Lattice Boltzmann method applied to the laminar natural convection in an enclosure with a heat-generating cylinder conducting body

In this paper, a numerical investigation of laminar convective flows in a differentially heated, square enclosure with a heat-conducting cylinder at its center, is carried out. The flow and the temperature are computed using respectively the lattice Boltzmann equation and finite-difference with suitable coupling to take natural convection into account. The investigation is performed for $\mathit{Pr}=0.71$, Rayleigh numbers of $\mathit{Ra}={10}^3\text{–}{10}^6$ and temperature-difference ratio of $\mathrm{\Delta }{T}^1=0\text{–}50$. The average hot and cold walls Nusselt numbers, the flow and temperature fields are presented and discussed. For a constant Ra, the average Nusselt number at the hot and cold walls (${\mathit{Nu}}_h$ and ${\mathit{Nu}}_c$) vary linearly with $\mathrm{\Delta }{T}^1$: ${\mathit{Nu}}_h$ decreases with $\mathrm{\Delta }{T}^1$ while ${\mathit{Nu}}_c$ increases with $\mathrm{\Delta }{T}^1$.     

Hydrogen production from woody biomass by steam gasification using a CO2 sorbent

In ${\mathrm{H}}_2$ production from woody biomass by steam gasification using CaO as a ${\mathrm{CO}}_2$ sorbent, the effect of reaction parameters such as the molar ratio of CaO to carbon in the woody biomass $([\mathrm{Ca}]/[\mathrm{C}])$, reaction pressure, and reaction temperature was investigated on ${\mathrm{H}}_2$ yield and conversion to gas. In the absence of CaO, the product gas contained ${\mathrm{CO}}_2$. On the other hand, in the presence of CaO ($[\mathrm{Ca}]/[\mathrm{C}]=1,2$, and 4), no ${\mathrm{CO}}_2$ was detected in the product gas. At a $[\mathrm{Ca}]/[\mathrm{C}]$ of 2, the maximum yield of ${\mathrm{H}}_2$ was obtained. The ${\mathrm{H}}_2$ yield and conversion to gas were largely dependent on the reaction pressure, and exhibited the maximum value at $0.6\mathrm{MPa}$. It is noteworthy that ${\mathrm{H}}_2$ was obtained from woody biomass at a much lower pressure compared to other carbonaceous materials such as coal $(>12\mathrm{MPa})$ and heavy oil $(>4.2\mathrm{MPa})$ in steam gasification using a ${\mathrm{CO}}_2$ sorbent. ${\mathrm{H}}_2$ yield increased with increasing reaction temperature. Woody biomass is the one of the most appropriate carbonaceous materials in ${\mathrm{H}}_2$ production by steam gasification using CaO as a ${\mathrm{CO}}_2$ sorbent, taking the reaction pressure into account.     

Natural convection flows in porous trapezoidal enclosures with various inclination angles

Simulations were carried out using penalty finite element analysis with bi-quadratic elements to investigate the influence of uniform and non-uniform heating of bottom wall within a trapezoidal enclosure of various inclination angles $(\phi )$. Parametric study has been carried out for a wide range of Rayleigh number $(\mathit{Ra})({10}^3?\mathit{Ra}?{10}^6)$, Prandtl number $(\mathit{Pr})(0.026?\mathit{Pr}?988.24)$ and Darcy number $(\mathit{Da})({10}^{-3}?\mathit{Da}?{10}^{-5})$. Numerical results are presented in terms of stream functions, isotherm contours and Nusselt numbers. The heat transfer is primarily due to conduction at lower values of Darcy number $(\mathit{Da})$ and convection dominant heat transfer is observed at higher Da values. The intensity of circulation increases with increase in Darcy number. Increase in the intensity of circulations and larger temperature gradient are also observed with increase in $\phi$ from 0° to 45° especially at larger Pr and Ra. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating at all Rayleigh and Darcy numbers, but average Nusselt number is lower for non-uniform heating. Local heat transfer rates are found to be relatively greater for $\phi =0°$. It is observed that the local heat transfer rate at the central portion of bottom wall is larger for non-uniform heating case. Average Nusselt number plots show higher heat transfer rates at the bottom wall for $\phi =0°$ as compared to $\phi =45°$ and $\phi =30°$. It is observed that the average heat transfer rate at the bottom wall is found to be invariant with respect to $\phi$ at higher Ra for non-uniform heating. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and the power law correlations between average Nusselt number and Rayleigh numbers are presented for convection dominated regimes.     

Accelerating ray convergence in incident heat flux calculations using Sobol sequences

In this paper an improved quadrature scheme based on the reverse Monte Carlo method implemented using Sobol sequences to generate ray orientations is presented. This has the property that a more uniform pattern of rays on the unit hemisphere is produced compared to the usual implementation of the reverse Monte Carlo method. The use of Sobol sequences gives a ray convergence rate for the incident heat flux that is asymptotically equivalent to $O(N_{\mathrm{Ray}}^{?1})$. The generation of ray directions using Sobol sequences means that the Central Limit Theorem no longer holds. In its place a Gaussian variable is formulated from the incident intensity distributions calculated using Sobol sequences. This makes it possible to calculate confidence limits for a prediction of incident heat flux and the confidence limits contract with ray number at a rate of $O(N_{\mathrm{Ray}}^{?1}ln(N_{\mathrm{Ray}}))$. An extension to the Monte Carlo method combined with Sobol sequences is also presented that exploits the shape of the incident intensity distribution to a receiver. The new methodology is relatively simple to implement and shows some promising improvements in computational efficiency.     

The electronic excitation of N2 and burning velocity measurements in low-pressure,pre-mixed ammonia-fluorine flames

The electronic emission spectrum of N₂ has been obtained for the first time from a flame system. The N₂ first and second positive band systems have been observed in pre-mixed ammonia-fluorine flames burning in the 1.0 to 4.0-mm Hg pressure range. It is proposed that the N₂ excitation to the A³Σ_u⁺ and B³Π_g states arises from binary collisions between N atoms and NH radicals produced by the rapid stripping of the ammonia molecule in the reaction zone. It is further postulated that the C³Π_u state, which is 11.1 eV above the ground state, is populated by energy pooling according to

$N_2(A^3{\sum }_u^{+})+N_2(A^3{\sum }_u^{+})\to N_2(X^1{\sum }_g^{+})+N_2(C^3{\Pi }_u)$

.The measured value of the flame's burning velocity and the estimated reaction time, at 4.0 mm Hg, were (3.5 ± 0.7) × 10³ cm sec^?1 and 10 μ sec, respectively. This burning velocity is 1 to 2 orders of magnitude higher than those measured in flames supported by oxygen.     

Heatline analysis on natural convection for nanofluids confined within square cavities with various thermal boundary conditions

Natural convection of nanofluids in presence of hot and cold side walls (case 1) or uniform or non-uniform heating of bottom wall with cold side walls (case 2) have been investigated based on visualization of heat flow via heatfunctions or heatlines. Galerkin finite element method has been employed to solve momentum and energy balance as well as post processing streamfunctions and heatfunctions. Various nanofluids are considered as Copper–Water, ${\mathrm{TiO}}_2$–Water and Alumina–Water. Enhancement of heat transfer with respect to base fluid (water) has been observed for all ranges of Rayleigh number $(\mathit{Ra})$. Dominance of viscous force or buoyancy force are found to play significant roles to characterize the heat transfer rates and temperature patterns which are also established based on heatlines. In general, convective closed loop heatlines are present even at low Rayleigh number $(\mathit{Ra}={10}^3)$ within base fluid, but all nanofluids exhibit dominant conductive heat transport as the flow is also found to be weak due to dominance of viscous force for case 1. On the other hand, convective heat transport at the core of a circulation cell, typically represented by closed loop heatlines, is more intense for nanofluids compared to base fluid (water) for case 2 at Ra = 10⁵. It is also found that heatlines with larger heatfunctions values for nanofluids coincide with heatlines with smaller heatfunction values for water at walls. Consequently, Nusselt number which is also correlated with heatfunctions show larger values of nanofluids for all ranges of Ra. Average Nusselt numbers show that larger enhancement of heat transfer rates for all nanofluids at $\mathit{Ra}={10}^5$ and Alumina–Water and Copper–Water exhibit larger enhancement of heat transfer rates.     

Investigation on heat and mass transfer in hygroscopic random charged fiber webs

Hygroscopic charged fiber webs include a large number of interconnected capillaries formed by randomly distributed pores. The simultaneous heat and mass transfer in hygroscopic charged fiber webs is different from traditional flows in macro-channels resulted from the electrokinetic phenomena in micro-channels. In this paper, a mathematical model is presented with consideration of a quintic polynomial pore size distribution evaluated from a series of experiments and the electrokinetic phenomena resulting in a higher flow friction. The liquid diffusion coefficient in this model can be expressed as $D_l({\epsilon }_l)=\frac{\sigma \cos \phi {\sin }^2\beta (r_{\text{max}}-r_{\text{min}})n{\epsilon }_l^{n-1}}{4\mu (1+A·\Theta ){?}^{n-1}}\frac{{\Gamma }_1{\Delta }^4-{\Omega }_1}{{\Gamma }_2{\Delta }^4-{\Omega }_2{\Delta }^2}$. With specification of initial and boundary conditions, the governing equations are solved numerically and distributions of the temperature, the moisture concentration, and liquid water content in hygroscopic fiber webs are obtained. The comparison with the experimental measurements shows the rationality of this model in simulating the coupled heat and mass transfer in hygroscopic charged fiber webs with consideration of the electrokinetic phenomena.