Momentum Transfer Equations Research Articles

Heat and mass transfer analysis of s-PTT nanofluid in microchannels under combined electroosmotic and pressure-driven flows with wall slip using the homotopy perturbation method

The heat and mass transfer of the electroosmotic flow in microchannel transporting viscoelastic nanofluid is investigated considering Brownian motion of nanoparticles and slip boundary conditions. The simplified Phan-Thien-Tanner model is employed to describe the rheological behavior of fluid and the nonlinear Navier model with non-zero slip critical shear stress is considered at walls. The governing nonlinear momentum, mass, and heat transfer equations are solved using the Homotopy Perturbation Method. The study reveals that increasing the fluid elasticity, nanoparticle concentration, and size significantly enhances the flow rate, heat and mass transfer. Additionally, elasticity and Reynolds number decrease the friction factor. Reducing the double-layer thickness and increasing the Reynolds number lead to higher flow rates and fluid velocities. Notably, the findings emphasize the critical role of the slip conditions on the Sherwood and Nusselt numbers.

Process intensification in the direct contact membrane distillation (DCMD) desalination by patterning membrane surface: A CFD study

In this research, the impact of pattern geometry on the intensification of the performance of surface patterned membranes for saline water desalination by direct contact membrane distillation (DCMD) is investigated by computational fluid dynamics (CFD) simulation. The Comsol Multiphysics software was applied to solve the governing transport equations for heat, momentum, and mass transfer. The result of the model was validated by the published experimental data, and the maximum deviation was <10 %. The target was to maximize the permeate flux by altering surface pattern geometry and dimensions. Based on the previous studies, a prism pattern was chosen in this work, and the influences of pattern type (3 types), pattern dimension (25–150 µm valley depth), and the distance between the valleys (0–400 µm) were studied on the temperature polarization coefficient (TPC) and DCMD permeate flux. The results showed that the pattern with a valley depth of 25 µm and a distance between the valleys of 300 µm had the best performance in DCMD operation. In this situation and feed temperature of 80 °C, a TPC of 0.78 and a water flux of 49.3 kg m-12.h were attained. The characteristics of flow close to the patterned membrane surface were also investigated, and it was observed that there are weak shear stresses in the lower zone of the valleys, while stronger shear stresses are created in the upper regions that are responsible for improving the TPC and water flux in the patterned membranes.

THE IMPACT OF SOLAR RADIATION ON THE TEMPERATURE REGIME OF A ROOM IN WINTER

The article is devoted to the computational studies of the air-thermal state of office premises taking into account the effect of solar radiation coming through window openings. The study was conducted for a room with two windows using two heating devices installed under them. The air-temperature regime of premises in winter, characterized by the highest thermal energy consumption for heat supply, is considered. The study is based on the solution of a three-dimensional nonlinear heat transfer problem described by a system of equations of turbulent momentum and energy transfer. The k-e turbulence model is used to close this system. The results of numarical modeling of the physical situation under study are presented. The research data on the features of the air-thermal state of the premises under solar radiation conditions are given. The results of a comparative analysis of the air-temperature conditions of office premises corresponding to the solution of the specified heat exchange problems in the presence and absence of solar radiation are presented and the effects of solar radiation on the structure of the air flow and the thermal state of the premises are established. It is shown that in the presence of solar radiation, the air flow picture and the character of the temperature fields in the premises change significantly. In particular, in these conditions, the increase in the average temperature of the premises for the studied period is 2.5 °С. The possibility of a certain reduction of the load on the heating system in the presence of solar radiation is noted. Bibl. 17, Fig. 5.

A numerical study on MHD Casson fluid flow in a non-uniform rough channel with temperature-dependent properties using OHAM

This study explores the complex dynamics of magnetohydrodynamic (MHD) Casson fluid in a non-uniform rough channel, focusing on the effects of temperature-dependent viscosity and variable thermal conductivity under no-slip boundary conditions. The study employs an innovative approach by utilising a rough surface with irregular textures to analyse flow patterns and assess drag forces on channel objects. A novel mathematical model, governed by continuity, momentum, and heat transfer equations, is developed and transformed into dimensionless, nonlinear Ordinary Differential Equations (ODEs) using non-dimensional quantities and fundamental assumptions. The Optimal Homotopy Analysis Method (OHAM) is applied to solve these equations to enhance convergence speed and accuracy. The research explores the impact of surface roughness on velocity profiles and temperature distributions under various physical constraints. Numerical simulations are conducted to determine skin friction coefficients and Nusselt numbers. Furthermore, the study examines the influence of confined boluses on fluid flow in diverse physiological conditions. A comprehensive analysis is performed to elucidate the combined effects of surface roughness on fluid passage, including flow separation, pattern alterations, pressure distribution and drop, heat transfer characteristics, and flow resistance. The intricate interplay between temperature-dependent viscosity, varying thermal conductivity, and surface roughness is thoroughly investigated to explain the complex dynamics of MHD Casson fluid movement in non-uniform channels. Implementing a magnetic field over the rough, non-uniform channel is found to provide stability and prevent fluid overflow. This research has significant real-world applications, including soil erosion prevention, blood flow regulation in arteries, and optimisation of hydropower channels and penstocks. By enhancing our understanding of flow dynamics through rough and non-uniform channels, this study contributes valuable insights into both theoretical fluid mechanics and practical engineering applications.

Numerical Analysis of MHD Casson Fluid Flow over a Stretching Surface with Chemical Reaction and Variable Thermal Conductivity

The motivation of the current article is to explore the Numerical analysis of MHD Casson fluid flow over a Stretching surface. Three dimensional, non-linear of an incompressible fluid flow in the presence of chemical reaction and variable thermal conductivity is considered. The mathematical model effectively describes the current flow analysis. The Governing equations are simplified with the help of boundary layer approximations. Non-linear coupled equations for momentum, energy and mass transfer are tackled with MATLAB bvp4c. The behavior of various non-dimensional parameters which are involved in the derived set of equations are described and explained in detailed through graph.

An analytical study on the influence of magnetic field-dependent viscosity on viscous and ohmic dissipative second-grade fluid boundary layers

This article aims to investigate the magnetohydrodynamic (MHD) boundary layer flow of a second-grade non-Newtonian fluid over a horizontally stretching sheet, considering magnetic field-dependent (MFD) viscosity, as well as viscous and Ohmic dissipations. Analytical solutions for previously unexplored momentum and heat transfer equations involving MFD viscosity are derived. Two boundary conditions, namely Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF), are taken into account. Governing dimensional partial differential equations (PDEs) are transformed into non-dimensional ordinary differential equations (ODEs) using similarity transformations. Closed-form analytical solutions for flow are derived, considering stretching velocity, MFD viscosity, second-grade fluid properties, and suction impacts. Heat transfer equations are transformed into Gauss-hypergeometric form, yielding solutions in terms of confluent hypergeometric functions. Analytical expressions for skin friction, local Nusselt number, and non-dimensional wall temperature are derived. A unique solution is obtained for the flow equation. It is found that both second-grade and magnetic viscosity parameters expand the momentum boundary layer while the magnetic parameter reduces thickness. Thermal boundary layer thickness increases with a higher second-grade parameter, magnetic viscosity, and Eckert number. Moreover, analytical solutions are validated against published results for a special case.

Computational and Experimental Research on the Influence of Supplied Gas Fuel Mixture on High-Temperature Fuel Cell Performance Characteristics

Currently, the process of creating industrial installations is associated with digital technologies and must involve the stage of developing digital models. It is also necessary to combine installations with different properties, functions, and operational principles into a single system. Some tasks require the use of predictive modeling and the creation of “digital twins”. The main processes during the fuel cell modeling involve electrochemical transformations as well as the movement of heat and mass flows, including monitoring and control processes. Numerical methods are utilized in addressing various challenges related to fuel cells, such as electrochemical modeling, collector design, performance evaluation, electrode microstructure impact, thermal stress analysis, and the innovation of structural components and materials. A digital model of the membrane-electrode unit for a solid oxide fuel cell (SOFC) is presented in the article, incorporating factors like fluid dynamics, mass transfer, and electrochemical and thermal effects within the cell structure. The mathematical model encompasses equations for momentum, mass, mode, heat and charge transfer, and electrochemical and reforming reactions. Experimental data validates the model, with a computational mesh of 55 million cells ensuring numerical stability and simulation capability. Detailed insights on chemical flow distribution, temperature, current density, and more are unveiled. Through a numerical model, the influence of various fuel types on SOFC efficiency was explored, highlighting the promising performance of petrochemical production waste as a high-efficiency, low-reagent consumption fuel with a superior fuel utilization factor. The recommended voltage range is 0.6–0.7 V, with operating temperatures of 900–1300 K to reduce temperature stresses on the cell when using synthesis gas from petrochemical waste. The molar ratio of supplied air to fuel is 6.74 when operating on synthesis gas. With these parameters, the utilization rate of methane is 0.36, carbon monoxide CO is 0.4, and hydrogen is 0.43, respectively. The molar ratio of water to synthesis gas is 2.0. These results provide an opportunity to achieve electrical efficiency of the fuel cell of 49.8% and a thermal power of 54.6 W when using synthesis gas as fuel. It was demonstrated that a high-temperature fuel cell can provide consumers with heat and electricity using fuel from waste from petrochemical production.

Plasma propagation velocity dependence on driving and restricting forces

According to the time-averaged expression for an alternating electric field, the normalized electromagnetic pressure is proportional to the square of the voltage intensity and inversely proportional to the square of the voltage repetition frequency. Moreover, the plasma propagation velocity is either directly proportional, inversely proportional, or nonproportional to the normalized electromagnetic pressure at all neutral gas flow rates. Because the plasma current is only directly proportional to the normalized electromagnetic pressure at all neutral gas flow rates, the dependence of the plasma density on the electromagnetic pressure changes to obtain a balance of dependence. In the momentum transfer equation, plasma density does not originally depend on electromagnetic pressure, but the dynamic pressure associated with the neutral gas flow also exerts a force on the plasma through collisions. Therefore, when the ionization generation of plasma by collisions between the plasma and neutral particles is dominant over recombination by collisions, the plasma density is square proportional or directly proportional to the electromagnetic pressure.

Oil–Water Hydrodynamics Model during Oil Displacement by Water in Down-Hill Mobile Pipeline

In the process of water displacing oil within mobile pipelines, it is common that the oil tends to accumulate at the elevated sections of inclined pipelines, leading to an issue of residual oil accumulation. In this paper, the mechanism of carrying accumulated oil out of the pipeline with water flow is discussed. Taking the residual oil layer in down-hill pipelines as a research object, a hydrodynamic model of the water-oil displacement process is established based on the theory of liquid–liquid two-phase flow and the application of the momentum transfer equation. It has been found that the use of this model can enhance the computational speed by 15% without affecting the accuracy of the calculations. Subsequently, the model is used to analyze the impact of different initial water-phase velocities, inclination angles, initial oil-phase heights, and pipeline diameters on the oil-carrying process of water flow. The results indicate that increasing the initial water-phase velocity, the angle of inclination, and the initial oil-phase height all enhance the fluctuation in the oil–water interface, making it easier for the oil phase to be carried away from the pipeline. Conversely, when all other parameters are held constant, an increase in the pipeline diameter tends to stabilize the oil–water interface, thereby making it more difficult for the residual oil to be carried away by the water flow.

Modeling and experimental analysis of CO2 methanation reaction using Ni/CeO2 monolithic catalyst

In this study, the effect of the cell density of monolithic catalysts was investigated and further mathematically modeled on cordierite supports used in CO2 methanation. Commercial cordierite monoliths with 200, 400, and 500 cpsi cell densities were coated by immersion into an ethanolic suspension of Ni/CeO2 active phase. SEM–EDS analysis confirmed that, owing to the low porosity of cordierite (surface area < 1 m2 g−1), the Ni/CeO2 diffusion into the walls was limited, especially in the case of low and intermediate cell density monoliths; thus, active phase was predominantly loaded onto the channels’ external surface. Nevertheless, despite the larger exposed surface area in the monolith with high cell density, which would allow for better distribution and accessibility of Ni/CeO2, its higher macro-pore volume resulted in some introduction of the active phase into the walls. As a result, the catalytic evaluation showed that it was more influenced by increments in volumetric flow rates. The low cell density monolith displayed diffusional control at flow rates below 500 mL min−1. In contrast, intermediate and high cell density monoliths presented this behavior up to 300 mL min−1. These findings suggest that the interaction reactants-catalyst is considerably more affected by a forced non-uniform flow when increasing the injection rate. This condition reduced the transport of reactants and products within the catalyst channels and, in turn, increased the minimum temperature required for the reaction. Moreover, a slight diminution of selectivity to CH4 was observed and ascribed to the possible formation of hot spots that activate the reverse water–gas shift reaction. Finally, a mathematical model based on fundamental momentum and mass transfer equations coupled with the kinetics of CO2 methanation was successfully derived and solved to analyze the fluid dynamics of the monolithic support. The results showed a radial profile with maximum fluid velocity located at the center of the channel. A reactive zone close to the inlet was obtained, and maximum methane production (4.5 mol m−3) throughout the monolith was attained at 350 °C. Then, linear streamlines of the chemical species were developed along the channel.

Exact solutions to the oberbeck–boussinesq equations for convective stokes flows

To study large-scale convective flows (fluid motion in a thin layer), it is possible, for initial studies, to consider the Stokes approximation when integrating the Oberbeck–Boussinesq equation. The convective derivative in the momentum transfer equations and in the heat conduction equation is in this case assumed to be identically equal to zero. The paper discusses several approaches to constructing exact solutions for slow (creeping) flows of a non-uniformly heated fluid. Formulas for three-dimensional flows in the Lin–Sidorov–Aristov class are given for steady flows. The hydrodynamic fields are described by polynomials. Exact solutions are given for the velocity field nonlinearly depending on two spatial coordinates (longitudinal, or horizontal) with coefficients of nonlinear forms, which depend on the third coordinate. The study shows how it is possible to automate the computation of unknown coefficients for the formation of hydrodynamic fields (velocities and temperatures).

Analysis of Entropy Generation for MHD Heat Transfer Flow of Viscous Fluid Embedded in a Porous Channel Due to Thermal Radiation

The study investigates the effect of convective flow on entropy generation for MHD heat transfer flow of viscous fluid embedded in a porous channel due to thermal radiation. The governing equations were transformed using the non-dimensional parameters. The solution of the resulting coupled dimensionless differential equations with a constant coefficient describing the momentum, energy, and mass transfer equations was obtained by using the method of undetermine coefficient. The parameters embedded in the flow are thermal radiation , Prandtl number, entropy generation , Suction/injection parameter , heat source/sink , porous material . In addition, physical quantities of engineering interest such as the Bejan number , Brinkman number , volumetric flow rate , skin friction coefficient, and heat transfer rate were computed. It is noticed that velocity and temperature increase significantly with an increase in heat source and suction parameters, while a reverse trend is observed when heat sink and injection are present. It is also evident that, the heat source increases the temperature profile in the presence of injection parameter, and a reverse trend is observed when the heat sink increases in the presence of the suction parameter. skin friction is decreasing with increase higher values of porous material in both at when injection and , volume flow rate reduces with increasing values of heat source and shot-up with decreasing values of heat sink, its observed that entropy generation is increasing for higher values of ...........

Darcy-Forchheimer nanofluid flow and heat transfer with convective boundary conditions: Insights from differential transform method

In this work, we use the sophisticated differential transform method (DTM) to derive solutions to the complicated momentum, heat, and mass transfer equations that characterize Darcy-Forchheimer nanofluid flow over a stretching surface with convective boundary conditions. The investigation includes the nuanced effects of heat sources and chemical reactions and also addresses the synergistic effects of Brownian motion and thermophoresis. By applying an appropriate similarity transformation, the governing partial differential equations (PDEs) are gracefully transformed into an elegant system of nonlinear coupled ordinary differential equations (ODEs), a problem that is ingeniously solved using DTM. The veracity of our results is underpinned by a careful validation against previous scientific work that illuminates the path to scientific clarity. As the mathematical tapestry unfolds, the enchanting interplay of physical parameters on fluid dynamics is revealed, manifesting in visually captivating graphs and illuminating tables. Of particular note is the transformative influence of the magnetic parameter, which stages a ballet in which an increase in skin friction and the Nusselt number causes a diminuendo. Meanwhile, the solutal concentration decreases as the Brownian motion, Lewis number, and chemical reaction parameters increase, while it waltzes in reverse harmony with the thermophoresis parameter. Beyond equations and diagrams, this investigation promises to cast a luminous beacon on practical realms, imparting invaluable insights for industries ensconced in the realm of heat exchangers, the alchemy of lubricant refining processes, and the grand tapestry of scientific and engineering domains.

One-dimensional multi-fluid model of the plasma wall transition

A one-dimensional multi-fluid model of the plasma wall transition is presented. The plasma is composed of singly charged positive ions, electrons and negative ions. Positive ions are assumed to obey the continuity, momentum transfer and energy transport equation, while the electrons and negative ions are treated by the continuity and momentum transfer equation. For the positive ions the closure is done by assuming that heat flux in the plasma is zero, while both negative species are treated as isothermal, with the pressure gradient term being proportional to the density gradient. The potential drop in the pre-sheath can be determined either by the electrons or the negative ions – depending on their densities in the unperturbed plasma. It is shown how the boundary density of both particle species can be in some cases determined very precisely.

Heat and Mass Transport of Casson Nanofluid in A Peristaltic Curved Channel

This study focuses on theoretical inquiry into transition of heat and mass of flowing Casson Nanofluid in a curved channel, in two dimensions, through peristalsis. The flow is assumed to be characterised by low Reynolds number and long wavelength approximations. The coupled governing non-dimensional equations of momentum, heat and mass transfer which are solved using BVP. Various parameters related with the flow are applied to study its effect on velocity, temperature and also nanofluid concentration. Also, the consequences of thermophoretic diffusion of nanoparticles and Brownian motion are discussed. The Casson parameter's effect on velocity profile is discussed.

CFD simulation of drag-reducing fluids in a non-Newtonian turbulent pipe flow

The conveyance of fluids from one terminal to another incurs considerable expenses primarily due to the significant costs associated with addressing pressure losses arising from shear stresses and friction along the inner surface during the pumping operations within pipelines. This study was conducted with the objective of simulating turbulent flow in pipes containing drag-reducing fluids. This was achieved through the utilization of both RKE and RNG versions of a non-Newtonian model for low Reynolds numbers, based on the k-ε model, along with a non-Newtonian damping function. The outcomes were subsequently compared to simulations carried out by Pinho and experimental data sourced from the existing literature. To simulate the flow in pipelines, computational fluid dynamics (CFD) software was employed, which incorporated non-linear molecular viscosity and a damping function to accurately account for near-wall effects. In addition, this research entailed the optimization of C and C0 parameters in the damping function and the stress term, which quantifies the cross-correlation between fluctuating viscosity and the fluctuating rate of strain. Furthermore, non-Newtonian terms were incorporated into the equations for turbulent kinetic energy (k), dissipation rate (ε), and momentum transfer. The study involved a comprehensive comparison of model predictions with experimental data across various flow parameters, including friction factor, axial velocity, turbulent kinetic energy, and Reynolds shear stresses. The results revealed a significant enhancement in the model's ability to predict critical flow parameters, such as friction factor, mean axial velocity, and Reynolds stress profiles. Nevertheless, the model displayed some limitations in predicting turbulent kinetic energy. Notably, the average error in calculating the friction factor for the fluids under investigation was found to be 5.45%, marking a substantial improvement compared to the Pinho model, which exhibited an average error of 32.49%.

Matematyczne modele hydromechaniki przepływu wielofazowego o zmiennej masie

The paper discusses the mathematical model of hydromechanics of multiphase flows with varying mass. A multiphase flow is considered a continuum consisting of a set of a large number of different groups of particles. The derivation of motion equations and similarity criteria are given taking into account both the externally attached (or detached) mass and phase transitions within the medium. The equations of mass, momentum and energy transfer for individual phases and the medium as a whole are derived based on fundamental conservation laws. It was demonstrated that in the absence of sources (or flow-offs) of mass, momentum and energy, the known equations of single- and multi-phase flow hydromechanics follow as a special case from the obtained systems of motion equations and similarity criteria. The obtained motion equations are valid for the description of an ingredient of mixture and the medium as a whole, regardless of their physical and mechanical properties. Thermodynamic and rheological state equations, as well as expressions for heat flow, interfacial mass forces phase transitions, and heat exchange between phases can be used to close them. The implemented models make it possible to simulate both the stationary distribution of parameters along the wellbore during production and non-stationary processes that occur, for example, when the pump shaft speed changes during oil production. The developed approaches were implemented in the DataFlow software tool for analysis of the hydrodynamics of multiphase hydrocarbon flows, taking into account heat exchange with the rocks surrounding the well, and phase transitions in the fluid. Using the software package, test calculations were carried out to demonstrate the performance of the proposed and implemented models.

Numerical simulation of the particle wall mass transfer rates on rough surfaces confining turbulent natural convection flows

We performed numerical simulations of the particle mass transfer rates on the horizontal and vertical thermally active rough walls confining a turbulent natural convection flow. We considered the air flow conditions in a cubical cavity (L=1.22m, Ra=5.4·108, Pr=0.71) with two opposed pairs of consecutive walls at different temperatures, for which measurements of the particle deposition velocities are reported in the literature. The simulations were carried out by solving the momentum, thermal energy and particle mass transfer equations using a series of two-dimensional computational cell units to determine spatial evolution and development of the particle concentration boundary layer in the vicinity of hot and cold rough walls. Different flow conditions, wall orientations, sizes of roughness elements, particle diameters and temperature increments between the wall and the bulk fluid, typically found in indoor environments, have been considered and consequently, results can be used to estimate the particle deposition rates in real scenarios. At large mass transfer particle Péclet numbers, corresponding to spherical particles with diameters of 0.5–1 μm, the wall mass transfer rates of particles on rough textures typically increase by a factor of about 3 in comparison with the deposition on smooth surfaces. The thermophoretic effect significantly decreases the particle deposition on hot surfaces and increases it on cold surfaces, especially at large particle Péclet numbers. The numerical predictions of the deposition velocities are in good agreement with the measurements reported in the literature for the same flow conditions considered.

A Review: Membrane Reactor for Hydrogen Production: Modeling and Simulation

A membrane reactor is a multifactional vessel used for H2 production. Hydrogen's three spectrum colors are dependent on carbon present. Two types of membrane with high permeability to hydrogen (polymeric and metallic) Hydrogen is produced in two systems: conventional reactors and membrane reactors (which separate and purify hydrogen in a single vessel). There are many types of membrane reactors according to design (catalytic membrane reactor (CMR), fixed bed reactor (FBMR), fluidized bed reactor (FBMR), etc. The transport mechanism of H2 through the membrane by a "sorption-diffusion mechanism" and the government equations that are used for membrane reactor modeling and simulation, such as continuity, momentum, mass, and heat transfer equations of the CMR, and the thickness of the membrane. These equations are solved by MATLAB, COMSOL, and the Finite Element Method to simulate the MR at different parameters: rate of conversion, rate of sweep gas, temperature, pressure, rate of H2 permeation through a membrane, and activity of the catalyst. We summarized theoretical studies for membrane reactors, including the operation conditions, type of hydrocarbon feed, type of production method, kind of catalyst, and heat effect.

Mathematical inspection of heat transfer and unsteady viscous flow in a tunnel with trapezoidal shaped slender wall

An exploration is made to investigate numerically and theoretically the time dependent flow of blood along with heat transfer through abnormal artery having trapezoidal shaped plaque. The flow is taken to be Newtonian, laminar, unsteady and incompressible. A suitable geometrical model is constructed to simulate the trapezoidal stenosis affected artery. The governed 2-dimensional momentum and heat transfer equations are conventionalized by assuming mild trapezoidal stenosis. The renovate partial differential equations are further converted into ordinary differential equations by assist of transformations. The novelty of the work is to consider unsteady blood flow through trapezoidal shape stenosed artery. A technique of finite difference is used to discretize the updated dimensionless model numerically. Comprehensive graphical outcomes for a flow of blood are obtained. The effect of trapezoidal plaque on blood velocity, pressure and temperature are shown by surface graph inside the artery and also shown with the help of line graph.