Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries

A composite correlation of the average Nusselt number and the channel Rayleigh number for buoyant air flow through inclined channels with uniform heat flux boundaries is presented. The form of the correlation is based on dimensional analysis and is a superposition of the developing and fully developed flow limits. In the limit of fully developed flow, an analytical solution for the Nusselt number is derived. The developing flow limit follows the format of the correlation for a single plate. The composite relationship based on the top wall temperature is $\overline{\text{Nu}}={\left[\frac{6.25(1+r)}{{\text{Ra}}^{″}\sin ?}+\frac{1.64}{({\text{Ra}}^{″}\sin ?{)}^{2/5}}\right]}^{-1/2}$, where r is ratio of the heat flux at the top and bottom wall. At inclination angles of $30°\le ?\le 90°$, this correlation predicts the available data base for $10\le {\text{Ra}}^{″}\le {10}^5$ and agrees with the analytical solution for $1\le {\text{Ra}}^{″}\le {10}^2$.     

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.     

Kinetics of collisional ionization of alkali metal atoms and recombination of electrons with alkali metal ions in flames

The rate constant k₂ has been measured in flames of H₂ + O₂ + N₂ for the ionization of alkali metal atoms M in collisions with flame species X in

$M+X\to M^{+}+e^{?}+X$

. Results are compared with every previously reported measurement of k₂ in similar flames for each alkali metal. It is concluded that

$k_2=(9.9\pm 2.7)\times {10}^{?9}{T}^{1/2}exp?(?V/RT)$

, ml molecule ^?1 sec^?1, where V is the ionization potential of the alkali metal atom and T the temperature. k₂ does not depend on flame composition and is the same for each alkali to a good approximation.The third-order recombination rate constant k_?2 for the reverse of (II) can be written as

$k_{?2}=(4.1\pm 1.1)\times {10}^{?24}{T}^{?1}$

, ml² molecule^?2 sec^?1. There is no significant dependence of k_?2 on flame composition or on which alkali metal is considered. These facts enable the rates of the forward and reverse processes in (II) to be estimated in flames generally.     

Comments on the equation of state of the products of high density explosives

The problem of the thermal equation of state of the products of solid explosives is considered. It is assumed that the products are in chemical equilibrium, that the specific chemical heat released is independent of the loading density, and that the detonation density is proportional to the loading density. Using the energy conservation equation and thermodynamic relationships, it is then shown that the thermal equation of state must satisfy the following relationship:

$F[T^{(1?K)/2K}\upsilon ;{\upsilon }^{(1+K)/(1?K)}p]=0$

. where K is a constant and F is an arbitrary function of its two arguments. It is then argued that the experimental knowledge of detonation velocity, pressure, density, and particle velocity versus loading density is not enough to check the validity of an assumed thermal equation of state of the products and to compute the detonation temperature. In particular, it is explained why similar detonation pressures, densities, and particle velocities, but completely different detonation temperatures have been calculated by various authors, using similar detonation velocity data but different thermal equations of state.     

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.     

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.     

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.     

Dissolution kinetics of borogypsum in di-ammonium hydrogen phosphate solutions

This work examines the dissolution kinetics of borogypsum in di-ammonium hydrogen phosphate solutions ((NH₄)₂PO₄) in a batch reactor. The parameters selected were the reaction temperature (15–53 °C), di-ammonium hydrogen phosphate concentration (1–4 M), stirring speed (50–800 rpm), and solid/liquid ratio (1/50–1/5). The dissolution rate increased by increasing the temperature (from 0.32 to 0.82), di-ammonium hydrogen phosphate concentration (from 0.35 to 0.821), and by decreasing solid-to-liquid ratio (from 0.77 to 0.24). The dissolution rate increased up to stirring speed of 600 rpm (from 0.135 to 0.56), and then decreased with increasing stirring speed (from 0.56 to 0.351). The dissolution rate was described by first-order pseudo-homogeneous reaction model. The activation energy of this study was calculated as 42.103 kJ mol^?1. A kinetics model including the used parameters in this study was suggested as follows:

$?\ln \left(1?X\right)=223.63C^{0.911}{\left(S/L\right)}^{?0.7689}{W}^{0.6212}{e}^{\left(?5064.2/T\right)}t$