Unsteady stagnation-point flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet

Entropy and Bejan Number Influence on the Liquid Film Flow of Viscoelastic Hybrid Nanofluids in a Porous Space in Terms of Heat Transfer

The aim of this study is to determine the influence of the various parameters on the flow of thin film motion on an inclined extending surface. Maxwell fluid is used as a base fluid, and magnesium oxide (MgO) and titanium dioxide (TiO₂) are used as nanocomponents. The width of the thin film is considered variable and varied according to the stability of the proposed model. The magnetic field is used in the vertical track to the flow field. The entropy generation and Bejan number are examined under the influence of various embedded parameters. The outputs of the liquid film motion, thermal profile, and concentration field are also shown with the help of their respective graphs based on the collected data. The solution of the model involves key features such as entropy generation, Bejan number, drag force, and heat transfer rate. Brinkman number, magnetic parameter, radiation parameter, thickness parameter β, and unsteadiness parameter S are also deliberated graphically. The percentage improvement for the enhancement of heat transfer has been calculated and compared for both the nanofluid and hybrid nanofluids. The results are validated through comparison with the existing literature.

Special Non-Newtonian Third-Grade Fluid Flow with Magnetic Field: A Numerical Study

The Buongiorno model is utilized for the non-Newtonian third-grade fluid. With non-linear radiation and magnetic action, it incorporates both Brownian motion and thermophoresis processes. Aim this research is to look at non-Newtonian third-grade fluid boundary layer flow with non-linear solar energy thermal radiation and the magnetic effect. The similarity transformation is used to convert nonlinear PDEs into ODEs. Then numerically solved by shooting technique and the sixth-order R-K method. For various physical parameters, derived findings are graphically discussed. We believe that the current findings can be utilized to explain the non-Newtonian properties of second and third-grade fluids, as well as for applications in tribology, the automobile industry, and other fields.

Numerical analysis of a second-grade fuzzy hybrid nanofluid flow and heat transfer over a permeable stretching/shrinking sheet

In this work, the heat transfer features and stagnation point flow of Magnetohydrodynamics (MHD) hybrid second-grade nanofluid through a convectively heated permeable shrinking/stretching sheet is reported. The purpose of the present investigation is to consider hybrid nanofluids comprising of Alumina \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {{\text{Al}}_{{2}} {\text{O}}_{{3}} } \right)$$\end{document}Al2O3 and Copper \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {{\text{Cu}}} \right)$$\end{document}Cu nanoparticles within the Sodium Alginate (SA) as a host fluid for boosting the heat transfer rate. Also, the effects of free convection, viscous dissipation, heat source/sink, and nonlinear thermal radiation are considered. The converted nonlinear coupled fuzzy differential equations (FDEs) with the help of triangular fuzzy numbers (TFNs) are solved using the numerical scheme bvp4c. The numerical results are acquired for various engineering parameters to study the Nusselt number, skin friction coefficient, velocity, and temperature distribution through figures and tables. For the validation, the current numerical results were found to be good as compared to existing results in limiting cases. It is also inspected by this work that with the enhancement of the volume fraction of nanoparticles, the heat transfer rate also increases. So, it may be taken as a fuzzy parameter for a better understanding of fuzzy variables. For the comparison, the volume fraction of nanofluids and hybrid nanofluid are said to be TFN [0, 0.1, 0.2]. In the end, we can see that fuzzy triangular membership functions (MFs) have not only helped to overcome the computational cost but also given better accuracy than the existent results. Finding from fuzzy MFs, the performance of hybrid nanofluids is better than nanofluids.

Unsteady Three-Dimensional Flow in a Rotating Hybrid Nanofluid over a Stretching Sheet

The problem of an unsteady 3D boundary layer flow induced by a stretching sheet in a rotating hybrid nanofluid is studied. A dimensionless set of variables is employed to transform the system of partial differential equations (PDEs) to a set of nonlinear ordinary differential equations (ODEs). Then, the system of ODEs is solved numerically using the MATLAB software. The impacts of different parameters, such as copper nanoparticles volume fraction, radiation, rotation, unsteadiness, and stretching parameters are graphically displayed. It is found that two solutions exist for the flow induced by the stretching sheet. Furthermore, the increasing nanoparticle volume fraction enhances the skin friction coefficient. It is noticed that the skin friction coefficient, as well as the heat transfer rate at the surface, decrease as the rotating parameter increases. Additionally, the thermal radiation as well as the unsteadiness parameter stimulate the temperature.

Impact of Nonlinear Thermal Radiation on the Time-Dependent Flow of Non-Newtonian Nanoliquid over a Permeable Shrinking Surface

Symmetry and fluid dynamics either advances the state-of-the-art of mathematical methods and extends the limitations of existing methodologies to new contributions in fluid. Physical scenario is modelled in terms of differential equations as mathematical models in fluid mechanics to address current challenges. In this work a physical problem to examine the unsteady flow of a third-grade non-Newtonian liquid induced through a permeable shrinking surface containing nanoliquid is considered. The model of Buongiorno is utilized comprising the thermophoresis and Brownian effects through nonlinear thermal radiation and convective condition. Based on the flow symmetry, suitable similarity transformations are employed to alter the partial differential equations into nonlinear ordinary differential equations and then these ordinary differential equations are numerically executed via three-stage Lobatto IIIa formula. The flow symmetry is discussed for interesting physical parameters and thus this work is concluded. More exactly, the impacts of pertinent constraints on the concentration, temperature and velocity profiles along together drag force, Sherwood and Nusselt numbers are explained through the aid of the tables and plots. The outcomes reveal that the dual nature of solutions is gained for a specific amount of suction and flow in the decelerating form A < 0 . However, the unique result is obtained for flow in accelerating form A ≥ 0 . In addition, the non-linear parameter declines the liquid velocity and augments the concentration and temperature fields in the first result, whereas the contrary behavior is scrutinized in the second result.

Multiple physical aspects during the flow and heat transfer analysis of Carreau fluid with nanoparticles

The current work is concerned with the two-dimensional boundary layer flow of a non-Newtonian fluid in the presence of nanoparticles. The heat and mass transfer mechanism for Carreau nanofluid flow due to a radially stretching/shrinking sheet is further investigated in this article. The governing physical situation is modelled in the form of partial differential equations and are simplified to a system of non-linear ordinary differential equations by employing dimensionless variables. Numerical simulations for non-dimensional velocity, temperature and concentration fields has been performed with the assistance of built-in Matlab solver bvp4c routine. One significant computational outcome of this study is the existence of multiple numerical solutions for the flow fields. The impacts of various developing parameters, for instance, Weissenberg number, power-law index, shrinking parameter, suction parameter, Prandtl number, Schmidt number, Brownian motion and thermophoresis parameter on the velocity, temperature and nanoparticles concentration are visualized through tables and graphical experiment. The numerical results demonstrate that the rates of heat and mass transfer are raised by higher Weissenberg number for first solution and an inverse is seen for second solution. Moreover, an increasing trend is seen in nanofluids temperature for both solutions with greater values of thermophoresis parameter. In addition, the numerical results obtained by the applied technique are validated with existing literature and found to be in an excellent agreement.

Axisymmetric rotational stagnation point flow impinging radially a permeable stretching/shrinking surface in a nanofluid using Tiwari and Das model

In this paper, the problem of normal impingement rotational stagnation-point flow on a radially permeable stretching sheet in a viscous fluid, recently studied in a very interesting paper, is extended to a water-based nanofluid. A similarity transformation is used to reduce the system of governing nonlinear partial differential equations to a system of ordinary differential equations, which is then solved numerically using the function bvp4c from Matlab. It is found that dual (upper and lower branch) solutions exist for some values of the governing parameters. From the stability analysis, it is found that the upper branch solution is stable, while the lower branch solution is unstable. Sample velocity and temperature profiles along both solution branches are graphically presented.