Flow Of Second Grade Fluid Research Articles

Artificial boundary method for the fractional second-grade fluid flow on a semi-infinite plate with the effects of magnetic field and a power-law viscosity

As a typical representative of viscoelastic fluids, second-grade fluids have many applications, such as paints, food products, and cosmetics. In this paper, the equation for describing the fractional second-grade fluid with the power-law viscosity on a semi-infinite plate under the influence of a magnetic field is studied. The numerical solution is obtained using the finite difference method. To handle the semi-unbounded region, the (inverse) z-transform is applied to establish the absorbing boundary condition (ABC) for the solution at the cut-off point. In addition, the numerical example analyzes the superiority of the ABC over the directly truncated boundary condition and the effects of different parameters on the velocity distribution. The conclusion is that the slip parameter, power-law exponent parameter, and power-law index parameter promote the fluid flow, while the magnetic field and fractional parameter hinder the fluid flow.

Comparison of unsteady MHD flow of second grade fluid by two fractional derivatives

A study is conducted on the unsteady motion of a free convective flow of second grade fluid, energy transfer, and Darcy’s law over an oscillatory smooth vertical plate. The study compares two different approaches in developing a fractional model: the Caputo-Fabrizio operator with nonsingular kernel and the constant proportional Caputo fractional operator with Fourier’s and Fick’s laws. By applying the Laplace method and transforming the provided set of equations into nondimensional form, we obtained semi-analytical results and presented these results through graphical analysis. The study examines how different flow parameters, including the fractional parameters, affect the velocity, mass, and heat profiles of the physical system. The results suggest that the physical model using constant proportional Caputo derivative leads to higher temperature, stronger concentration, and increased velocity compared to the Caputo-Fabrizio model. This highlights the importance of selecting an appropriate fractional model when studying complex physical systems. It is also depicted from the whole analysis that field variables with novel hybrid fractional derivative constant proportional Caputo exhibits a more effective and declining tendency than Caputo-Fabrizio.

Comparative Analysis with Data Prediction of Non-linear Radiative Nano Second-Grade and Newtonian Fluid in Presence of Sinusoidal Magnetic Force

This study aims to enhance the comprehension of the fundamental fluid behavior by comparing Newtonian fluid with second-grade fluid under the influence of periodic magnetic fields, nonlinear radiative nanomaterial, and a porous stretched surface featuring a heat source. The governing equations' dimensionless forms are generated by applying the proper transformations, and the explicit finite difference (EFD) method is used to solve the numerically-derived solution while carefully maintaining stability and convergence standards. The results include velocity, heat, and mass transfer oscillation profiles; streamlines, and isothermal lines. Nusselt and Sherwood numbers are correlated with different factors according to tabular studies, and data prediction and regression are done using graphical representations. This study revealed that, in contrast to Newtonian fluid, second-grade fluid flow elevates velocity profiles with variations in chemical reaction parameters and mass Grashof numbers. Conversely, the thermal non-linear radiation and heat source in second-grade fluid particles effectively enhance the temperature field, although the temperature increase is more pronounced in Newtonian fluid compared to second-grade fluid. Also, second-grade fluid flow exhibits a lower mass transmission rate but higher stress sharing and heat transmission rates compared to Newtonian fluid flow. The implications of this research may impact prostate cancer treatment, as cancer patients have already benefited from the use of magnetic fields to regulate drug release from nanoparticles. Although the greater stress sharing and heat transmission rates may be used for targeted therapy, the lower mass transmission rate raises the possibility of benefits in controlled release scenarios.

Thermal radiation and MHD effect on the double-diffusive convective flow of second-grade fluid over a stretching sheet

Thermal radiation and MHD effect on the double-diffusive convective flow of second-grade fluid over a stretching sheet

Fractional Second-Grade Fluid Flow over a Semi-Infinite Plate by Constructing the Absorbing Boundary Condition

The modified second-grade fluid flow across a plate of semi-infinite extent, which is initiated by the plate’s movement, is considered herein. The relaxation parameters and fractional parameters are introduced to express the generalized constitutive relation. A convolution-based absorbing boundary condition (ABC) is developed based on the artificial boundary method (ABM), addressing issues related to the semi-infinite boundary. We adopt the finite difference method (FDM) for deriving the numerical solution by employing the L1 scheme to approximate the fractional derivative. To confirm the precision of this method, a source term is added to establish an exact solution for verification purposes. A comparative evaluation of the ABC versus the direct truncated boundary condition (DTBC) is conducted, with their effectiveness and soundness being visually scrutinized and assessed. This study investigates the impact of the motion of plates at different fluid flow velocities, focusing on the effects of dynamic elements influencing flow mechanisms and velocity. This research’s primary conclusion is that a higher fractional parameter correlates with the fluid flow. As relaxation parameters decrease, the delay effect intensifies and the fluid velocity decreases.

Unsteady slip flow of special second-grade fluid induced by Fe3O4 particles past a movable sheet with magnetic and nonlinear heat source/sink

PurposeFerrofluids are aqueous or non-aqueous solutions with colloidal particles of iron oxide nanoparticles with high magnetic characteristics. Their magnetic characteristics enable them to be controlled and manipulated when ferrofluids are exposed to magnetic fields. This study aims to inspect the features of unsteady stagnation point flow (SPF) and heat flux from the surface by incorporating ferromagnetic particles through a special kind of second-grade fluid (SGF) across a movable sheet with a nonlinear heat source/sink and magnetic field effect. The mass suction/injection and stretching/shrinking boundary conditions are also inspected to calculate the fine points of the features of multiple solutions.Design/methodology/approachThe leading equations that govern the ferrofluid flow are reduced to a group of ordinary differential equations by applying similarity variables. The converted equations are numerically solved through the bvp4c solver. Afterward, study and discussion are carried out to examine the different physical parameters of the characteristics of nanofluid flow and thermal properties.FindingsMultiple solutions are revealed to happen for situations of unsteadiness, shrinking as well as stretching sheets. Greater suction slows the separation of the boundary layers and causes the critical values to expand. The region where the multiple solutions appear is observed to expand with increasing values of the magnetic, non-Newtonian and suction parameters. Moreover, the fluid velocity significantly uplifts while the temperature declines due to the suction parameter.Originality/valueThe novelty of the work is to deliberate the impact of mass suction/injection on the unsteady SPF through the special second-grade ferrofluids across a movable sheet with an erratic heat source/sink. The confirmed results provide a very good consistency with the accepted papers. Previous studies have not yet fully explored the entire analysis of the proposed model.

Mass and heat transfer in the boundary layer region of modified second-grade fluid flow over a linearly stretched sheet embedded in porous media

Here, we have improved a model to describe the flow variables, velocity, mass and heat transfer in the boundary layer region of modified second-grade fluid flow over a linearly stretched sheet in a porous media. The modified model is used to study the qualitative impact of buoyancy parameter, second-grade fluid parameter, magnetic parameters, porous parameter, power-law index, and chemical reaction parameter on the flow profiles, radial and axial velocities, temperature, and concentration. Starting with the steady-state governing equations of mass, momentum, heat, and concentration of the fluid flow, we obtained the boundary layer approximations of the flow near the linearly stretched sheet with the no-slip boundary condition. Similarity transformation has been used to convert the partial differential equations system into a nonlinear ordinary differential equations system. The radial velocities, temperature, and concentration profiles have been solved numerically, and the qualitative influence of the flow parameters on the flow variables has been simulated and graphically presented for comparison. We have observed that radial and axial velocities were increasing for the shear-thinning and shearthickening fluids with solutal Grashof number, thermal Grashof number and second-grade fluid parameters. In contrast, the porous and chemical reaction parameters slow down both fluids’ radial and axial velocities. The temperature and concentration increase with the porous and magnetic parameters. However, thermal and solutal Grashof and second-grade fluid parameters suppress temperature and concentration. In shear-thickening fluids, chemical reaction parameters enhance concentration but suppress in shear-thinning fluids.

Thermo-solutal convective conditions impact in dual stratified stagnation-point flow of second-grade (SG) fluid with chemical reaction

In various engineering and industrial utilizations, the heat-mass transportation concept has been rigorously witnessed, for illustration air conditioning of room, nuclear reactors cooling and abundant other realistic conditions. This scrutiny elaborates buoyancy-driven viscoelastic magnetized flow configured by stretched vertical surface. Heat-transfer effects are explored through Ohmic dissipations and radiation aspects. Chemical reaction characteristics are deliberated to address the mass-transfer effects. In addition, the stratification phenomenon together with Robin conditions is introduced. Mathematical systems are simplified under BLT (boundary-layer theory). Non-dimensional analysis is done by introducing similarity variables. Homotopic criteria is utilized to compute convergent solutions. Consequence of controlling variables emerging in non-dimensional problem is analyzed via pictorial and tabular illustrations. It is evident that temperature field together with heat transference rate are enlarged when radiation and thermal Biot parameters are augmented.

Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model

Abstract This research delves into dynamics of magnetohydrodynamic second-grade fluid flow influenced by the presence of gyrotactic microorganisms on a stretching sheet. The study takes into account various factors such as thermal radiation, chemical reactivity, and activation energy, all of which contribute to the complex behavior of fluid flow in this system. The interaction between the magnetic field and the fluid, combined with the biological aspect introduced by gyrotactic microorganisms, adds complexity to the overall analysis. The mathematical model is presented in the form of partial differential equations (PDE)s. Using the similarity variables, the modeled PDEs are transformed into ordinary differential equations. Homotopy analysis method is used for the solution of the modeled equations. After a detailed insight into this investigation, it is established that the velocity distribution declined for growth in magnetic factor and second-grade fluid parameter. The thermal characteristics are augmented for the greater values of radiation, thermophoretic and Brownian motion factors, while these profiles are weakened for upsurge in thermal relaxation time factor and Prandtl number. The concentration characteristics declined with the enhancement in Schmidt number, mass relaxation time, chemical reaction, and Brownian motion factors, while they amplified with enhancement in activation energy and thermophoresis factors. The microorganisms’ profiles are the declining functions of bioconvection Lewis and Peclet numbers. This study included a comparative analysis, which aligns closely with existing research, demonstrating a strong concordance with established findings.

Bioconvective flow analysis of non-Newtonian fluid over a porous curved stretching surface

The aim of current investigation is to explore the two-dimensional Darcy flow of second grade fluid with homogenous and heterogeneous reactions toward a porous curved stretching surface. The thermal features the bioconvective flow are observed with the impact of joule heating, nonlinear thermal radiation, and non-uniform heat source/sink. The thermal stratification conditions are imposed on the boundary of the surface with magnetic field which is normal to surface. Flow model momentum and energy equations are converted into the system of nonlinear ordinary differential equations with some appropriative transformation. These nonlinear equations are tackled numerically with the utilization of Bvp4c approach. The graphical and tabulated results are obtained and discussed thoroughly. It is noticed that for the larger Darcy-Forchheimer number F, porosity parameter [Formula: see text], and Hartman number M, the fluid velocity decreases, while curvature parameter [Formula: see text] exhibits the reverse trend on the velocity field. Further, increment in the fluid temperature is observed by the escalation of the Hartman number M and Eckert number Ec, because more resistance produces larger energy in the fluid. This research contributes to understanding the complex interplay of parameters governing fluid dynamics and thermal behavior near porous curved surfaces, shedding light on the impact of various factors on velocity and temperature distributions.

MHD boundary layer flow due to an exponentially stretching surface through porous medium with radiation effect

The purpose of this article is to study the boundary layer flow and heat transfer of the MHD second-grade fluid. By utilizing similarity transformations, the governing equations are transformed into a set of non-linear ordinary differential equations. To get semi-analytical formulations of velocity, temperature, and other variables, we use the homotopy analysis technique (HAM). Then, we employ the Wolfram Language function NSolve to get the solutions. The main finding of the present work is that the flow variables have been influenced by the magnetic field parameter, the porous parameter, and the radiation parameter.

Analytical Solution of Diffusion Thermo Effect on MHD Second Grade Fluid Flow with Heat Generation and Chemical Reaction through an Accelerated Vertical Plate

Abstract: The objective of this model is to examine the Dufour effect on unsteady free convection second-grade fluid flow past an accelerated moving plate subjected to the magnetic field through a porous medium. The thermal radiation and chemical reactions are also taken into account. The constitutive governing equations of the model with all levied initial and boundary conditions are written in non-dimensional form. The non-dimensional equations that govern the flow model are transformed into a time-fractional model using the Caputo, Caputo–Fabrizio, and Atangana–Baleanu time-fractional derivatives. The Laplace transform technique is applied to the differential equations of the flow model to obtain the exact solution for concentration, temperature, and velocity fields. The expression for the Sherwood number, the Nusselt number, and skin friction are also derived analytically. The effects of diffusion-thermo, chemical reactions, second-grade parameterfractional parameter (γ), porosity, magnetic parameter, heat absorption/generation, and thermal radiation on velocity profiles are studied through various figures. It is observed that the velocity profiles for Caputo–Fabrizio fractional derivatives are higher as compared to Caputo and Atangana–Baleanu fractional derivatives. It is also seen that for the value of fractional parameter γ→1, the velocity profiles obtained via Caputo, Caputo–Fabrizo, and Atangana–Baleanu derivatives are identical. Keywords: Second-grade fluid, Free convection, Chemical reaction, Diffusion thermo, Heat generation, Caputo, Caputo–Fabrizio, Atangana–Baleanu fractional derivative.

Darcy–Forchheimer flow of second-grade fluid in a porous medium using Cattaneo–Christov model

This research paper examines the Darcy–Forchheimer flow of second-grade hybrid nanofluid with thermophoretic particle deposition on a solar collector plate in a porous media. This study performs an extensive exploration of entropy generation. Solar collector plates play a crucial role in energy storage in solar power plants. They help to store and regulate energy at extreme temperatures. This work analyzes the performance of a solar collector plate when the conventional fluid of Ethylene Glycol (EG) is reciprocated by nanoparticles of zirconium dioxide and copper. The ramifications of Magntohydrodynamic (MHD) and Cattaneo–Christov heat and mass flux are also investigated. The expressions of mass and energy are generated by using the Cattaneo–Christov model of heat and mass flux. The Homotopy analysis method (HAM) is utilized to achieve the results of differential equations against various dimensionless parameters. The fluctuating behavior of velocity, concentration and temperature profiles is discussed graphically in this paper. Furthermore, tables are included for the numerical values of skin friction, Sherwood number and Nusselt number for several parameters. As the value of the Darcy parameter raises, the fluid’s velocity distribution continuously reduces. The temperature distribution reduces along with the greater values of the thermal relaxation parameter. The concentration profile has shown decreasing impact due to the increasing value of the concentration relaxation parameter.

Chemical reaction on Unsteady MHD Convection Flow of Second grade fluid over an unbounded perpendicular absorbent plate

ABSTRACT We discuss in this paper the chemical reaction impacts on complimentary convectively flow of the gelatinous secondary graded fluid past a countless vertical porous plate underneath the effects of uniform transversal magnetic field. Time reliant penetrability as well as fluctuating suction are also explored. The prevailing equations are resolved with the regular perturbation method for the small amplitudes of the permeability. The solutions for the velocities, temperature as well as concentrations have been obtained computationally; in addition, behaviour is also explored. The skin fiction, the Nusselts number as well as Sherwood numbers are also found in addition to those behaviour computationally conferred. It is concluded that the velocity is reduced with enhancement in the intensity of the magnetic field and Prandtl number whereas it is enhanced by the ever-increasing thermal Grashofs number. The magnitude of the temperature of the flow field diminished with increase in the Prandtl number, heat source parameter. The concentration of the flow field is reduced by a rise into the Schmidt number and chemical reaction parameters.

Chemical reaction on MHD convective flow of second-grade fluid through a vertical porous channel with non-uniform wall temperature

We have examined the impacts of the suction and/ or injection on the magnetohydrodynamic convection fluctuating flow of secondary order fluids through the absorbent medium into a perpendicular channel by non-uniformed walls’ temperature. The fluid is subjected to a transversal magnetic domain as well as the velocity slips near the left side plate. The systematic resolutions of the non-dimensional equations were found and the impacts of the governed variables on velocity, temperatures, concentration profiles, skin frictions, rates of temperature and mass transports were explored. It is motivating to note that skin friction enhances channel plates as permeability enlarges. The magnitude of the velocity retards with an enhancement in Hartmann number and enlarges with an increase in the permeability parameter.

Mathematical analysis of heat and mass transport under thermal radiations and dissipation for electrically conducting second-grade fluid

This research deals with heat and mass transport in 2D, steady laminar unidirectional flow of second-grade fluid inside converging/diverging stretchable channel with no slip effects. The similarity equations were engaged for the model development and acquired a model in the form of a joint system of ODEs comprising the innovative effects of thermal radiations, magnetic field and dissipation function. Then, mathematical treatment of the model was done via HAM Package and the results were furnished under the inspiration of physical constraints. It is pointed out that the fluid moves quite slowly in diverging cases than that of converging ones under multiple Re values, whereas magnetic field effects are almost negligible for the velocity profile. The temperature of the fluid can be enlarged by increasing Ec and Pr and Rd is not proven good in this study. Further, as far as the mass transport is concerned, the dominant contribution of Sc is observed for both stretching/shrinking walls.

Exact Solutions for Non-Isothermal Flows of Second Grade Fluid between Parallel Plates.

In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is time-independent and driven by the pressure gradient. On the channel walls, various boundary conditions are stated. Namely, we consider the no-slip conditions, the threshold slip conditions, which include Navier's slip condition (free slip) as a limit case, as well as mixed boundary conditions, assuming that the upper and lower walls of the channel differ in their physical properties. The dependence of solutions on the boundary conditions is discussed in some detail. Moreover, we establish explicit relationships for the model parameters that guarantee the slip (or no-slip) regime on the boundaries.

Thermal Conductivity and Mixed Convection Influence on the Flow of Viscoelastic Fluid Due To Inclined Cylinder

The thermal flow of second grade fluid with Soret and Dufour effects has been observed in this investigation. The problem is modified with mixed convection and thermal radiation applications. The thermal conductivity with variable relations is used to analyze the transport phenomenon. Further, the applications of mixed convection and magnetic force has also been focused. The convective thermal and concentration flow constraints are used for the current flow problem. The shooting numerical scheme is used to calculate the numerical observations. The major impact of parameters is visualized for flow parameters. It is observed that the velocity profile increases for curvature parameter and viscoelastic fluid parameter. The assumptions of variable thermal conductivity enhanced with transport phenomenon. The Nusselt number declined for variable thermal conductivity parameter.

Numerical investigation of unsteady flow and heat transfer of a free convective second-grade fluid passing through exponentially accelerated vertical porous plate

Numerical investigation of unsteady flow and heat transfer of a free convective second-grade fluid passing through exponentially accelerated vertical porous plate

Chemical reactive second-grade nanofluid flow past an exponential curved stretching surface: Numerically

The exponentially stretching curved surface is considered for second-grade fluid flow. The slip effects are applied at the assumed surface. The Brownian motion, chemical reaction, and thermophoresis effects are studied to determine the influence of the second-grade fluid. The boundary layer approximation is applied to the governing equation which is reduced in terms of partial differential equations. These partial differential equations become the dimensionless form after using the appropriate transformations. Further, the numerical approach is imposed on the dimensionless system to calculate the problem-related results. Graphs and tables are used to show how involving physical parameters have an effect. The velocity profile and skin friction have been increased due to increasing values of curvature parameters. The velocity function declined due to an increment in the second-grade fluid parameter. It means that the thickness of the boundary layer shown as decline when the second-grade fluid parameter rises while the second-grade fluid parameter has an inverse relation with viscosity. The Prandtl number increased which increased the temperature function. Physically, the thickness of the thermal boundary is controlled by the Prandtl number, and temperature increases by increasing the value of the Prandtl number.