Gas Fluid Flow Research Articles

Computational particle fluid dynamics simulation of gas–solid flow in a 3 MWth dual-circulation fluidized bed for chemical looping process

Regulation of gas–solid flow is crucial for optimizing the operation efficiency of dual-circulating fluidized beds that are considered to be the most appropriate type of chemical-looping reactors. Herein, a computational particle fluid dynamics method was employed to simulate the gas–solid flow in a 3-MWth dual-circulating fluidized bed used for chemical-looping combustion and gasification. The influence of structural difference between units on particle residence time was determined. The multi-parameter control mechanism of pressure, particle circulation, and particle residence time in a whole-loop system was investigated. Results revealed that under stable particle circulation, the particle residence time in the fuel reactor is much longer than that in the air reactor. The axial forces on the particles are reduced upon increasing particle density and size, leading to particle accumulation in the dense-phase zone. When the particle properties are stable, increasing the fluidizing gas flow rates by the same proportion leads to identical pressure drops on the involved two loop seals, which cause symmetrical alterations in the particle circulation rate between the air and fuel reactors. The dual-circulating fluidized bed exhibits certain multi-condition adaptability, which is limited by the stock bin volume. Overall, this study is beneficial for effective and economical optimization of the operation of chemical-looping dual-circulating fluidized beds.

Experimental and CFD-DEM study on local packing distribution and thermofluidic analysis of binary packed bed

In recent years, binary-packed beds have drawn attention due to their higher packing density and greater heat extraction capacity than mono-sized packed beds. In the past, the research on binary-packed beds mainly focused on finding empirical correlations for hydraulic permeability and equivalent thermal conductivity. Studies on fluid flow and heat transfer characterisation of the packed bed filled with binary particles are relatively scarce. In this work, the fluid flow and heat transfer analysis of purge gas flowing through the binary packed bed (1 ≤ size ratio ≤ 7 and at a volume of large particles = 40 %) is investigated using non-destructive experimental and Computational fluid dynamics-Discrete element modelling (CFD-DEM) approaches. An empirical correlation is developed for the local packing distribution inside binary packed beds. Based on the CFD-DEM results, the Ergun equation is modified to present the analytical equation for calculating the pressure drop for binary-packed beds at lower and higher Reynolds numbers. Further, the effect of the different size ratios on the fluid flow and heat transfer behaviour of the purge gas for binary-packed beds is investigated. The local packing factor increases with increasing the size ratio since small particles occupy the void among the large particles. This effect also increases the region with zero or negative flow at a higher size ratio. It is found that the purge gas penetrates deeper with an increasing size ratio; therefore, the heat extraction behaviour and the Nusselt number increase with increasing size ratios.

Rapid Prediction of Hot-Air Temperature of Kalugin Top Combustion Hot Blast Stove by Means of Computational Fluid Dynamics Numerical Simulation

Based on the three-dimensional (3D) steady-state CFD numerical simulations conducted previously on an industrial Kalugin top combustion hot blast stove, a two-dimensional (2D) transient CFD numerical model for a single channel (hole) of a column of checker bricks in the regenerator of the same hot stove was established in the present work. The average mass flowrate and temperature of the flue gas flowing into the checker brick holes during the combustion period predicted by the 3D model were used as the inlet boundary conditions of the 2D model. Inside the hole of the checker bricks, processes of fluid flow and heat transfer of the flue gas during the combustion period and those of cold air during the hot-air-supply period were simulated using the 2D model for multiple operation cycles (combustion and hot-air-supply periods) of the hot stove, enabling rapid predictions of hot-air temperature under different operating conditions. The simulation results show that when the fuel gas flowrate and air consumption coefficient during the combustion period are controlled within the range of 80,000–100,000 Nm3/h and 1.02–1.28, respectively, a hot-air temperature in the range from 1273 °C to 1295 °C can be obtained during the hot-air-supply period. Applying this optimized operating condition to the industrial hot stove investigated in this study can achieve significant effects of reducing fuel gas flowrate by 8.6% and increasing hot-air temperature by 32 °C. In addition, a regression analysis on the numerical simulation results and the data measured from the industrial hot stove yields a roughly linear relationship between the dome temperature during the combustion period and the hot-air temperature during the hot-air-supply period, that is, the hot-air temperature would be increased by about 16 °C for every increment of 10 °C in the dome temperature, for instance. Therefore, the influences of the operating parameters on heat transfer characteristics in the regenerator and on hot-air temperature obtained in the present work provide a useful reference for guiding the hot stove operation optimization to achieve significant energy saving and emission reduction through facilitating more efficient combustion to minimize fuel gas consumption in steel plants.

Effect of agitation and aeration on gas dispersion efficiency in coaxial mixers containing yield‐pseudoplastic fluids: Experimental and numerical analysis

AbstractAerated stirred vessels are commonly employed to enhance gas dispersion. However, the associated high energy consumption is a challenging feature, particularly when dealing with complex non‐Newtonian fluids. Coaxial mixers comprising a central impeller and a close‐clearance impeller have emerged as an energy‐efficient alternative that effectively intensifies gas dispersion. Hence, the objective of this study is to investigate the effect of aeration and agitation on the gas dispersion effectiveness of a coaxial mixer containing a yield‐pseudoplastic fluid. An anchor‐pitched blade turbine was employed to disperse air into a 1 wt.% xanthan gum solution, and the analysis primarily focused on characterizing the gas holdup and fluid flow behaviour. Gas holdup data were obtained experimentally using electrical resistance tomography (ERT), while computational fluid dynamics (CFD) simulations provided a detailed analysis of fluid flow patterns within the coaxial mixer. The rotational speed of the impeller exhibited a non‐monotonic effect on the gas holdup, and a significant influence of the interaction between variables was identified. For instance, the experimental data showed that the aeration effect varied with the anchor speed. Nevertheless, the variables' interaction effect was explained by the change in flow pattern observed numerically. Furthermore, the CFD results demonstrated that high gas holdup does not necessarily indicate intensified mixing. Therefore, combining experimental data and numerical simulations enables a more accurate characterization of mixing performance. These findings contribute to the understanding and improvement of mixing performance in such a complex system, which is crucial for designing efficient operations.

A very high order Flux Reconstruction (FR) method for the numerical simulation of 1-D compositional fluid flow model in petroleum reservoirs

Compositional reservoir simulation is an extremely important tool for modeling the fluid flow in complex petroleum reservoirs, as in cases where the reservoir fluid is volatile and composed of several pseudo-components with distinct characteristics, or reservoirs that require the use of enhanced oil recovery process. For these cases, simpler black-oil models are not suitable. The compositional model involves the solution of a large system of partial differential equations, that comprises the mass conservation, the Darcy’s law and the fugacity constraints. However, the high number of equations and constraints render the compositional problems extremely complex and computationally demanding solutions. To improve accuracy and reduce the high computational costs, one can use higher than first or even second-order methods to approximate the advective flux terms in the hyperbolic conservation laws that describe the multicomponent transport in the reservoir. Those very high-order schemes can replace low-order approaches, such as the First Order Upwind (FOU) method, which is traditionally used in commercial petroleum reservoir simulators (CMG, 2019; ECLIPSE, 2022), obtaining more accurate solutions with reduced computational cost. In this work, we consider a three-phase and isothermal fluid flow of water, oil and gas and assume that there is no mass transfer between the water and the hydrocarbon phases. Physical dispersion and capillary effects are neglected. To solve the system of Partial Differential Equations (PDEs), we used the classical IMPEC (Implicit Pressure Explicit Composition) approach and, to model the complex phase behavior, we used the Peng–Robinson equation of state (PR-EOS). The classical Two Point Flux Approximation (TPFA) method is used to spatially discretize the diffusion terms in the pressure equation. For the first time in literature the very high order Flux Reconstruction (FR) method is adapted for the numerical simulation of the compositional model in petroleum reservoirs. The FR method is a numerical scheme employed to discretize the hyperbolic conservation laws using general grids. To avoid spurious oscillations in the vicinity of solution discontinuities, the h-MLP (hierarchical Multi-dimensional Limiting Process) is applied in the reconstruction stage. For the time integration, we have used the third-order Runge–Kutta approach. To appraise the robustness of our formulation, we have solved some one-dimensional benchmark problems found in literature and compared the FR solution with the FOU method and with the second-order Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) method. From our results, the FR method has shown improved accuracy, efficiency and capability of detecting sharper shocks when compared to the other methods that we have considered for the numerical modeling of the compositional flow in the present paper.

A non-newtonian fluid flow due to porous media with mass transfer and slip

The Casson viscous gas fluid flow with mass transpiration and radiation is demonstrated in this paper. A similarity transformation is utilized to interpret the representing construction of nonlinear PDEs by nonlinear ODEs. Then, using an exact analysis of the momentum equation, we constructed the dual solutions to the flow problem. This solution domain aids in the solution of the energy equation under the incomplete gamma function condition. The effect of radiation can also be seen in the heat equation. Physical parameters of interest, such as Brinkman number, porous media, thermal radiation number, induced slip, suction/injection and shear stress, are examined and graphically depicted. The gas slip velocity is used to simulate the slip flow model of the overall mass transfer on the moving sheet. Models of first- and second-order slip are introduced to induce the total mass transfer on the moving sheet. Additionally, the suction that causes the slip velocity rather than surface movement is investigated. The neighboring gases are forced to flow in the opposite direction of sheet movement by the mass suction-induced slip. As a result, the slip-induced suction and sheet movement cause the solution space to increase. The closed-form exact solutions are achieved for both the stretching and shrinking sheet cases. For stretched sheet instances, there is never a uniform solution. However, depending on the values of the Casson and wall mass transfer parameters, the solution in the case of the shrinking sheet may or may not exist, and if it does, it may or may not be unique or may have a dual nature. The research also demonstrates that stronger mass suction is required for a consistent flow of Casson fluid. The impacts of inverse Darcy number, induced slip parameter, Casson fluid and suction/injection on the flow and heat transfer properties of the fluid are examined under the influence of radiation, and the solution of each profile is shown in the form of figures along with the outcomes of the interface velocity and heat transfer rate at the surface.

Modeling of the movement of rich gas in a porous medium in immiscible, near miscible and miscible conditions

Gas injection is one of the most common enhanced oil recovery techniques in oil reservoirs. In this regard, pure gas, such as carbon dioxide (CO2), nitrogen (N2), and methane (CH4) was employed in EOR process. The performance of pure gases in EOR have been investigated numerically, but till now, numerical simulation of injection of rich gases has been scared. As rich gases are more economical and can result in acceptable oil recovery, numerical study of the performance of rich gases in EOR can be an interesting subject. Accordingly, in the present work the performance of rich gases in the gas injection process was investigated. Methane has been riched in liquefied petroleum gas (LPG), natural gas liquid (NGL), and Naphtha. Afterwards, the process of gas injection was simulated and the effect of injection fluids on the relative permeability, saturation profile of gas, and fractional flow of gas was studied. Our results showed that as naphtha is a heavier gas than the two other ones, IFT of oil-rich gas with naphtha is lower than other two systems. Based our results, gas oil ratio (GOR) and injection pressure did not affect the final performance of injection gas that has been riched in NGL and LPG. However, when GOR was 1.25 MSCF/STB, rich gas with naphtha moved with a higher speed in the domain and the relative permeability of each fluid and fractional flow of gas were affected. The same result was achieved at higher injection pressure. When injection pressure was 2000 psi, movement of gas with higher speed in the domain, alteration of relative permeability and changes in the fractional flow of gas were obvious. Therefore, based on our result, injection of naphtha with low pressure and high GOR was suggested for considered oil.

Environment-Forming Effect of Bubble Gas Emissions in the Golubaya Bay, Black Sea: Oxygen Regime and Bacterial Mats

Gas seep and fluid flows from the seabed are an environment-forming factor of the aquatic environment, mainly due to their influence on the dissolved gases in the water, including dissolved oxygen. During the summer seasons from 2019 to 2021 in the area of shallow water gas emission site off the southern coast of the Heracles Peninsula, series of vertical probing profiles were carried out to determine hydrological parameters of the water: dissolved oxygen concentration (O2), temperature (T), salinity (S), and flow velocity (U). The study area is an underwater ledge with faults in the form of three canyons composed of dense limestones, two of which contained bubble gas emissions. Significant variability in O2 was identified in canyons where gas emissions are observed: from 1 to 80% saturation in the bottom layer, in contrast to normoxia at the background sites. Hypoxia was observed in the bottom layer above the emission sites in the absence of turbulence at temperature stratification. The values S decreased with depth, and the maximum difference reached 0.4‰. The bubble gas was dominated by methane (68.5–75.5%), and the carbon isotope composition of the bubble methane gas varied from –67.9 to –59.8‰ VPDB in 2019 and 2020, respectively. This generally indicates that the CH4 is of predominantly microbial genesis, was formed under different conditions, and matured in various periods of research during the monitoring period. Bacterial mats (mostly sulfur-oxidizing bacteria) were found in the areas of gas emissions.

A new approach to the estimation of real characteristics of multi-phase flows in gaslift educator

It is known that the multi-phase flows are widespread in the oil-gas production, as well as in the collection and transportation of hydrocarbons from offshore fields. These gravitational upward and downward flows are characteristic for the rising pipes of gaslift and flow wells, as well as for the risers of subsea multi-phase pipelines. A new approach for the estimation of the real parameters of multi-phase flows considering the phase displacement is offered in the paper and the perspectives of their definition based on the microscopic parameters of well operation shown as well. A possibility of the specification of the real density, real gas content and phase displacement of gas-fluid flows in the rising pipes of gas-lift wells based on the actual operation data in the context of the wells of Guneshli (OFP-15) offshore field is shown.

Using Dispersed Gas Fluid Flow for Cooling of Energy Stressed Elements of Tokamak Structure

Using Dispersed Gas Fluid Flow for Cooling of Energy Stressed Elements of Tokamak Structure

Sorption enhanced steam methane reforming in a bubbling fluidized bed reactor: Simulation and analysis by the CPFD method

This work reports the modelling and simulation results of a bubbling fluidized bed reactor using the Computational Particle Fluid Dynamics (CPFD) method of the Barracuda® software. The reactor under investigation is the carbonator installed in the ENEA ZECOMIX research infrastructure, where Steam Methane Reforming (SMR) happens simultaneous with CO2 capture via solid sorbents. In this intensified process, namely Sorption Enhanced Steam Methane Reforming (SE-SMR), steam methane reforming is coupled with high temperature CO2 sorption and calcium looping (CaL) process, in order to increase the H2 yield, beyond thermodynamic limits. Currently, the reactor is operated in batch mode and is used also for sorbent regeneration, by switching the fluidizing gas flow from steam/methane to oxy-burner combustion products. With the aim of studying the process when it is operated as a closed loop, in this paper the reactor is continuously fed by a fresh sorbent flow and a riser/calciner reactor for sorbent regeneration, to be connected with the carbonator, has been sized. The continuous circulation of solid material between the two reactors ensures the maintenance of different operating temperatures and therefore greater operational optimization.The numerical analysis presented in this paper will serve as a valid support for the experimental activities. For this purpose, a sensitivity study on the SE-SMR process has been conducted, by varying the main operating conditions (e.g. sorbent conversion, sorbent/catalyst ratio, fluidizing gas flow), to evaluate the hydrogen purity yield. Two different kinetic mechanisms have been compared for the gas phase reactions. A post-processing routine has been written, in order to analyze bubbles sizes and velocities inside the fluidized environment. The effect of sorbent and catalyst particles segregation has been also investigated. The same modelling approach has been used for the sizing of the fast riser calciner reactor.

Pore-scale study of three-phase displacement in porous media

Carbon capture, utilization, and storage have been an effective way to deal with global climate issues. Injecting CO2 into depleted oil reservoirs can reach the dual goal of carbon storage and enhanced oil recovery. To optimize the gas injection strategy, it is necessary to understand the underlying mechanisms of three-phase fluid flow of oil, water, and gas. In this study, a lattice Boltzmann color gradient model is used to investigate the pore-scale three-phase displacement process in porous media. Gas is injected into the porous domain initially occupied by water and oil. Typical microscopic behaviors, including coalescence and split-up, pinch-off, double and multiple displacement, as well as parallel flow, are identified and discussed. Effects of water content (ϕ), capillary number (Ca), wettability and viscosity ratio (M) on the flow pattern, and oil recovery rate are explored. The oil ganglia inhibit the development of gas fingers, causing stronger viscous fingering characteristics with increasing ϕ. The fingering pattern is located in the crossover zone for the Ca from 5 × 10−5 to 5 × 10−4. As ϕ increases, the oil recovery rate reduces. The oil ganglia tend to occupy small pores as oil wettability enhanced, making it more difficult to be drained out. The reduction of oil viscosity is beneficial to improve connectivity, thereby effectively enhancing the oil recovery. Finally, the CO2 storage rate is also evaluated. It is found that the storage rate is very sensitive to the initial oil–water distributions. In general, the storage rate increases as ϕ decreases, Ca increases, and oil wettability enhances.

Sinking dynamics and splitting of a granular droplet

A granular droplet that is composed of smaller and denser particles in a bed of larger and lighter particles is found to sink and split when subjected to a combination of vibration and fluidizing gas flow. Despite visual similarities with fluid-like instabilities, the observed phenomenon is a result of the particulate character of granular matter. Combining experiments and numerical simulations, we show that the droplet of high-density particles causes the formation of an immobilized zone that obstructs the downwards motion of the droplet and causes the droplet to spread and ultimately to split. We further investigate the conditions required for droplet splitting.

Flow Simulation and Influence Factors Analysis of CO2 Foam Fracturing in Annulus Injection

CO2 foam fracturing fluid is widely used in unconventional oil and gas production because of its easy flowback and low damage to the reservoir. Nowadays, the fracturing process of CO2 foam fracturing fluid injected by coiled tubing is widely used. However, the small diameter of coiled tubing will cause a large frictional pressure loss in the process of fluid flow, which is not beneficial to the development of fracturing construction. In this paper, the temperature and pressure calculation model of gas, liquid, and solid three-phase fluid flow in the wellbore under annulus injection is established. The model accuracy is verified by comparing the calculation results with the existing gas, solid, and gas and liquid two-phase model of CO2 fracturing. The calculation case of this paper shows that compared with the tubing injection method, the annulus injection of CO2 foam fracturing fluid reduces the friction by 3.06 MPa, and increases the wellbore pressure and temperature by 3.06 MPa and 5.77°C, respectively. Increasing the injection temperature, proppant volumetric concentration, and foam quality will increase the wellbore fluid temperature and make the CO2 transition to the supercritical state while increasing the mass flow rate will do the opposite. The research results verify the feasibility of the annulus injection of CO2 foam fracturing fluid and provide a reference for the improvement of CO2 foam fracturing technology in the field.

Multiscale simulation of rapid solidification of an aluminium–silicon alloy under additive manufacturing conditions

At present, most multiscale simulation approaches to model the temperature evolution of the molten pool, and the resulting microstructure evolution for selective laser melting, assume an equilibrium freezing range and steady state solidification conditions. This is despite the solidification conditions being observed to be highly unsteady and non-equilibrium. These two assumptions lead to inaccurate predictions of the temperature evolution of the molten pool and thus microstructure predictions. To demonstrate this, an approach to scale-bridging computational models of the laser additive manufacturing process is presented, in which the temperature history is passed from a macroscale molten pool simulation to a microscale phase-field simulation. This linkage is achieved by volume mapping of the temperature field from the grid of the molten pool simulation to the grid of the microstructure simulation. To describe the system evolution at the scale of the molten pool, a computational fluid dynamics (CFD) method that captures the laser–metal interaction, vapour production, gas recoil pressure, fluid flow, surface tension, Marangoni flow, and heat conduction, convection, and radiation is applied. To capture the chemical kinetics of the phase-transition, a non-equilibrium CALPHAD-integrated phase-field (PF) model is applied. The discrepancy between the predictions of the solid front isotherm is quantified as ⩾ 100 K for an Al-10Si alloy under the large observed cooling rate. This leads to a spatial discrepancy in the solidification front between the CFD model, which assumes equilibrium freezing behaviour, and the PF model, which does not, of approximately 10 µm over 50 µs in the present case. Under these conditions, present formulations of multiphase CFD cannot accurately predict the solidification behaviour because of the assumption of equilibrium at the solid–liquid interface. Strategies for reconciling this discrepancy for materials that exhibit rapid solidification under large thermal undercooling will need to be developed for multiscale simulation of additive manufacturing to advance.

Bio-oil from biomass fast pyrolysis: Yields, related properties and energy consumption analysis of the pyrolysis system

Based on a comprehensive study of biomass fluidized bed device, a fast pyrolysis experiment to produce bio-oil was carried out using rice husks as raw material. The effects of reaction temperature, fluidized gas volume, and feed rate on the yield of bio-oil were studied. Experiments showed that the best temperature for bio-oil yield was 500 °C, the best fluidizing gas flow rate was 22 m³/h and the best feed rate was 2.65 kg/h. The physical and chemical properties of bio-oil were analyzed, and the results showed that the density, acidity, calorific value, and viscosity of the first-level bio-oil were greater than those of the second-level bio-oil. Among the components, the contents of acids (18.74%), ketones (22.51%), esters (16.90%), and phenols (17.91%) were relatively high. Aspen Plus software was used to analyze the energy consumption of the reaction model. Most of the energy in the fast pyrolysis of biomass is consumed for the preheating and cooling of nitrogen, which accounts for 60% of the total energy consumption. The combustion of the coke and non-condensable gas, which are produced as by-products can be used for preheating raw materials to realize self-heating production. Combine experiment and simulation will promote its industrialization.

How negative is the pressure used in the surgical wound treatment with negative pressure therapy ?

The study aims to assess the significance of negative pressure therapy in the treatment of surgical wounds and using the ANSYS simulation software for fluid dynamics calculation will give us the possibility to determine the fluid flow dynamics inside the vacuum kit during its use. Material and methods: To predict the speed, pressure and temperature of the fluid inside a vacuum kit, we used numerical modeling, using the finite element method, of the gas fluid flow phenomenon. Results: The pressure of the liquid fluid is higher in the area of contact with the wound, compared to the pressure of the liquid fluid in the outlet area of the capillary tube, accentuating with increasing pressure applied to the end of the tube. 32% of the fluid pressure at the interface between the sponge and the wound. Conclusions: The rate of pressure transmission inside the sponge is variable favoring the appearance of ischemia areas on contact with the wound.

Full-loop study of a dual fluidized bed cold flow system: Hydrodynamic simulation and validation

The unsteady behaviors of the air-silica sand flow in a lab-scale dual fluidized bed gasification cold flow system have been studied. A two-dimensional computational fluid dynamics full-loop model with poly-size distribution in solid phases was developed as an innovation of this study to investigate the effects of crucial parameters on system hydrodynamics. The results showed a decrease in the mixture static pressure from the bottom to the upper regions of the system, which maintained the system operations stable. The riser air inlet velocity and the gasifier static bed height were found to play considerable roles in enhancing the total sand flow rates. The same tendencies in the prediction and experiment of both the mixture pressure and the sand flow rate showed the feasibility of the proposed model. Besides, the residual evaluation enhanced data reliability and supported model validation. Especially, undesirable phenomena possibly occurring in the system operation under improper conditions could also be predicted. Accordingly, the inventory of bed material and the fluidizing gas flow rates should be suitably regulated to maintain pressure balances, trouble-free continuous flow, optimal sand circulation rate, and low solids loss. Furthermore, the obtained results in this study can be used as a reference for optimizing the designs and operational conditions of large-scale plants.

FIRE GAS PLUMES DURING THE 1927 YALTA EARTHQUAKES

In the Black Sea near Yalta in 1927 there were massive methane outbursts, accompanied by flames over the water. The fire was associated with methane emissions that entered through tectonic faults. The faults were caused by seismic movements. The article analyses the depth structure of the focal zones and the nature of the seismic process and assesses the nature of the manifestations of the fires. The main factor is thought to be methane, which rises from the earth’s crust during earthquakes. The electric spark discharges generated by friction and collision of the earth’s crust ignited methane gas. The massive gas emissions of millions of cubic meters that can be called gas plumes have been fixed. The spatial and temporal direction of the fire phenomena has been established. The main fire outbreaks over the water extended in two directions. The first, the Sevastopol­Evpatoria zone, stretches submeridionally to the coast and follows the Mykolayiv fault system. The second one is the Yalta­ Alushta zone with north-eastern extension. It is associated with tectonic faults within the Circum­Black Sea region, fault zone. This fault zone is active even at present, as indicated by seismicity, the structure of the consolidated crust and sedimentary strata, bottom topography forms, etc. Analysis of geological and geophysical materials, and seismicity of the northern Black Sea region, indicate that the fire events during the Yalta earthquakes in 1927 were caused by massive methane ejections as a result of a powerful mantle gas-fluid flow into the dissolved zones of the crystalline basement along the tectonic faults of different scales within the Odessa­Sinop and Circum Black Sea fault zones. Earthquakes triggered the activation of tectonic faults in benthic sedimentary horizons for the migration of focused deep-seated gas-fluid streams.

Analysis of MHD slightly rarefied gas flow over a permeable stretching surface based on second-order velocity slip

In this paper, a steady solution is presented for the equations that represent the MHD rarefied gas fluid flow and heat transfer due to a permeable stretching sheet with second-order velocity slip and thermal slip phenomenon. By using nondimensional transformations, the system of partial differential equations governing the problem is transformed into another system of nonlinear ordinary differential another equations. Novel solutions are investigated for the resulting ordinary differential equation which describe the momentum equation. The numerical results obtained agreed very well with previously reported cases available in the literature. Additionally, the effects of the magnetic parameter, first- and second-order velocity slip parameter, conductivity parameter, thermal slip parameter and the suction (injection) parameter on both the velocity and temperature profiles and on the local skin-friction coefficient are discussed and presented through tables and graphs.