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.     

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 $1\le {\text{Ra}}^{″}\le {10}^2$.     

A preliminary solar-hydrogen system for Jordan: Impacts assessment and scenarios analysis

Energy sector in Jordan faces serious challenges today. Jordan as a non-oil country depends by 96% on imported fuel to cover its demands. The present work seeks to improve an alternative fuel that can support the goals of National Energy Strategy in Jordan. Therefore; a mathematical model was developed to investigate the possibility of producing solar-hydrogen fuel in Jordan. Ma'an city was chosen to be the location of solar-hydrogen plant. The high solar insulation and the availability to supply the plant with water from Aqaba Gulf directly and/or from Red-Sea Dead-Sea Cannel make Ma'an the suitable location for the plant. A system with photovoltaic (PV) cell array and proton electron membrane (PEM) electrolyzer was suggested to be the connection system for the plant. Accordingly, two different scenarios were proposed for hydrogen production with different hydrogen production doubling time, the first scenario is ${\mathit{\theta }}_{\mathit{h}1}=2+0.15\left(\mathit{n}?1\right)$ year, while the second scenario is ${\mathit{\theta }}_{\mathit{h}2}=4+0.15(\mathit{n}?1)$ year. Eight different economic, social, and environmental parameters, which directly affect solar-hydrogen production, were evaluated and investigated for Jordan up to year 2060. Accordingly, the research study concluded that solar-hydrogen fuel can potentially offer a good option as an alternative fuel for Jordan. Starting the production at year of 2020 can provide a good sharing in energy demand sector by the end of the year 2060.     

Drag force acting on bubbles in a subchannel of triangular array of rods

Forces acting on spherical bubbles in a subchannel of a rod bundle with triangular rod arrangement (the pitch to diameter ratio is $P/D=1.34$) have been studied at low bubble Reynolds numbers O(0.1) ? O(1). The bubble motion has been simulated resolving the interface of the bubble by using the lattice Boltzmann method. Steady drag and virtual mass forces have been determined from the simulation results. Based on the simulation data, the relation $C_D=16.375/{\mathit{Re}}_T$ could be established between the steady drag coefficient $C_D$ and the terminal Reynolds number ${\mathit{Re}}_T$ when the diameter ratio $\lambda =d/D$ of the bubble d and the channel D is less than 0.2. It is found that the virtual mass coefficient can achieve as high value as 7.2, which is a consequence of strong wall effects. Considering interactions between bubbles, cooperation in the axial direction and hindering in the lateral direction could be observed. We demonstrate that the relation between the terminal velocity of a bubble and that of the suspension follows a Richardson–Zaki like correlation, but the exponent is not only a function of the Eotvos and Morton numbers, but it also depends on the particle configuration.     

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.     

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.