thus a non-Maxwellian velocity distribution function is employed for each of the gas species. Analytical results show that the existence of a temperature gradient in the plasma causes a nonuniform distribution of the local heat flux density on the sphere surface, while the total heat flux to the whole particle is independent of the temperature gradient. The nonuniformity of the local heat flux distributioln is small even for the case with a temperature gradient as great as 10~6 K/m, but it may significantly enhance the thermophoretic force on an evaporating particle. Heat transfer is mainly caused by atoms at low gas temperatures with negligible ionization degree, while it can be attributed to ions and electrons at high plasma temperatures.     

MHD mixed convection flow adjacent to a vertical plate with prescribed surface temperature

The steady MHD mixed convection flow adjacent to a bounding surface immersed in an incompressible viscous fluid is considered. The governing system of partial differential equations is first transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference scheme. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles. It is found that dual solutions exist for both assisting and opposing flows. The range of the mixed convection parameter for which the solution exists increases in the presence of a magnetic field.     

Magnetohydrodynamic natural convection in a vertical cylindrical cavity with sinusoidal upper wall temperature

A series of numerical simulations were performed in order to study liquid metal MHD natural convection in a vertical cylindrical container with a sinusoidal temperature distribution at the upper wall and the other surfaces being adiabatic. Starting from the basic hydrodynamic case, the effect of vertical (axial) and horizontal magnetic fields is assessed. Depending on the magnitude of the Rayleigh and Hartmann numbers, both turbulent and laminar (azimuthally symmetric or not) flows are observed. The results show that the increase of Rayleigh number promotes heat transfer by convection while the increase of Hartmann number favors heat conduction. The vertical magnetic field reduces the Nusselt number more than the horizontal. The circulation patterns for the most convective cases are confined close to the top corner of the container with the simultaneous formation of a secondary flow pattern at the bottom corner, while for the more conductive cases only one circulation pattern exists covering the entire domain.     

Motion of droplets induced by the Marangoni force on a wall with a temperature gradient

Motion of silicone oil and water droplets induced by the Marangoni force was numerically simulated by using two‐ and three‐dimensional second‐order finite difference methods with the CIP and the level set methods. The surface tension was introduced by the continuum surface force (CSF) method. The results clearly showed the flow induced by the Marangoni force and the dependence of droplet velocity on droplet size, contact angle, temperature gradient, and fluid properties. The Marangoni force balanced with the viscous force in the small contact angle case; on the other hand, in the large contact angle case, it balanced with the normal component of surface tension. As for the effect of fluid properties on droplet motion, the temperature coefficient of surface tension had a much larger effect than did viscosity, thermal diffusivity, or surface tension. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(2): 81–93, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20004     

Entropy generation for compressible natural convection with high gradient temperature in a square cavity

Entropy generation due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subjected to different side wall temperatures for compressible and incompressible natural convection flows. Based on the obtained velocity and temperature values, the distributions of local entropy generation, average entropy generation and average Bejan number are determined and compared for compressible and incompressible regimes. It is found that the entropy generated for compressible flow always is more than incompressible flow. The study is performed for Ra = 10⁴–10⁸, ε = 0.01(incompressible regime) and 0.6 (compressible regime), Ge = 10⁻⁵ and Pr = 0.7.     

Three-dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature

Three-dimensional laminar slip-flow and heat transfer in rectangular microchannels having constant temperature walls are studied numerically using the finite-volume method for thermally and simultaneously developing flows. The Navier–Stokes and energy equations are solved with velocity slip and temperature jump at the wall. A modified convection–diffusion coefficient at the wall–fluid interface is defined to incorporate the temperature-jump boundary condition. Validity of the numerical simulation procedure is established and the effect of rarefaction on hydrodynamicaly developing flow field, pressure gradient and entrance length is analyzed. A correlation for the fully developed friction factor is presented as a function of Knudsen number (Kn) and aspect ratio (α). The influence of rarefaction on the Nusselt (Nu) number is investigated for thermally and simultaneously developing flows. The effect of velocity slip is found to increase the Nu number, while the temperature-jump tends to decrease it, and the combined effect could result in an increase or a decrease in the Nu number. In the fully developed region, there could be high as 15% increase or low as 50% decrease in Nu number is plausible for the range of parameters considered in this work.     

Three-dimensional effects and arm effects on modeling a vertical axis tidal current turbine

Three-dimensional effects in studying a vertical axis tidal current turbine are modeled using a newly developed vortex method. The effects on predicting power output and wake trajectory are analyzed in particular. The numerical results suggest that three-dimensional effects are not significant when the height of the turbine is more than seven times the turbine radius. Further discussions are presented focusing on the relationship between the turbine height and the angle of attack and the induced velocity on a blade of the turbine without arms. Besides the three-dimensional effects, arms effects are quantified with an analytical derivation of the polynomial formula of the relationship between arm effects and the tip speed ratio of the turbine. Such a formula provides a correction for existing numerical models to predict the power output of a turbine. Moreover, a series towing tank tests are conducted to study the three-dimensional effects as well as the arm effects. Good agreements are achieved between the results obtained with numerical calculations with the arm effects correction and the towing tank tests. Finally, three-dimensional effects are examined experimentally together with the arm effects by using an end-plate test, which suggests that the combinational effect is rather minimal. For turbine designers at the early design stage, we recommend that a two-dimensional model is acceptable considering the high cost of the three-dimensional model.     

动力电池内部温度梯度反演计算

电池在充放电过程中内部温度的分布特征对于锂离子电池热管理系统的设计十分重要。根据电池的物理结构,将圆柱型电池内部平均分成若干等温层,建立了电池沿径向的产热和传热模型,将测试获得的电池表面温度和热流密度作为边界条件,假设热量从中心向外传递过程中等温层之间的热流密度线性增加,提出了一种计算电池沿径向内部温度分布的方法,并在电池内部中心放置热电偶,验证了该方法的准确性。计算结果表明,电池内部温度并非线性分布,在靠近电池中心位置处相邻等温层之间的温度梯度较小,而在靠近电池表面区域附近相邻等温层之间的温度梯度较大。该计算方法在20～40 ℃环境温度区间内具有较高的精度,而在−10 ℃环境温度下误差会偏大些。     

Heat loss from buried vertical plate with assigned temperature distribution

Thermal losses for a buried vertical thin plate can be expressed as a function of the assigned temperature distribution, the medium conductivity and the geometrical properties that describe the model. When the geometrical properties reduce to one, the plate-ground thermal resistance can be expressed regardless of plate dimension, depending only on temperature distribution given at surface plate and its temperature difference with medium.     

Powering a wireless temperature sensor using sediment microbial fuel cells with vertical arrangement of electrodes

The application of wireless sensors is an important approach for monitoring natural water systems in remote locations; however, limited power sources are a key challenge for successful application of these sensors. Sediment microbial fuel cells (SMFCs) have shown potential as a sustainable power source with low maintenance requirements to power wireless sensors. This study examines electricity generation in lab-scale SMFCs with the sediment from Lake Michigan. Two SMFCs are operated in parallel with a difference in cathode arrangement (floating cathode vs. bottom cathode). The data show that the SMFC with a floating cathode produces more electricity and results in a shorter charging time when an ultracapacitor is connected to the circuit. To control electricity delivery and voltage elevation to a value that can drive a wireless temperature sensor, a power management system (PMS) is developed. With the PMS, both SMFCs can consistently power the wireless temperature sensor for data transmission to a computer, although the number of recorded data within the same period differs. This research provides an effective PMS for power control and valuable experience in SMFC configurations for the next onsite test of the developed SMFCs in Lake Michigan.     

Routes to chaos of natural convection flows in vertical channels

The aim of the present study is the analysis of the transition to turbulence of natural convection flows between two infinite vertical plates. For the study of the problem, a number of Direct Numerical Simulations (DNSs) have been performed. The continuity, momentum and energy equations, cast under the Boussinesq assumption, are tackled numerically by means of a pseudospectral method, through which the three-dimensional domain is decomposed with Chebychev polynomials in the wall-normal direction and with Fourier modes in the wall-parallel directions. For low Rayleigh number values, the predictions of the flow regimes are consistent with the classical analytical results and linear stability analyses. In particular, the first bifurcation (Ra ≈ 5800) from the so-called laminar conduction regime to steady convection is correctly captured. By increasing the Rayleigh number beyond a second critical value (Ra ≈ 10200), the flow regime becomes chaotic. This transition to chaos is found to be related with the amplification of spanwise instabilities occurring at scales larger than the channel gap, H. The study of the return of the system from the chaotic regime to the laminar base flow reveals a phenomenon of hysteresis, i.e. the chaotic regime persists even at Ra-values lower than the second critical value. From a numerical point of view, the predicted flow regimes appear to be extremely sensitive to the domain size, grid resolution and perturbation amplitude. These aspects are shown to be of crucial importance for the prediction of the heat transfer performance, and, hence, should be taken into consideration when numerical methods are used for the simulation of real-world problems.