Second-grade Fluid Research Articles

Magnetized heat transfer visualization through computational modeling of third-grade fluid via exponentially stretching cylinder

The steady MHD boundary-layer axis-symmetric flow of a third-grade fluid passing through an exponentially expanded cylinder in the vicinity of a magnetic field is investigated in this study. The problem is mathematically modeled. Suitable similarity transformations are carried out to convert the partial differential equations into nonlinear ordinary differential equations. The Runge–Kutta fourth-order shooting technique is used to solve the transmuted system of nonlinear ODEs. Graphical representations of numerical findings are used to examine the effects of various physical factors on the velocity and temperature profiles. The influence of fluid variables on the velocity curve, such as third-grade parameters, second-grade parameters, and Reynolds number, is illustrated and explored. The skin-friction coefficient expression is computed and given. The widths of the velocity and momentum boundary layers are revealed to be increasing functions of the curvature parameter. It is found that the third-grade fluid has a higher velocity profile than Newtonian and second-grade fluids. Also, the stretched cylinders cause a more progressive shift in heat and mass pattern for flow than flat plates do.

Analysis of a Magneto Hydrodynamic Second-Grade Fluid in a Porous Medium with Temperature Dependent Thermal Conductivity

Analysis of a Magneto Hydrodynamic Second-Grade Fluid in a Porous Medium with Temperature Dependent Thermal Conductivity

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.

Second-grade fluid with carbon nanotubes flowing over an elongated curve surface possessing thermal radiation and internal heat generation effects

Second-grade fluid with carbon nanotubes flowing over an elongated curve surface possessing thermal radiation and internal heat generation effects

Rotational Stagnation Point Non-Newtonian Second-Grade Fluid Flowing over Spiraling Disk

Rotational Stagnation Point Non-Newtonian Second-Grade Fluid Flowing over Spiraling Disk

Analysis of Boundary Layer Flow Second-Grade Hybrid Nanofluid Subject to Lorentz Force

The suspension of nanoparticles in a fluid has been a sure way of steadily improving fluid behaviour. A further improvement in the fluid behaviour is achieved by the suspension of two dissimilar nanoparticles in a base fluid. This study analyses the boundary layer flow of second-grade hybrid nanofluid subject to Lorentz force. By considering Titanium Oxide and Molybdenum disulfide nanoparticles, due to their great lubricating and efficient heat transfer properties, the governing non-linear equations are formulated and rendered dimensionless with the help of similarity variables. The resulting boundary condition equations are transformed to initial condition equations by use of shooting technique and numerically solved by 4th-order Runge Kutta method in MATLAB bvp4c. It is noted that the fluid’s velocity profile increases with the increase in volume fraction and fluctuates with increasing fluid parameters and magnetic strength. The temperature profile grows with the Prandtl number and magnetic field and decreases with the increase in volume fraction and the second-grade fluid parameter.

Axisymmetric stagnation-point flow of non-Newtonian nanomaterial and heat transport over a lubricated surface: Hybrid homotopy analysis method simulations

Abstract The heat transfer phenomenon associated with the lubricated surfaces offers applications in the manufacturing processes, thermal systems, industrial systems, and engineering phenomenon. It is a well-established fact that improvement in heat transfer is recently successfully claimed with the interaction of nanoparticles. Following such motivation in mind, the prime objective of current continuation is to perform the prediction of heat transfer in second-grade material subject to the lubricated surface. The lubricants are filled with non-Newtonian power law material. The varying thickness of the thin lubricating layer permits an imperfect slip surface. The second-grade fluid interfaces with the boundary condition. The modified semi-analytical tool termed as hybrid homotopy scheme is used to perform the simulations. Shooting and homotopy methods are combined in this new approach. Relevant effects of parameters on physical phenomenon are explained. The importance of influencing parameters in relation to the velocity field, temperature, and concentration profiles is investigated graphically. It is claimed that analytical computations existed for shear thinning case. It is observed that there is a noticeable drop in concentration and thermal profiles due to the variation of viscoelastic parameter. The control of free stream velocity is claimed due to the interaction of slip parameters.

MHD nanofluid flow with energy transfer over a porous stretching surface by using a second-grade fluid model

The main attention of this research is to examine the nature of the flow behavior of nanofluids and energy transfers past an expanding sheet with second-grade fluid model. The system is also situated in an absorbent area, which affects the effects of heat and mass transport and chemical reaction. The numerical calculations and visualization for various flow parameters are performed using a finite difference code that is developed in the built-in bvp4c solver scheme of MATLAB. This involves adopting a set of new variables to change the character of the governing equations of this study. To the best of the authors’ knowledge, many authors have contributed to this field, but they do not take into account the above fluid model associated with the energy transfers with the influences of Brownian motion, thermophoresis effect, and chemical reaction parameters, etc., in their study. Major findings of this study is to achieve a higher amount of thermal transference using the physical parameters, such as magnetic, visco-elastic, thermophoresis, and Brownian motion parameters, etc. Also, using smaller values of the magnetic parameter can be an effective way to minimize the impact of drag force of the fluid at the surface. The considering fluid model has multifarious industrial applications, such as food and cosmetic industry and pharmaceutical and biomedical industry, etc., due to its versatile rheological characteristics.

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.

Stability of non-Newtonian nanofluid movement with heat/mass transportation passed through a hydro magnetic elongating/contracting sheet: multiple branches solutions

Nanomaterials have found wide applications in many fields, leading to significant interest in the scientific world, in particular automobile thermal control, heat reservoirs, freezers, hybrid control machines, paper creation, cooling organisms, etc. The aim of the present study is to investigate the MHD non-Newtonian nanofluid and time-based stability analysis to verify the stable branch by computing the smallest eigenvalue across a slendering, extending, or shrinking sheet with thermal radiation and chemical reactions. The basic flow equations have been obtained in terms of PDEs, which are then converted to ODEs in dimensionless form via a suitable transformation. Based on the MATLAB software package bvp4c, the numerical solution has been obtained for the system of equations. A comparative study of the present and published work is impressive. The influence of evolving factors such as Prandtl number, Schmidt number, magnetic factor, heat generation/absorption, thermal, thermophoresis factor, chemical factor, second-grade fluid factor, and Brownian number on the velocities, energy, and concentration patterns is discussed through graphs. It is perceived that the temperature distribution enriches owing to the greater magnitude of the heat source. Furthermore, it is observed that a greater magnitude of radiation improves the temperature curves. It is also investigated from the present analysis that concentration and temperature profiles increase due to the growing values of the thermophoresis factor.

Heat transfer analysis of generalized second-grade fluid with exponential heating and thermal heat flux

The aim of present work is to apply the Caputo–Fabrizio fractional derivative in the constitutive equations of heat transfer. Natural convection flow of an unsteady second grade fluid over a vertical plate with exponential heating is discussed. The generalized Fourier law is substituted in temperature profile. A portion of the dimensionless factors are utilized to make the governing equations into dimensionless structures. The solutions for temperature and velocity profiles of Caputo–Fabrizio model are acquired through the Laplace transform method. These solutions are greatly affected through the variation of different dimensionless variables like Prandtl number, Grashof number, and second-grade fluid parameter. Finally, the influence of embedded parameters is shown by plotting graphs through Mathcad. From the graphical results it is concluded that, the temperature of the fluid decreases with the increasing values of the Prandtl number and Second grade fluid parameter and increases with the passage of time. The velocity of the fluid increases with increasing values of the Grashof number, second grade parameter and time while decreases with increasing values of fractional parameter and Prandtl number.

Study of heat transfer in MHD viscoelastic fluid of second grade over a stretching porous sheet with electromagnetic effects and nonuniform source/sink

This work is devoted to the study of non-Newtonian fluid of second grade. This model assumes that the flow and heat transfer in MHD viscoelastic fluid is subject to convective boundary conditions in the presence of electromagnetic field and nonuniform source/sink. The flow is considered over a porous sheet. The governing partial differential equations are converted as ordinary differential equations using suitable similarity transformations. The resulting coupled of nonlinear differential equations are successfully solved by means of Optimal Homotopy Asymptotic Method (OHAM). The effects of different physical parameters such as: the second-grade viscoelastic parameter, thermal radiation parameter or Eckert number are analyzed. Several closed form analytical approximate solutions for dimensionless stream function and temperature are presented for some particular cases. Our procedure is based upon an original construction of the solutions using a moderate number of the convergence-control parameters. These parameters lead to very high precision, comparing our approximate solutions with numerical solutions. Let us note that every nonlinear differential equation is reduced to two linear differential equations. The values of the convergence-control parameters are determined using rigorous mathematical procedures. OHAM is an iterative approach which rapidly converges after only one approximation, is effective, explicit, simple and easy to apply. These remarks are in fact the true power of our procedure to solving nonlinear problems without the presence of small or large parameters in the governing equations or boundary/initial conditions.

A new model of time-dependent fractional second grade fluid for two-dimensional channel flow with heat transfer

The goal of the current paper is to create a novel model for the two-dimensional flow (TDF) of a second-grade fluid and the transfer of heat due to free convection. The second-grade fluid travels through the porous media and is electrically conducted. The governing equation for fluid velocity and temperature is formulated as a set of partial differential equations jointly. The model is developed in fractional form by applying the Caputo-Fabrizio (CF) fractional derivative approach. The two-dimensional flow problem is modeled in terms of one-sided coupled fractional partial differential equations with corresponding physical conditions imposed on the fluid flow and temperature. The problem is initially converted to a dimensionless form and then solved for the exact solutions by applying joint Fourier and Laplace transforms. Exact solutions are examined for fluid velocity and temperature and then in limiting cases are reduced to some well-known fluid motions. Some special cases are also obtained from the general solutions. For the numerical results, Mathcad-15 software is used and the results are plotted in various graphs. The temperature, and velocity profiles are discussed and highlighted for embedded flow parameters. The model obtained in this work is new and can be extended for other fluid models hence this article provides a base for future research.

Exact Solutions of Second-Grade Fluid Equations

The second-grade fluid equations describe the motion of relaxing fluids such as aqueous solutions of polymers. The existence and uniqueness of solutions to the initial–boundary value problems for these equations were studied by D. Cioranescu, V. Girault, C. Le Roux, A. Tani, G. P. Galdi, and others. However, their studies do not contain information about the qualitative properties of solutions of these equations. Such information can be obtained by analyzing their exact solutions, which is the main goal of this work. We study layered flows and a model problem with a free boundary, construct an analog of T. Kármán’s solution, which describes the stationary motion of a second-grade fluid in a half-space induced by the rotation of the plane bounding it, and propose a generalization of V. A. Steklov’s solution of the problem on unsteady helical flows of a Newtonian fluid to the case of a second-grade fluid.

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.

Thermal features of Darcy-Forchheimer on a micropolar fluid flow over a curved stretching surface with homogenous-heterogeneous reactions

The main focus of contemporary study is to explore the Darcy magnetized flow of a micropolar second-grade fluid by consideration of homogeneous-heterogeneous reactions over a curved stretching surface. The thermal aspects of the fluid flow are analyzed with the inclusion of joule heating and thermal radiation effects. Moreover, magnetic field is imposed normal to the surface and thermal stratification condition is considered on the boundary of surface. An appropriate transformation is used to convert the flow model into a set of ordinary differential equations, which are nonlinear in the nature. The numerical solutions of this nonlinear system of equations are obtained using the bvp4c technique on MATLAB. The velocity, temperature, concentration, and micro-rotation distribution variation for various parameter is shown graphically and with numerical data. The main finding in the current problem to see that that greater estimation of micropolar parameter improves the angular velocity of the fluid, whereas linear velocity of fluid declines for larger values of magnetic parameter because of the resistance effect take place due to magnetized flow. Furthermore, it seems that curvature parameter produces the improvement in the linear and angular velocity of the fluid.

Flow instabilities of second-grade fluid over a stretching sheet

The work at hand studies thin-film flow instabilities in a non-Newtonian second-grade fluid moving over a stretching sheet. The analysis considers the free surface evolution equation of the thin second-grade viscoelastic fluid model based on the long-wave approximation method. We undertook a linear stability analysis using a normal mode approach and obtained expressions for the linear time growth rate, linear phase speed, and critical wavenumber, which illustrates the linear stability structure of the flow system. Furthermore, the multi-scale analysis of the fluid’s weakly non-linear stability characteristics reveals the presence of subcritical instability in the linear stability zone. The study shows that the varying flow parameters affect the threshold amplitude, which influences the stable and unstable zones in the subcritical region. The outcomes show a stabilizing effect spanning the range of non-dimensional parameters, such as the second-grade parameter ranging from 0 to 100 in values, the surface tension parameter ranging from 0 to 100 in values, and the modified Froude number from 0 to 100 in values.

Numerical exploration of slip effects on second-grade fluid motion over a porous revolving disk with heat and mass transfer

Revolving-disk systems are employed in various industrial settings including turbine engineering, chemical and food processing industries and others. The current article scrutinizes a second-grade fluid motion generated by an infinite porous disk having partial slip character. Heat transfer induced by heating of the disk surface and by viscous and ohmic heating effects is modeled and analyzed under thermal slip condition. Accompanying mass transfer process with thermophoretic diffusion is also formulated. A self-similar system is obtained akin to the case of no-slip case discussed in a previously published study. The adoption of velocity slip assumption induces non-linearity in the boundary conditions in velocity components. Computational procedure embedded in MATLAB bvp4c platform is opted to simulate the system for full range of slip parameters. In contrast to a previously published work pertaining to the no-slip case, present numerical methodology gives accurate results for wide ranges of Prandtl number and elasticity parameter. Boundary layer formations above the disk are examined under various controlling parameters. A comparative assessment of slip and no-slip cases is presented through both graphical illustrations and tabulated results for the resisting torque, the Nusselt number and the Sherwood number. Current numerical findings match very well with the existing homotopy solutions for the no-slip case. The presence of a wall slip mechanism leads to a clear suppression of all the velocity components. Furthermore, an augmentation in the thermal/concentration slip coefficient significantly reduces the thermal/solutal penetration depth. Additionally, we observe a noticeable increase in the driving torque as the elasticity parameter enhances. The slip action of the surface is also predicted to raise the torque required by the disk.

Comprehensive analysis of magnetized second-grade nanofluid via Fourier's and Cataneo-Christove models past a curved surface

This study presents the computer simulations of the magnetized effects of Cattaneo-Christov double diffusion models on the heat and mass transport behavior of a second-grade nanofluid flowing in two dimensions across a curved stretching and shrinking surface. Moreover, the features of convective heat transfer, slip velocity, viscous dissipation, porosity, and heat source/sink with a chemical reaction are also used. Considering the concentration and thermal relaxation times, the classical models of heat and mass diffusion (Fourier and Fick's laws) are extended to the generalized form in regard to the double diffusion Cattaneo-Christov models. Evaluating the current physical study including the Lorentz forces allows us to better understand how the magnetic field affects the process of double diffusion coupled with Joule heating. The system of highly nonlinear, two-dimensional, coupled partial differential equations caused by the moment of second-grade fluid across a curved sheet is solved using the bvp4c scheme. The key findings proves that the concentration and temperature of classical Fourier and Fick's law causes to rise faster than that of Cattaneo-Christov heat and mass flux model respectively as well as the concentration and temperature of Newtonian fluid causes to rise faster than that of second grade nanofluid. The generalized Fourier and Fick's law respectively generate greater heat and mass transport than the classical Fourier and Fick's law as well as the second-grade nanofluid generate greater heat and mass transport than the Newtonian fluid.