Wall Mass Transfer Rate Research Articles

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.

Heat transfer analysis of unsteady MHD slip flow of ternary hybrid Casson fluid through nonlinear stretching disk embedded in a porous medium

The original article's purpose is to assess transfer of heat exploration for unsteady magneto hydrodynamic slip flow of ternary hybrid Casson fluid via a nonlinear flexible disk placed within a perforated medium of a magnetic field in the presence. Unsteady nonlinearly stretched disk inside porous material causes flow to occur. In the investigation, convective circumstances on wall temperature are also considered. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriate transformations, and the Keller-box technique is employed for their solution. In forced convection, the variable radiation has no direct impact on fluid velocity, but it is noticed that in the case of aiding flow, fluid velocity rises with an increase in radiation parameter, and the opposite is true in the case of opposing flow. Furthermore, it is experiential that fluid concentration and velocity goes up in creative chemical reactions, and both profiles decrease in detrimental chemical reactions. Moreover, a slightly greater unsteadiness characteristic lowers fluid, concentration, temperatureand velocity. Physical parameters' effects on fluid temperature, concentration, and velocity, as well as on wall shear stress, energy, and mass transfer rates, are studied.

Second-order slip flow of a magnetohydrodynamic hybrid nanofluid past a bi-directional stretching surface with thermal convective and zero mass flux conditions

The nanoliquid concept has variety of applications toward biomedicine, heat exchangers, cooling of electrical devices, foods, and transportation. It is important to add various kinds of solid nanoparticles, such as silica, copper, silver, alumina, graphene, gold, and so on to the base fluids to increase the thermal efficiency of common fluids like engine oil, kerosene oil, water, sodium alginate, etc. This research explores the second-order slip flow of a Cu-Fe3O4/H2O past a bi-directional stretching surface. The current research takes into account the conditions of thermal convection, zero mass flux, and velocity slips. It is important to note that the hybrid nanoliquid flow’s wall mass transfer rate is eliminated by the zero mass flux at the wall. Furthermore, a strong magnetic field, thermophoresis, activation energy, exponential heating, chemical reaction, and Brownian motion are also studied. The mathematical framework of this report is presented in the form of PDEs which are then converted into ODEs via appropriate similarity transformations. A semi-analytical method called HAM, is used in order to solve the transformed ODEs. The convergence of HAM is shown with the help of Table. The impacts of physical parameters on the flow distributions are shown with the help of Tables and Figures. The findings of this study demonstrate that the velocity distributions of the hybrid nanofluid flow are decreased as the magnetic constraint is augmented. The ratio parameter has an inverse relationship to the primary velocity and has direct relationship to the secondary velocity. The energy profile has augmented due to the higher thermal Biot number. The present analysis is validated by comparing the new results with reported results.

Thermophoretic and Suction/blowing Effects on MHD Mixed Convection Flow over an Inclined Plate Combined with Heat Generation, Chemical Reaction and Radiation

This paper examined the thermophoresis effect and suction/injection process on steady MHD in a semi-infinite inclined porous plate. Chemical reaction, heat generation and thermal radiation are taking into account. The governing partial differential equations are transformed via similarity technique into a system of nonlinear ordinary differential similarity equations, which are solved numerically by applying the Lobbato IIIa-finite-difference method. Favorable comparisons with previously published work are performed. Numerical pertinent results for the velocity, temperature and concentration profiles as well as for the skin-friction coefficient, wall heat transfer and mass transfer rates are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution. The main results are the dominant influence of suction/injection process to control the principal boundary layers and the role played by the combined chemical reaction, heat generation and thermal radiation on the changes in the quantities of interest.

Heat and Mass Transfer at the Wall of a Square Mechanically Stirred Gas‐Liquid‐Solid Catalytic Reactor

AbstractWall mass and heat transfer rates in a square gas‐sparged, mechanically stirred reactor were measured by the electrochemical technique under the effect of various geometrical and hydrodynamic variables. For the 45° impeller, the mass transfer data fit the equation Sh = 0.7Sc0.33Re0.2Reg0.5 with an average deviation of ±6.9 %. For the 90° impeller, the data fit the equation Sh = 0.95Sc0.33Re0.14Reg0.53 with an average deviation of ±7.5 %. Gas sparging enhanced the wall mass transfer rates by factors of up to 2.61 and 3 for the 90° and 45° impellers, respectively, with a significant decrease in the total power consumption. The contribution of the present results to the operation of multiphase mechanically agitated vessels in different aspects is outlined.

Large-scale energetic coherent structures and their effects on wall mass transfer rate behind orifice in round pipe

This paper first uses a low-speed stereoscopic particle image velocimetry (SPIV) system to measure the convergent statistical quantities of the flow field and then simultaneously measure the time-resolved flow field and the wall mass transfer rate by a high-speed SPIV system and an electrochemical system, respectively. We measure the flow field and wall mass transfer rate under upstream pipe Reynolds numbers between 25 000 and 55 000 at three specific locations behind the orifice plate. Moreover, we apply proper orthogonal decomposition (POD), stochastic estimation and spectral analysis to study the properties of the flow field and the wall mass transfer rate. More importantly, we investigate the large-scale coherent structures’ effects on the wall mass transfer rate. The collapse of the wall mass transfer rates’ spectra by the corresponding time scales at the three specific positions of orifice flow suggest that the physics of low-frequency wall mass transfer rates are probably the same, although the flow fields away from the wall are quite different. Furthermore, the spectra of the velocity reconstructed by the most energetic eigenmodes agree well with the wall mass transfer rate in the low-frequency region, suggesting that the first several energetic eigenmodes capture the flow dynamics relevant to the low-frequency variation of the wall mass transfer. Stochastic estimation results of the velocity field associated with large wall mass transfer rate at all three specific locations further reveal that the most energetic coherent structures are correlated with the wall mass transfer rate.

Incidences of aligned magnetic field on unsteady MHD flow past a parabolic accelerated inclined plate in a porous medium

AbstractAn exact analysis of a radiative hydromagnetic flow behavior over a tilted parabolic plate through a permeable medium along with variable species concentration and fluid temperature in the presence of a slanted magnetic field parameter, chemical reaction, and heat generation has been carried out in this study. Closed‐form analytical benchmark solutions for flow‐governing equations are obtained by using the Laplace transform method. Thereafter, the incidences of different important physical entities on the nondimensional velocity field, temperature distribution, and species concentration are presented using graphs, whereas impacts of various physical entities on wall shear stress, heat and mass transfer rates are presented in tables. It is worth noting that an increase in the magnetic field and its inclination angle causes the reduction in the fluid velocity. However, wall shear stress increases with the increase of magnetic field and its inclination angle. The novel results in this article can be used to improve quicker cooling and producing miniaturized heat flow systems with upgraded efficiency and cost‐effectiveness.

Analytical study of heat and mass transfer in MHD flow of chemically reactive and thermally radiative Casson nanofluid over an inclined stretching cylinder

The main purpose of this study is to give a mathematical analysis of heat and mass transfer in a boundary layer flow of Casson fluid over an inclined stretching cylinder in the presence of magnetic nanoparticles. The effects of Casson parameter, curvature of the cylinder, angle of inclination, Buoyancy force, external magnetic field, thermal radiation, Joule heating, viscous dissipation, heat source and chemical reaction are taken into account. Appropriate transformations are incorporated to convert the governing partial differential equations and the boundary conditions suitable for computation. The elegant optimal homotopy analysis method is used to obtain analytic approximations for the resulting system of nonlinear differential equations. The features of flow characteristics such as velocity, temperature and concentration profiles in response to the variations of the emerging parameters are simulated and examined in detail. Extensive analysis is also made to explore the influences of relevant constraints on the rates of momentum, heat and mass transfer near the surface of the cylinder. Among the many outputs of the study, it is found that increasing the non-Newtonian Casson parameter can slowdown the flow velocity and enhance the temperature and concentration profiles. It is also revealed that significant enhancement of wall friction and mass transfer rate can be achieved by increasing the curvature of the cylinder. Further, the analytic approximations obtained by implementing the optimal homotopy analysis method to the present model are in close agreements with previous studies under common assumptions.

Effects of viscous dissipation and chemical reaction on MHD squeezing flow of Casson nanofluid between parallel plates in a porous medium with slip boundary condition

The present numerical study investigates magnetohydrodynamic squeezing flow of Casson nanofluid embedded in a porous medium with velocity slip under the influence of viscous dissipation and chemical reaction. Buongiorno’s nanofluid model is considered in this study. Suitable similarity transformations are used to convert the governing nonlinear partial differential equations into the system of nonlinear ordinary differential equations. Then, the equations are solved using an implicit finite difference scheme known as Keller-box method. The present method is validated by comparing the numerical results of skin friction coefficient, Nusselt and Sherwood numbers with previous published results and found to be in good agreement. Graphical results for velocity, temperature and nanoparticles concentration as well as wall shear stress, heat and mass transfer rate are examined with pertinent parameters. Findings reveal that fluid velocity and wall shear stress increase when the plates move closer. Also, increment of Casson and Hartmann number reduce the fluid velocity, temperature and nanoparticles concentration. The presence of viscous dissipation and thermophoresis enhance the fluid temperature and the convective heat transfer rate. Moreover, the rate of convective mass transfer decrease when Brownian motions of nanoparticles occurs, while it rises with increase in chemical reaction and thermophoresis.

Darcy-Forchheimer relation in Casson type MHD nanofluid flow over non-linear stretching surface

Present article aims to discuss the characteristics of Casson type nanofluid maintained to flow through porous medium over non-linear stretching surface in the perspective of heat and mass transfer developments. A Casson type incompressible viscous nanofluid passes through the given porous medium via Darcy-Forchheimer relation. Slip boundary conditions are used for velocity, temperature and concentration of the nanoparticles. Brownian diffusion and thermophoresis is attended. An induced magnetic field effect is involved to accentuate the thermo-physical characteristics of the nanofluid. The model incorporates boundary layer formulations and small magnetic Reynolds for practical validity. A fourth order Runge-Kutta (RK) scheme is enforced to solve the system numerically. Graphs are prepared for various progressive values of non-dimensionalized parameters whereas; variation in wall drag factor, heat and mass transfer rates is analyzed through numerical data. Results indicate that momentum boundary layer reduces for stronger inertial impact and the resistance offered by the porous media to the fluid flow. Temperature is found as a progressive function for the Brownian motion factor and thermophoresis. The magnitude of wall drag factor, heat transfer and mass transfer rates shows reduction for progressive values of slip parameters.

Similarity solution of MHD slip with energy mass transport through chemically reacting stretching permeable surface in porous media with variable properties

In this paper, a mathematical model is presented for magnetohydrodynamic viscous incompressible boundary layer flow of an electrically conducting chemically reacting fluid over a moving permeable flat vertical surface in a porous medium with variable fluid properties. A linear momentum slip boundary condition is included. Temperature and concentration difference between the wall and the environment are assumed to vary with the axial distance according to power law forms. Furthermore, a concentration-dependent mass diffusivity is featured to provide for a more realistic simulation of relevance to materials processing systems. The governing equations with associated boundary conditions are transformed into similarity equations using appropriate variables furnished with Lie group algebraic methods. The resulting nonlinear differential ordinary boundary value problem is then solved numerically with a Runge–Kutta–Fehlberg fourth–fifth order numerical method. The effects of the governing parameters on the boundary layer flow characteristics (velocity, temperature, concentration, wall shear stress, heat and mass transfer rates) have been investigated, displayed graphically and discussed. The computations indicate that variable mass diffusivity plays a significant role on transport characteristics. It is also shown that concentration magnitudes increase whereas the rate of mass transfer at the wall decreases with increasing mass diffusivity. Comparison of numerical and analytical results with results from the open literature show excellent agreement. Further verification of the general model is conducted with the Spectral Relaxation Method (SRM). The study is relevant to electroconductive polymeric sheet processing in manufacturing operations and smart coating systems.

Unsteady MHD Flow of Cassonnano Fluid with Chemical Reaction, Thermal Radiation and Heat Generation/Absorption

The hydromagnetic mixed convection flow of Cassonnano fluid under the influence of chemical reaction,thermal radiation and heat generation or absorption is investigated. The flow is induced due to unsteady nonlinearly stretching sheet saturated in a porous medium. The governing nonlinear coupled partial differential equations are converted into the system of coupled ordinary differential equations using similarity transformations and then solved numerically via Keller box method. The effects of pertinent parameters on velocity, temperature and nanoparticles concentration as well as wall shear stress, heat and mass transfer rate are analyzed and displayed graphically. The results for skin friction coefficient and local Nusselt number are compared with previously published work and found to be in good agreement. Findings demonstrate that increase in Casson parameter enhanced the friction factor and heat transfer rate. It is noticed that the heat transfer rate is declined with increment in Brownian motion and thermophoresis parameters. The nanoparticles concentration is seen to be higherin generative chemical reaction and opposite effect is observed in destructive chemical reaction. Increase in unsteadiness parameter decreased the fluid velocity, temperature and nanoparticles concentration. The magnitude of wall shear stress is also reduced with increase in unsteadiness and porous medium parameters.

Entropy Analysis on Unsteady MHD Flow of Casson Nanofluid over a Stretching Vertical Plate with Thermal Radiation Effect

This article proposes to study the entropy analysis on an unsteady magnetohydrodynamic flow of Casson nanofluid and convective heat transfer over a time dependent stretching vertical plate. We have treated Buongiorno’s model to characterize the thermophysical properties of nanofluid. The effect of thermal radiation and viscous dissipation of energy for non-Newtonian nanofluid and the external magnetic field are examined. The set of partial differential equations for time dependent flow of nanofluid are reduced to a system of coupled ODEs by a suitable similarity transformation. These reduced equations are solved by employing the fourth order Runge–Kutta-Fehlberg method along with shooting technique. The flow behavior of non-Newtonian Casson nanofluid, heat transfer characteristics, nanoparticle concentration profiles and entropy analysis have been made to understand the impact of different dimensionless parameters. Furthermore, the expression for dimensionless wall shear stress, heat and mass transfer rate over a heated vertical plate have been investigated. The study shows that entropy generation sharply increases with Casson parameter, whereas it increases near the plate with the thermal radiation. The entropy generation measuring through Bejan number has significant impact in aeronautics propulsion and power engineering to predict the efficient performance of the entire system.

Transport phenomena in MHD mixed convective nanofluid flow

Purpose This study aims to investigate the unsteady magnetohydrodynamic mixed convective nanofluid flow by using Buongiorno two-phase model to achieve an appropriate mechanism to improve the efficiency of solar energy systems by mitigating the energy losses. Design/methodology/approach The transport phenomena occurring in this physical problem are modelled using nonlinear partial differential equations and are non-dimensionalised by using non-similar transformations. The quasilinearisation technique is used to solve the resulting system with the help of a finite difference scheme. Findings The study reveals that the effect of the applied transverse magnetic parameter is to increase the temperature profile and to reduce the wall heat transfer rate. The Brownian diffusion and thermophoresis parameters that characterise the nanofluids contribute to the reduction in wall heat transfer rate. The presence of nanoparticles in the fluid gives rise to critical values for the thermophoresis parameter describing the behaviour of the wall heat and mass transfer rates. Wall heating and cooling are analysed by considering the percentage increase or percentage decrease in the heat and mass transfer rates in the presence of nanoparticles in the fluid. Research limitations/implications The investigation on wall cooling/heating leads to the analysis of control parameters applicable to the industrial design of thermal systems for energy storage, energy harvesting and cooling applications. Practical implications The analysis of the control parameters is of practical value to the solar industry. Social implications In countries, such as South Africa, daily power cuts are a reality. Any research into improving the quality of energy obtained from alternate sources is a national necessity. Originality/value From the literature survey in the present study, it is found that no similar work has been reported in the open literature that analyses the time-dependent mixed convection flow along the exponentially stretching surface in the presence of the effects of a magnetic field, nanoparticles and non-similar solutions.

Natural nonlinear convection of dusty fluid in a suspension of multi-wall carbon nanotubes nanoparticles with different temperature of water and suction

This study addresses the nonlinear free convective flow of a conducting dusty nanofluid (multi wall carbon nanotubes + water + micrometer sized dust particles) over a stretched cylinder at different temperatures (10 °C and 50 °C) in the presence of Cattaneo–Christov heat flux, heat source. The mainly arising equations of motion such as continuity, momentum and energy are simplified with the suitable dimensionless variables and solved numerically using the Runge–Kutta method. A numerical simulation is executed with inclusion of multi-wall carbon nanoparticles and dust particles into different temperatures (10 °C and 50 °C) of base fluid water. Calculations for the wall friction coefficient and Nusselt number are carried out and demonstrated in tables. To authenticate the attained results we have offered the comparison with the already published results. A few graphical pictures are plotted to scrutinize the physical insight of the numerically modeled problem for the several flow parameters and found that the multi-walled carbon nanotubes + water at 10 °C dusty nanofluid shows better heat and mass transfer rate compared to temperature at 50 °C. Due to nonlinear convection the friction factor is reduced in the presence of the magnetic field. The Biot number encourages the wall friction, heat and mass transfer rates of both cases.

Effects of surface roughness on mixed convection nanoliquid flow over slender cylinder with liquid hydrogen diffusion

The influence of surface roughness on boundary layer flow characteristics over moving surfaces is of considerable research interest in recent times. In the present study, the effects of surface roughness on flow over moving slender cylinder are analyzed in presence of mixed convection nanoliquid boundary layer flow. The problem is modelled in terms of highly nonlinear dimensional partial differential equations, which are written in non-dimensional form with the help of non-similar transformations. The resulting equations are reduced to linear partial differential equations by utilizing Quasilinearization technique, which are discretized using implicit finite difference scheme. The results obtained during the numerical simulation are then depicted through graphs in terms of various profiles and gradients and are analyzed with proper physical explanations. The roughness of slender cylinder surface is represented in a deterministic model as a sine wave form and yields sinusoidal variations in the values of skin-friction coefficient, wall heat and mass transfer rates. It is observed that the surface roughness effects are more prominent away from the orifice. The local frequency of gradients increases (i.e. wavelength decreases) with the increase in the frequency of surface roughness (n). The addition of nanoparticles into the ordinary fluid enhances the skin-friction coefficient and wall mass transfer rate. However, due to its effects, significant reduction is observed in the wall heat transfer rate. The phase difference of gradient oscillations arising in presence of nanoparticles is suppressed further away from the origin due to surface roughness. Interestingly, the amplitude of gradient oscillations remain higher in case of nanoliquid in comparison with that in case of ordinary fluid. Furthermore, the magnitude of wall mass transfer rate of liquid hydrogen is higher than that of nanoparticle wall mass transfer rate, which signifies the higher diffusivity of nanoparticles. The results of present study are of practical relevance to industrial applications such as polymer fibre coating and coating of wires.

Impact of Thermal Radiation on an Unsteady Casson Nanofluid Flow Over a Stretching Surface

This article employs the analytical approach to examine the heat and mass transfer characteristics on an unsteady flow of Casson nanofluid past an elongated surface with thermal radiation effect. A perturbation technique is adopted to solve the governing equations of the flow. Copper, Silver and Ferrous nanoparticles are suspended in water based nanofluid. Impacts of physical parameters like nanoparticle volume fraction, thermal radiation, magnetic field, stretching parameter, heat source/sink, a chemical reaction on velocity, thermal and concentration attributes along with wall friction, heat, and mass transfer rates are demonstrated with the aid of graphs and tables. Dual nature is witnessed for Newtonian and non-Newtonian fluid cases. Obtained results demonstrate the volumetric size, shape and conductive property of the nanoparticle play an important role in enriching the effectiveness of convection heat transfer of nanofluids. Also, Casson nanofluid has a tendency to reduce the velocity of the fluid due to its higher viscidness.

Non-similar Solutions of MHD Mixed Convection over an Exponentially Stretching Surface: Influence of Non-uniform Heat Source or Sink

In this paper, an analysis of magnetohydrodynamic (MHD) mixed convection over an exponentially stretching surface in the presence of a non-uniform heat source/sink and suction/injection is presented. The governing boundary layer equations are transformed into a set of non-dimensional equations by using a group of non-similar transformations. The resulting highly non-linear coupled partial differential equations are solved by using the implicit finite difference method in combination with the quasilinearization technique. Numerical results for the velocity, temperature and concentration profiles, as well as the skin friction coefficient, wall heat transfer and mass transfer rates are computed and presented graphically for various parameters. The results indicate that the velocity profile reduces, while the temperature profile increases in presence of the effects of magnetic field and suction at the wall. The velocity ratio parameter increases the skin-friction coefficient and the Schmidt number decreases the wall mass transfer rate. The temperature profile increases for the positive values of Eckert number and space as well as temperature dependent heat source/sink parameters, while the opposite behavior is observed for negative values of same parameters.

Influence of liquid hydrogen and nitrogen on MHD triple diffusive mixed convection nanoliquid flow in presence of surface roughness

An innovative study of influence of surface roughness and nanoparticles on mixed convection flow is considered in presence of liquid hydrogen and liquid nitrogen. In fact, in order to understand the effects of surface roughness and nanoparticles on the flow characteristics of MHD triple diffusive mixed convection nanoliquid flow along an exponentially stretching rough surface, the flow problem is modelled in terms of highly nonlinear partial differential equations subject to the appropriate boundary conditions. Then, those equations are made non-dimensional with the application of non-similar transformations. The resultant nonlinear dimensionless coupled partial differential equations with boundary constraints are solved by using the Quasilinearization technique in combination with the implicit finite difference scheme. The liquid hydrogen and liquid nitrogen are considered as species concentration components. The surface roughness is modelled by a sine wave representation and hence the sinusoidal variations have been observed in gradients such as skin-friction coefficient, heat and mass transfer rates. It is observed that the effects of surface roughness on the skin-friction coefficient are more prominent near the origin than that in downstream. The addition of nanoparticles into the ambient ordinary fluid enhances the skin-friction coefficient and reduces the magnitude of wall heat transfer rate for both cases of smooth and rough surfaces. The rapid variations have been observed in the wall mass transfer rate due to the surface roughness in comparison to that of skin-friction coefficient and wall heat transfer rate. Further, the magnitude of wall mass transfer rate of liquid nitrogen is higher than that of liquid hydrogen.

UCM flow across a melting surface in the presence of double stratification and cross-diffusion effects

Abstract In this article, we analyzed the upper convected Maxwell fluid (UCM) flow across a horizontal melting surface in the presence of cross-diffusion and double stratification (thermal and solutal) effects. We reconstructed the controlling equations as a group of nonlinear ordinary differential equations and then resolved by enforcing Runge-Kutta method with shooting technique. The influence of important parameters on the three common profiles (velocity, temperature, and concentration) is discussed through plots. Tables are utilized to discuss the wall friction, heat and mass transfer rates of both Newtonian and UCM flows. We witnessed that the thermal stratification, Soret number, Schmidt number and temperature dependent viscous parameter improve heat transfer rate. Setting the two flows side by side, it is worthy to mention that the temperature and concentration profiles looking high in the Newtonian fluid flow.