Shape effect on MHD flow of time fractional Ferro-Brinkman type nanofluid with ramped heating

Employing the Akbari Ganji Method (AGM) to conduct a semi-analytical analysis of transient Eyring-Powell compressible flow in a tensile Surface under the influence of a magnetic field

This study explores the transfer of mass and heat within unstable two-dimensional flows of non-Newtonian material under conditions involving radiation generation, absorption, and thermal radiation. Additionally, it investigates the impact of magnetic hydromagnetic joule (MHD) heating on these processes. The researchers converted the partial differential equations into ordinary ones through appropriate transformations. Subsequently, a new idea was considered, involving coupling fractional differential equations using the AGM method, with an order of 0.5 < a <0.8 and the initial condition x (0) = x0. A new technique is introduced to find the exact solution of fractional differential equations by solving the correct order differential equations. The primary aim of this paper is to explore the impact of parameter variations on velocity, temperature, local skin friction coefficient, and local Nusselt and Sherwood numbers. This article investigates the effect of multi-parameter changes on local skin friction coefficient and Schmidt number. In most fluid heat transfer problems, especially in non-Newtonian fluids, fractional differential equations are widely used in liquids. The obtained results indicate that the Lorentz force, influenced by the magnetic field parameter (Ha), diminishes the velocity distribution. Additionally, it is observed that the temperature profile decreases as the radiation parameter (R) increases.

Comprehensive Investigation of Thermal and Flow Features of Alloy Based Nanofluid Considering Shape and Newtonian Heating Effects via New Fractional Approach

The core purpose of this work is the formulation of a mathematical model by dint of a new fractional modeling approach to study the dynamics of flow and heat transfer phenomena. This approach involves the incorporation of the Prabhakar fractional operator in mathematical analysis to transform the governing system from a conventional framework to a generalized one. This generalized model evaluates the improvement in thermal efficacy of vacuum pump oil because of the inclusion of aluminum alloy nanoparticles. The flow of the under-observation nanofluid starts due to the combined effects of natural convection and the ramped velocity function at the boundary. Meanwhile, an analysis of the energy equation is conducted by taking the Newtonian heating mechanism into consideration. The characteristics of platelet-, brick-, cylinder-, and blade-shaped alloy nanoparticles are incorporated into the primary system using shape-dependent relations for thermal conductivity and viscosity. Both the classical and generalized models are solved to derive the exact solutions by first inserting some dimension-independent quantities and then operating the Laplace transform on the succeeding equations. These solutions are utilized for the development of graphical illustrations to serve the purpose of covering all features of the problem under consideration. Furthermore, changes in energy and flow functions due to the dominant influences of the relevant contributing factors are delineated with appropriate physical arguments. In addition, the numerical results of the skin friction coefficient and Nusselt number are displayed via multiple tables to analyze the disturbance in shear stress and discuss the contribution of the fractional parameters, the volume concentration of the considered nanoparticles, and the shape factor in the boost of the thermal potential of the considered nanofluid. The findings imply that aluminum alloy nanoparticles have the ability to produce a 44% enhancement in the thermal effectiveness of vacuum pump oil. Moreover, the flow velocity is reduced as the loading range of the nanoparticles rises.

Inspection of thermal jump conditions on nanofluids with nanoparticles and multiple slip effects

The significance of slip boundary conditions with thermal radiation implications on a steady flow of nano suspension over a rotating disk with a constant magnetic field is discussed in this research investigation. Here Iron oxide \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {Fe_{3} O_{4} } \right)$$\end{document}Fe3O4, Zirconium dioxide \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {ZrO_{2} } \right)$$\end{document}ZrO2, and Titanium \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {Ti} \right)$$\end{document}Ti are recruited as nanoparticles and water \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {H_{2} O} \right)$$\end{document}H2O as a host fluid. The appropriate similarities transformations are used to transfer main PDEs into a system of nonlinear ODEs. The set of ODEs is then solved via shooting approach (bvp4c solver) a built-in function in MATLAB. The depictical outcomes of the physical flow parameters like thermal radiation and velocity slip parameters are revealed and clarified with the assist of figures. The slip parameter significantly reduces the velocity profiles, according to this investigation. The pressure is declined for the higher estimates of the magnetic parameter. The thermal profile was uplifted for the rising values of the thermal radiation parameter. Meteorology, meteorological, atmospheric research, biochemical engineering, power engineering, transportation production, solar energy transformations, sensing micro fabrication, tumblers in polymer manufacturing, and other fields will benefit from this suggested model. The suggested study has been developed in response to these kinds of practical consequences. This work is unique in that it investigates the consequences of a magnetic field, slip boundary conditions, and thermal radiation on nanoparticles flow across a disk. The recent study is innovative, and it could be used by other researchers to learn more about the heat exchange behavior and reliability of working fluids.

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.

Time fractional model of electro-osmotic Brinkman-type nanofluid with heat generation and chemical reaction effects: application in cleansing of contaminated water

Drilling fluids execute a dominant role in the extraction of oil and gas from the land and rocks. To enhance the efficiency of drilling fluid, clay nanoparticulate has been utilized. The inclusion of clay nanomaterial to drilling fluids significantly elevate their viscosity and thermal conductivity. Therefore, the present investigation is focused on the analysis of time-fractional free convective electro-osmotic flow of Brinkman-type drilling nanofluid with clay nanoparticles. The heat generation and chemical reaction characteristics and influence of the transverse magnetic field have also been taken into an account. The local mathematical model is formulated in terms of coupled PDEs along with appropriate physical conditions. The dimensional governing equations have been non-dimensionalized by using relative similarity variables to encounter the units and reduce the variables. Further, the non-dimensional local model has been artificially converted to a generalized model by utilizing the definition of time-fractional Caputo–Fabrizio derivative with the exponential kernel. The graphical results are analyzed via computational software Mathematica, to study the flow behavior against inserted parameters. From graphical analysis it has been observed qualitatively that the velocity field has been raised against the greater magnitude of electro-osmosis parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Es$$\end{document}Es. Numerical table for Nusselt number is calculated from the obtained exact solutions. From the analysis 11.83% elevation in the rate of energy transition of drilling nanofluid has been reported in response of clay nanoparticles.

Comparative study of heat and mass transfer of generalized MHD Oldroyd-B bio-nano fluid in a permeable medium with ramped conditions

This article aims to investigate the heat and mass transfer of MHD Oldroyd-B fluid with ramped conditions. The Oldroyd-B fluid is taken as a base fluid (Blood) with a suspension of gold nano-particles, to make the solution of non-Newtonian bio-magnetic nanofluid. The surface medium is taken porous. The well-known equation of Oldroyd-B nano-fluid of integer order derivative has been generalized to a non-integer order derivative. Three different types of definitions of fractional differential operators, like Caputo, Caputo-Fabrizio, Atangana-Baleanu (will be called later as [Formula: see text]) are used to develop the resulting fractional nano-fluid model. The solution for temperature, concentration, and velocity profiles is obtained via Laplace transform and for inverse two different numerical algorithms like Zakian's, Stehfest's are utilized. The solutions are also shown in tabular form. To see the physical meaning of various parameters like thermal Grashof number, Radiation factor, mass Grashof number, Schmidt number, Prandtl number etc. are explained graphically and theoretically. The velocity and temperature of nanofluid decrease with increasing the value of gold nanoparticles, while increase with increasing the value of both thermal Grashof number and mass Grashof number. The Prandtl number shows opposite behavior for both temperature and velocity field. It will decelerate both the profile. Also, a comparative analysis is also presented between ours and the existing findings.

Heat and Mass Transfer Impact on Differential Type Nanofluid with Carbon Nanotubes: A Study of Fractional Order System

This paper is an analysis of flow of MHD CNTs of second grade nano-fluid under the influence of first order chemical reaction, suction, thermal generation and magnetic field. The fluid is flowing through a porous medium. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional derivatives. This shows the novelty of this work. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional derivatives. The solutions are evaluated by employing Laplace transform and inversion algorithm. The flow in momentum profile due to variability in the values of parameters are graphically illustrated among C, CF and ABC models. It is concluded that fluid velocity showed decreasing behavior for χ, P, ℏ2, Mo, Pr, ℵ and Sc while it showed increasing behavior for Gr, Gm, κ and Ao. Moreover, ABC fractional operator presents larger memory effect than C and CF fractional operators.

Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier's law

The present work used fractional model of Casson fluid by utilizing a generalized Fourier's Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.