Mass Grashof Number Research Articles

Significance of heat transfer in a reversible esterification of Arrhenius activation energy with partial slip

The significance of heat transfer during a reversible esterification process in a magnetohydrodynamic boundary layer Casson fluid flow along a vertical stretching plate is examined. The multi-slip conditions are considered in a porous medium. The presence of chemical process requiring an activation energy is considered in the analysis. The study also investigates the hydromagnetic boundary layer Casson fluid flow alongwith partial slip conditions across a vertical stretching plate. The incorporation of multi-slip constraints in a porous medium, alongside magnetic fields and other parameters, highlights its relevance in diverse engineering fields such as thermal engineering, polymerization, and biodiesel industries. Understanding the characteristics of such fluids under complex conditions is vital for optimizing heat and mass transfer in industrial applications, making this investigation timely and valuable. The nonlinear differential set of equations are solved numerically involving Runge Kutta based shooting approach of fourth order and the results are verified with the bvp4c tool and the findings are explored using graphical plots. The predominance of significant factors on flow configurations are analyzed and presented in graphs and tables. A comprehensive analysis is provided on the effects on velocity, concentration, and temperature of diverse parameters such as reaction rate constant, magnetic parameter, suction parameter, mass Grashof number, Prandtl number, Casson parameter, thermal radiation parameter and slip parameters. The tabular representation of the adverse effects of drag coefficient, rate of mass transfer and Nusselt number on flow configurations for various significant parameters is presented. It is inferred that for the case of reversible and irreversible flows, the shear stress rate escalates by 29% when the magnetic parameter elevates from 0.5 to 1.5 and about 35% when the Casson parameter elevates from 0.5 to 1.5. For the suction parameter, the coefficient of drag increased by 27% and 26% for irreversible and reversible flows respectively. When the reaction rate increases from 0.5 to 1.5, the rate of shear stress elevates by 0.5% and 0.02% for irreversible and reversible flows in order. The Nusselt number decreased about 7% and 8% when the magnetic parameter and Casson parameter rises from 0.5 to 1.5 respectively, for irreversible and reversible flows. It is noteworthy that the previous studies are in precise agreement with the present investigation.

The results of a magnetic field on flow past an inclined isothermal vertical plate with heat and varying mass diffusion

This work describes the influence of a magnetic environment on the circulation of matter and thermal energy over an accelerating advanced inclined isothermal sectional surface. The temperature is elevated to . The proximity intensity is increased to . The Laplace-transform approach is applied to solve the dimensionless analytical equation. In this research work different physical variables including thermal grashof number (Tg), mass grashof number (Tm), Schmidt number (Sc), Prandtl number(Pr), time(t), velocity profile ( ), temperature ( ), and intensity ( ) are investigated. The output of the graph produced by the Matlab software commands an energy equation, momentum equation, and concentration equation. The values are shown in an aligned pattern for a variety of flow variables. Diagrammatic representations of the fluid velocity profiles are provided. The velocity rises corresponding to different Tg and the velocity rises corresponding to different Tm. As the angle is decreased, the velocity increases differently. , As the different magnetic environment values lower, the velocity rises. Elevated values of angle ( ), Sc, Pr, and contribute to an enhancement in local skin friction, and an upsurge in Gr, Gc, and t leads to a reduction. A tabulated presentation of Nusselt quantities reveals a positive correlation with increasing Pr. Similarly, Sherwood quantities, as tabulated for various parameters, demonstrate a proportional increase with rising Sc.

Analysis of fractionalized Brinkman flow in the presence of diffusion effect

A vertical plate experiences a dynamic flow of fractionalized Brinkman fluid governed by fluctuating magnetic forces. This study considers heat absorption and diffusion-thermo effects. The novelty of model is the fractionalized Fourier’s and Fick’s laws. The problem is solved using the constant proportional Caputo derivative and Laplace transform method. The resulting non-dimensional equations for temperature, mass, and velocity fields are solved and compared visually. We explore the influence of various parameters like the fractional order, heat absorption/generation (Q), chemical reaction rate (R), and magnetic field strength (M) through informative graphs. Additionally, we contrast the velocity fields of fractionalized and regular fluids. The visualizations reveal that diffusion-thermo and mass Grashof number enhance fluid velocity, while chemical reaction and magnetic field tend to suppress it. For the interest of engineering, physical quantities such as Sherwood number, skin friction, and Nusselt number are computed. The present study satisfying all initial and boundary condition can be reduced to to previous published work which shows the validity of present work.

Unsteady MHD flow past an oscillating vertical plate with periodic temperature variation and exponential mass diffusion embedded in a porous medium with thermal and mass stratification effects

AbstractThe present study investigates the impacts of both mass and thermal stratification on unsteady magnetohydrodynamic flow past a plate swinging vertically on its own axis while entangled in a porous medium with periodic temperature variation and exponential mass diffusion. The technique of Laplace transform for the unitary Prandtl and Schmidt numbers is employed to obtain the closed‐form solution for the nondimensional system of partial differential equations that govern the system for velocity, temperature, and concentration fields. For various physical factors, such as stratification parameters, phase angle, thermal Grashof number, Darcy number, mass Grashof number, and time on velocity, temperature, concentration, skin‐friction, plate heat flux, and mass flux, numerical computations have been performed, and illustrated in graphs. It has been observed that the steady state is attained more swiftly when stratification is applied to the flow. The desire to enhance the knowledge of fluid flow in many technological as well as environmental circumstances, where such conditions are widely used could be the driving force behind this research. Significant results from the thermal and mass stratification are contrasted with the environment where stratification is absent. Understanding flow mechanisms in both naturally occurring and artificially created environments can be enriched by this innovative method.

Heat and mass transfer effects on an unsteady MHD boundary layer flow of fractionalized fluid

This research investigates the transient magnetohydrodynamic (MHD) flow of a non-integer Maxwell fluid over a vertical plate, taking into account the effect of diffusion-thermo and parameter of heat absorption. The fractional derivative Caputo-Fabrizio is employed to model the problem. Using the Laplace integral transform technique, we solve the dimensionless governing equations to obtain the profiles of velocity, concentration, and temperature, which are then presented in graphical form for easy comparison and interpretation. The influence of several parameters—specifically, the fractional parameter and heat absorption is thoroughly analyzed and illustrated through a series of graphical representations. Furthermore, a comparison between traditional as well as fractionalized velocity fields is provided. The results show that chemical reactions and magnetic fields reduce the velocity profile, while diffusion-thermo and mass Grashof number increase the fluid velocity.

Effects of Thermal and Mass Stratification on Unsteady MHD Flow Past an Oscillating Vertical Plate Embedded in a Porous Medium with Variable Surface Conditions

oscillating vertically in its own axis in which it is embedded in a porous medium with variable heat and mass diffusion. For concentration, temperature and velocity fields, the non-dimensional governing equations are solved using the Laplace transform method for the unitary Prandtl and Schmidt numbers, when the plate is oscillating in its own plane harmonically. Numerical computations are carried out and presented in graphs for different physical parameters like thermal Grashof number, phase angle, mass Grashof number, stratificationparameter and time on concentration, velocity, temperature, plate heat flux, mass flux and skin friction. The findings of this study can be utilized to enhance comprehension of MHD flow on vertical oscillating plate in combined stratified environments. Significant findings arising from the mass and thermal stratification are compared to the scenario in which stratification is absent.

Fractional analysis of unsteady magnetohydrodynamics Jeffrey flow over an infinite vertical plate in the presence of Hall current

The impact of Hall current on the multiphase thermal transfer of an incompressible electrically conductive Jeffrey flow over an infinitely vertical plate when heat absorption and chemical reaction are present has been examined. Partial differential equations have been used to describe the process, accounting for heat and mass transfer effects. This study uses extended Fourier's and Fick's laws together with the recently announced constant proportional Caputo (CPC) fractional operator. The fractional model is converted into a nondimensional form by applying some appropriate quantities. The nondimensional produced fractional model for momentum, heat, and diffusion equations based on the CPC fractional operator has been calculated semi‐analytically by applying the Laplace method. The Mathcad 15 software to sketch the graphs for several factors, like the Grashof number, mass Grashof number, Schmidt number, Prandtl number, Hall, and magnetic field parameters, is used to describe the velocity profile. Additionally, a graphical explanation is provided for the influence of the appeared parameters, particularly the effect of the fractional parameters. It is concluded that the result of the fluid model developed by the generalized constitutive relations is more accurate and generalized than the results of the artificially contracted fractional model. A fractional derivative is therefore the ideal option to achieve controlled concentration, temperature, and velocity. The current study is immediately relevant to geophysical, cosmically fluid dynamics, medical, biological, and any other processes that are significantly enhanced by a low gas density and a high magnetic field.

Rotation and Dufour Impact on Unsteady Flow Past a Parabolic Accelerated Vertical Plate with Uniform Temperature and Mass Diffusion

Objective : Fluid dynamics and heat transfer theory examine the Dufour phenomenon and the rotational influence of unstable parabolic flow across an accelerating infinite vertical plate. This scenario involves several parameters, including the "mass Grashof number (Gr), thermal Grashof number (Gc), Prandtl number (Pr), Hartmann number (Ha), Schmidt number (Sc), Dufour number (Dc), and acceleration parameter". Method : We have applied the Laplace transform method to the resulting PDE. This method converts the equations to algebraic form, making it easier to solve for velocity, temperature, and concentration in terms of time and space. Graphs can show the relationship between the acceleration parameter and numerous parameters such as mass and thermal Grashof, Hartmann (Ha), and Dufour (Df), as well as the consequent velocity profile. If the velocity increases when these variables change, we'll look at the physical reasons that generate this behaviour. We will examine the conclusions using experimental data or existing theoretical models, considering the model's assumptions and limits. Finally, highlight the significant facts and insights gained from the analysis. We will discuss potential future research possibilities, such as exploring more complex geometries or accounting for new physical effects. Findings : The increase in Dufour parameter value causes an increase in temperature and level trends, demonstrating the significant influence of these factors on the researched phenomena. Novelty: This research advances our understanding of heat and mass transfer phenomena by isolating the Dufour effect in a novel scenario involving unsteady flow around a rotating vertical plate, filling a gap in the existing body of knowledge that is dominated by MHD-inclusive investigations. Suggestions: This approach is fairly general and may be applied to find analysis of heat and mass transfer on Dufour effect for other effects such as Soret effect, Hall current of heat and mass transfer. Keywords: Uniform Temperature, Thermo diffusion (Dufour), Inverse Laplace, Rotational, Constant Mass

Effects of chemical reactions in the presence of temperature variations and isothermal mass diffusion over an inclined plate

A detailed study of the erratic circulation around an unbounded inclined plate under fluctuating temperature and isothermal mass dispersion was carried out with a chemical reaction. This work concentrated on the harmonic inclination of the plate in its plane, and the accurate solution of the non-dimensional governing formulations was made possible by the Laplace transform technique. To evaluate their impact on different profiles, the investigation examined a variety of physical factors, including phase inclination, chemical response variable, Schmidt number, thermal Grashof number, mass Grashof number, and duration. Notably, the speed per second increased with decreasing phase angle. Furthermore, a decrease in either the thermal radiation variable or the chemical response variable induced an increase in velocity.

Theoretical investigation of thermal and mass stratification effects on unsteady flow across a vertical oscillating plate with periodic temperature variation and variable mass diffusion

AbstractThis research paper examines the combined effects of thermal and mass stratification on unsteady flow past a vertical oscillating plate with periodic temperature variation and variable mass diffusion. The Laplace transform technique is introduced to deal with the linear coupled parabolic equations satisfying initial as well as boundary conditions and obtained solutions in closed form for concentration, temperature, and velocity. For example, to find the Laplace transform of an exponentially ordered piece wise continuous function , one can uses the formula , t being the time and s is a parameter. In this study, we explore the effects of different factors such as plate amplitude, plate frequency, thermal Grashof number, and the mass Grashof number on the concentration, velocity, and temperature profiles and shows them graphically. We see a decline in the fluid's velocity for thermal and mass stratification. Most interestingly, in presence of higher temperature gradient, as the frequency of the oscillations increases close to the plate surface, the fluid velocity declines. The reason behind this is that the flow system has a plate with very high fluctuations. We have found that the fluid's temperature goes up while the concentration goes down when there is a decrease in the thermal stratification and a rise in the mass stratification.

Magneto Hydrodynamic Effects on Unsteady Free Convection Casson Fluid Flow Past on Parabolic Accelerated Vertical Plate with Thermal Diffusion

The free convection MHD flow of a viscous, chemically reactive, electrically conducted, incompressible, and Casson fluid past a parabolically accelerated vertical plate was examined in the present article along with the transfer of the heat & mass in the incidence of thermal radiation. The inverse Laplace method is used to resolve the dimensionless equations. The concentration and temperature fields, axial and transverse velocity are examined for distinct parameters like the (Casson fluid), Sc (Schmidt number), Gr (thermal Grashof number), Pr (Prandtl number), and Gm (mass Grashof number). Utilizing the temperature of fluid and concentration of species as a solution is also proposed. Graphical representations of the fluctuations in temperature of fluid and velocity along species concentration are provided for several values of relevant flow parameters.

Entropy generation analysis for magnetohydrodynamic flow of chemically reactive fluid due to an accelerated plate

BackgroundThe mixed convection flow of viscous fluid due to an oscillating plate is inspected. The external heating effects and chemical reaction assessment are predicted. Moreover, the flow applications of the entropy generation phenomenon are claimed.ResultsThe dimensionless system is expressed in partial differential forms, which are analytically treated with the Laplace scheme. The physical aspects of the flow model are graphically observed. The optimized phenomenon is focused on flow parameters. The results for the Bejan number are also presented. The dynamic of heat transfer and entropy generation phenomenon is observed with applications of Bejan number.ConclusionsIt is claimed that an enhancement of entropy generation phenomenon is noticed due to heat and mass Grashof coefficients. The Bejan number declined due to mass Grashof number. Furthermore, the velocity profile boosted due to Grashof constant.

Investigation of Melting Heat Transfer in Viscous Nanofluid Flow Including Micro-Organisms and Entropy Generation Due to an Inclined Exponentially Stretching Sheet

This study investigates melting heat transfer and entropy production in viscous nanofluid flow consisting of micro-organisms over an inclined exponentially stretching permeable sheet. The flow is considered via porous medium. Impacts of heat transport characteristics are invoked in the energy equation. In concentration equation we have included chemical reaction impact. The regulating PDEs are transformed into nonlinear ODEs in non-dimensional form using adequate similarity transformation relations. The analytical solution of the problem is obtained utilizing HAM. Various plots are drawn to exhibit impacts of the regulating parameters (Prandtl number, Porous medium parameter, Thermal Grashof number, Mass Grashof number, Micro-organism Grashof number, Thermophoresis parameter, Radiation parameter, Bio-convection Levis number, Brownian motion parameter, Chemical reaction parameter, Suction parameter, Peclet number, and Melting parameter) occurred in the problem on relevant fields (flow, temperature and concentration distribution) and entropy production and discussed. Further values of significant physical quantities skin friction coefficient, Nusselt number, Sherwood number, and motile microbes density computed using MATLAB based bvp4c function and HAM are displayed in tabular mode and found in excellent agreement. For validity of the results skin friction coefficient and Nusselt number values are compared to prior research, apparently good agreement is found. The effect of melting surface parameter is found to reduce the fluid flow and temperature field. Entropy production lessens with rising values of slip parameters but effects of radiation and porous medium parameters are found to upsurge it. It is also noticed that bioconvection Lewis number and Peclet number reduce the micro-organism density profile. Inclusion of entropy analysis is a novel feature of the study. The solution methodology also enriched the novelty of the investigation. The results of the study may be applied to improve the efficiency of thermal, fluid flow and energy systems. This study may also find applications in bio-nano-coolant systems and heat transfer devices.

¬¬Chemical Reaction and Nonlinear Rosseland Approximation Effects On Double-Diffusive MHD Sisko Nanofluid Flow Over a Nonlinear Stretching Sheet in A Porous Medium with Concentration-Dependent Internal Heat Source

This study investigates the two-dimensional magnetohydrodynamics laminar flow of a Sisko nanofluid over a nonlinear stretching sheet in a porous medium, considering chemical reactions, nonlinear Rosseland approximation, and an internal heat source based on concentration. The governing boundary layer equations and associated boundary conditions are transformed into non-dimensional form using appropriate variables. The resulting non-dimensional equations are solved using the modified Adomian decomposition technique, implemented with the symbolic computing software MATHEMATICA. The influence of various parameters, including Prandtl number, thermophoresis parameter, Brownian motion parameter, chemical reaction parameter, Sisko fluid parameters, heat source parameter, radiation parameter, Darcy number, mass Grashof number, magnetic field, and Grashof number, on the flow fields of velocity, temperature, and nanoparticles volume fractions is depicted through graphical representations. The study reveals that the velocity profile is accelerated by the first value of the Sisko fluid parameter and Darcy number, but it diminishes in the presence of a magnetic field and the second Sisko fluid parameter. The temperature profile decreases with an increment in the Prandtl number, while it improves in proportion to increases in the heat source, thermophoresis, Brownian motion, and radiation parameters respectively. Additionally, an increase in the chemical reaction parameter leads to an increase in the concentration profile of the fluid.

Chemical process effects on sloped surface with changing mass and consistent temperature

The research extensively investigated the turbulent flow patterns surrounding an unbounded inclined plate under the conditions of uniform temperature and variable mass dispersion. Throughout this analysis, the study thoroughly considered the impact of chemical reactions within the system. Focusing on the harmonic inclination of the plate within its plane, the study employed the LT approach to accurately solve the non-dimensional governing equations. In scrutinizing various profiles, the investigation examined the impact of several crucial physical factors: chemical response variable, Schmidt number, thermal Grashof number, mass Grashof number, and duration. This study delves into the intricate influence of various factors on the complex flow dynamics surrounding inclined plates, specifically focusing on heat and mass transfer phenomena. By examining these relationships, the research provides crucial insights into improving the efficiency of thermal and mass transmission processes within systems that incorporate tilted surfaces. Moreover, this knowledge can potentially contribute to advancements in various fields, from renewable energy systems to manufacturing processes, where heat and mass transfer play pivotal roles.

MHD nonlinear natural convection from a uniformly moving porous vertical plate with constant heat and mass flux in the presence of thermal radiation, diffusion‐thermo, heat sink, and chemical reaction

AbstractAn attempt has been made to investigate the problem of nonlinear free convection heat and mass transfer flow past an infinite vertical porous plate embedded in a porous medium by taking into account thermal radiation and heat sink with constant heat and mass flux. Transversely oriented and of uniform strength , a magnetic field has been introduced to the fluid area. The nonlinear density variation with temperature as well as concentration are the basis for the current physical situation, which is explained by this mathematical model. Exact solutions are derived for momentum equation, energy equation, and species continuity equation under the relevant boundary conditions. The dimensionless governing equations are analytically solved. The influence of various physical parameters, such as Dufour number, Schmidt number, thermal Grashof number, magnetic parameter, mass Grashof number, heat sink, thermal radiation, Prandtl number, chemical reaction parameter on the flow, and transport characteristic, has been presented graphically and in tabular form. The novelty of the present investigation is that here both constant heat and mass flux at the plate are taken into account in addition to thermal radiation and heat sink. The findings of the mathematical study demonstrate that velocity, temperature, and skin friction intensify with a rise in the Dufour number this is due to the fact that the convection current becomes stronger as the Dufour number rises. Fluid's concentration declines as the Schmidt number grows, or the concentration rises as the mass diffusivity rises. Fluid temperature is enhanced with high thermal diffusivity. Frictional resistance on the plate hikes due to thermal buoyancy force.

Effect of radiation absorption and chemical reaction on MHD‐free convective flow through a porous medium past an infinite vertical porous plate in the presence of constant heat flux

AbstractAn incompressible, electrically conducting, and viscous fluid flowing steadily and freely across a uniformly porous media that is partially constrained by an infinitely long vertical porous plate is studied in the present article. Additionally, chemical reaction and radiation absorption effects are seen. Here, a magnetic field of uniform strength is applied transversely to the plate, a normal suction velocity is imposed on the fluid, and the heat flux is considered to be constant. The non‐dimensional momentum and energy equations are solved using the method of perturbation. The problem has been analytically resolved, and several parameters, including the Hartmann number, porosity parameter, thermal Grashof number, mass Grashof number, and transport properties like the Sherwood number, skin friction, and plate temperature, are graphically represented. The current study reveals a spike in the radiation absorption effect causes skin friction to drop, but on the other hand, a contrary effect is observed for plate temperature. One of the notable findings of this investigation is that the Sherwood number increases as chemical reaction parameter influence increases.

Heat and mass transfer through a vertical channel for the Brinkman fluid using Prabhakar fractional derivative

In industrial and manufacturing processes like printing, coating, and painting, non-Newtonian fluid flow plays an significant role. The primary focus of the current study is to develop and advance a flow model of Brinkman flow through a channel of two parallel vertical plates. The generalization of the constitutive relations for mass and heat fluxes is done by utilizing the advanced and more generalized definition of the Prabhakar operator. The Prabhakar operator involved the 3 parameters of Mittag-Leffler mapping as a kernel of an operator, therefore, this derivative is a more general and advanced fractional derivative as compared to the other fractional derivatives. The governing equations for this flow model can be calculated by coupling the foresaid generalized constitutive relations for heat and mass fluxes. Furthermore, to have better and deeper knowledge about the behavior of flow, the developed governing equations are transformed to dimensionless form by introducing suitable relations for the involved variables. We are interested in getting the exact result for the temperature, concentration, and velocity of the flow. To achieve this goal, the Laplace transform is utilized to prescribe partial differential governing equations for temperature, velocity, and concentration. The inverse of the Laplace transform is done applying Stehfest’s and Tzou’s algorithm to transform governing equations for temperature, velocity, and concentration. The inversion results that are obtained by Stehfest’s and Tzou’s algorithm are presented in graphical form. Further, the parametric analysis of the research outcomes is also explained graphically. For this purpose, the field variables, namely temperature, velocity, and concentration, are also plotted in some graphs. From the parametric study, it is concluded that by raising the values of the fractional parameter, velocity increases, while simultaneously a decreasing trend is seen for concentration and temperature for a short time. The effects of many variables, including fraction parameters, mass Grashof number, Grashof number, Prandtl number, Schmidt number, Brinkman parameters, and magnetic field, on concentration, temperature, and velocity are depicted graphically.

Effect of Jeffrey Fluid Flow and First Order Chemical Reaction on Magneto Convection of Immiscible Fluids in a Perpendicular Passage

In this article describes the effects of transfer heat and mass on free convective flow of developed fully electrically conducting with electrically Non-conducting immiscible fluids towards a perpendicular parallel passage. The resulting nonlinear governing coupled equations describes the fluid behaviour for velocity and temperature distributions are analysed and by applying method regular perturbation the differential equations are analytically solved with appropriate boundary and interface conditions for each fluid. Furthermore, the jump conditions for velocity and temperature are implemented on the left and right walls in the magnetic field existence in a perpendicular passage. The solutions are revealed through graphs for major parameters like thermal Grashof number, mass Grashof number, ratio of viscosity, width and conductivity, pressure gradient, Jeffrey parameter and chemical reaction parameter.

Soret and Dufour Effects on Chemically Reacting and Viscous Dissipating Nanofluid Flowing Past a Moving Porous Plate in the Presence of a Heat Source/Sink

Abstract This study performed a numerical investigation of the Soret and Dufour effects on unsteady free convective chemically reacting nanofluid flowing past a vertically moving porous plate in the presence of viscous dissipation and a heat source/sink. The equations directing the flow are non-dimensionalised, modified to ordinary differential equations and emerging equations are resolved computationally by using the bvp4c function in MATLAB software. The results obtained from this analysis indicate that the resulting velocity of the nanofluid increases with increasing Grashof number, mass Grashof number and porosity parameter. An increase in the Dufour number increases the fluid temperature, whereas the concentration profile declines with the increase in the Schmidt number. It is also observed that the skin friction coefficient, Nusselt number and Sherwood number increase with increasing magnetic field parameter, Eckert number and Schmidt number, respectively. The present study reveals the impact of Soret and Dufour effects on heat and mass transfer rates in chemically reacting and viscous dissipating nanofluids.