On the Cattaneo–Christov Heat Flux Model and OHAM Analysis for Three Different Types of Nanofluids

Finite element analysis of cross fluid model over a vertical disk suspended to a tetra hybrid nanoparticles mixture

Nanoparticles have numerous applications and are used frequently in different cooling, heating, treatment of cancer cells and manufacturing processes. The current investigation covers the utilization of tetra hybrid nanofluid (aluminum oxide, iron dioxide, titanium dioxide and copper) for Crossflow model over a vertical disk by considering the shape effects (bricks, cylindrical and platelet) of nanoparticles, electro-magneto-hydrodynamic effect and quadratic thermal radiation. In the current inspection model is first derived given PD-equations and then altered into a system of OD-equations by including similarity variables. The converted ordinary differential equations are solved by using the finite element procedure and the impact of the solution against numerous involved parameters is displayed through tables and graphs. It is observed that tetra-hybrid nanoparticles are recommended better in industrial applications where the highest production of thermal energy. Moreover, an enhancement of thermal production can be achieved utilizing different values of the magnetic parameter, time relaxation number, variable thermal radiation number and magnetic induction number but the opposite trend has been noticed with the effects of radiation number.

Investigation of the Three-Dimensional Hybrid Casson Nanofluid Flow: A Cattaneo-Christov Theory

We consider the Casson hybrid nanofluid (HN) (ZnO + Ag/Casson fluid) that flows steadily along a two-directional stretchable sheet under the influence of an applied changing magnetic flux and is electrically conducting. The basic Casson and Cattaneo-Christov double diffusion (CCDD) formulations are used for the simulation of the problem. This is the first study on the analysis of the Casson hybrid nanofluid by using the CCDD model. The use of these models generalize basic Fick's and Fourier's laws. The current produced due to the magnetic parameter is taken into consideration by using the generalized Oham law. The problem is formulated and then transformed to a coupled set of ordinary differential equations. The simplified set of equations is solved using the homotopy analysis method. The obtained results are presented through tables and graphs for various state variables. A comparative survey in all the graphs is presented for the nanofluid (ZnO/Casson fluid) with the HN (ZnO + Ag/Casson fluid). These graphs depict the effect of various pertinent parameters, like Pr, M, Sc, γ, Nt, m, Nb, δ₁, and δ₂, varying values over the flow. The Hall current parameter m and stretching ratio parameter γ show increasing trends for the velocity gradient, while the magnetic parameter and the flux of mass depict opposite trends for the same profile. The increasing values of the relaxation coefficients show an opposite trend. Furthermore, the ZnO + Ag/Casson fluid shows a good performance in the transfer of heat and thus can be used for cooling purposes to increase the efficiency of the system.

Time-Dependent Stagnation Point Flow of Water Conveying Titanium Dioxide Nanoparticle Aggregation on Rotating Sphere Object Experiencing Thermophoresis Particle Deposition Effects

The notion of thermophoretic particle deposition is used in a number of applications, including thermal exchanger walls. It is important to identify the transport processes in action in systems such as thermal precipitators, exhaust devices, optical transmission fabrication processes, and so on. Based on these application points of view, the present work studies the performance of nanoparticle aggregation stagnation point flow over a rotating sphere during the occurrence of thermophoretic particle deposition. The nonlinear governing equations are transformed into the ordinary differential equation by utilizing suitable similarity variables. The numerical outcomes of the reduced equations along with boundary conditions are solved by the Runge–Kutta–Fehlberg 45 (RKF-45) order method with shooting procedure. The numerical results are shown with the assistance of graphs. The impacts of various dimensionless constraints on velocity, thermal, and concentration profiles are studied under the occurrence and absence of nanoparticle aggregation. The study reveals that the primary velocity is enhanced with increasing values of the acceleration parameter, but secondary velocity diminishes. The impressions of the rotation parameter will improve the primary velocity. The concentration profiles will diminish with an improvement in the thermophoretic parameter. The surface drag force is greater in nanoparticles with aggregation than nanoparticles without aggregation in the Cfx case but a reverse behavior is seen in the Cfz case. Further, the rate of heat distribution increases with a rise in the solid volume fraction, whereas the rate of mass distribution grows as the thermophoretic parameter grows.

Effective Similarity Variables for the Computations of MHD Flow of Williamson Nanofluid over a Non-Linear Stretching Surface

The present study concerns investigating the two-dimensional Magnetohydrodynamics (MHD) boundary layer flow of Williamson nanofluid over a non-linear stretching sheet. The focus of this study is based on the global influence of the non-Newtonian Williamson fluid parameter (λ) rather than the local one that exists in the literature for linear and non-linear stretching cases. The mathematical model of the problem is based on the law of conservation of mass, momentum, and energy. The derived partial differential equations are transformed into ordinary differential equations by applying an appropriate similarity transformation. The subsequent equations are solved numerically by using the Shooting method. The physical quantities Skin friction coefficient, as well as the Sherwood and Nusselt numbers are computed locally. To validate the implemented shooting method, a comparison is made with the results obtained by Matlab function bvp4c, and good agreement is found. The Prandtl number, Pr, has an increasing impact of 25.14% on the wall temperature gradient. The impact of various physical parameters are presented through graphs and tables.

Analysis of Nanofluid Particles in a Duct with Thermal Radiation by Using an Efficient Metaheuristic-Driven Approach

This study investigated the steady two-phase flow of a nanofluid in a permeable duct with thermal radiation, a magnetic field, and external forces. The basic continuity and momentum equations were considered along with the Buongiorno model to formulate the governing mathematical model of the problem. Furthermore, the intelligent computational strength of artificial neural networks (ANNs) was utilized to construct the approximate solution for the problem. The unsupervised objective functions of the governing equations in terms of mean square error were optimized by hybridizing the global search ability of an arithmetic optimization algorithm (AOA) with the local search capability of an interior point algorithm (IPA). The proposed ANN-AOA-IPA technique was implemented to study the effect of variations in the thermophoretic parameter (Nt), Hartmann number (Ha), Brownian (Nb) and radiation (Rd) motion parameters, Eckert number (Ec), Reynolds number (Re) and Schmidt number (Sc) on the velocity profile, thermal profile, Nusselt number and skin friction coefficient of the nanofluid. The results obtained by the designed metaheuristic algorithm were compared with the numerical solutions obtained by the Runge–Kutta method of order 4 (RK-4) and machine learning algorithms based on a nonlinear autoregressive network with exogenous inputs (NARX) and backpropagated Levenberg–Marquardt algorithm. The mean percentage errors in approximate solutions obtained by ANN-AOA-IPA are around 10−6 to 10−7. The graphical analysis illustrates that the velocity, temperature, and concentration profiles of the nanofluid increase with an increase in the suction parameter, Eckert number and Schmidt number, respectively. Solutions and the results of performance indicators such as mean absolute deviation, Theil’s inequality coefficient and error in Nash–Sutcliffe efficiency further validate the proposed algorithm’s utility and efficiency.

Impact of Maxwell velocity slip and Smoluchowski temperature slip on CNTs with modified Fourier theory: Reiner-Philippoff model

The present article presents a novel idea regarding the implementation of Tiwari and Das model on Reiner-Philippoff fluid (RPF) model by considering blood as a base fluid. The Cattaneo-Christov model and thermal radiative flow have been employed to study heat transfer analysis. Tiwari and Das model consider nanoparticles volume fraction for heat transfer enhancement instead of the Buongiorno model which heavily relies on thermophoresis and Brownian diffusion effects for heat transfer analysis. Maxwell velocity and Temperature slip boundary conditions have been employed at the surface of the sheet. By utilizing the suitable transformations, the modeled PDEs (partial-differential equations) are renewed in ODEs (ordinary-differential equations) and treated these equations numerically with the aid of bvp4c technique in MATLAB software. To check the reliability of the proposed scheme a comparison with available literature has been made. Other than Buongiorno nanofluid model no attempt has been made in literature to study the impact of nanoparticles on Reiner-Philippoff fluid model past a stretchable surface. This article fills this gap available in the existing literature by considering novel ideas like the implementation of carbon nanotubes, CCHF, and thermal radiation effects on Reiner-Philippoff fluid past a slippery expandable sheet. Momentum, as well as temperature slip boundary conditions, are never studied and considered before for the case of Reiner-Philippoff fluid past a slippery expandable sheet. In the light of physical effects used in this model, it is observed that heat transfer rate escalates as a result of magnification in thermal radiation parameter which is 18.5% and skin friction coefficient diminishes by the virtue of amplification in the velocity slip parameter and maximum decrement is 67.9%.

Applications of Cattaneo-Christov fluxes on modelling the boundary value problem of Prandtl fluid comprising variable properties

Stretched flows have numerous applications in different industrial, biomedical and engineering processes. Current research is conducted to examine the flow phenomenon of Prandtl fluid model over a moveable surface. The phenomenon of mass and thermal transportation is based on generalized theory of Cattaneo–Christov which considers the involvement of relaxation times. In addition to these, variable characteristics of thermal conductivity and diffusion coefficient are considered as a function of temperature. The physical problem in Cartesian coordinate system is modeled via boundary layer theory which yields a coupled system of partial differential equations. Group scaling transportation is applied to model these PDEs system. The converted equations have been approximated via optimal homotopic scheme. The efficiency and validity of used approach has been shown by computing the error analysis and establishing a comparative study. It is noted that the enhancement in magnetic parameter plays a controlling role for velocity field and it augment the concentration and temperature fields. Furthermore, increase in thermal relaxation parameter and Prandtl number maintains the fluid temperature.

Bioconvection in Magneto Hydrodynamics Casson Nanoliquid (Fe3O4-Sodium Alginate) With Gyrotactic Microorganisms Over an Exponential Stretching Sheet

The present investigation focuses on the influence of motile gyrotactic microorganisms and thermal heat flux on three-dimensional convective flow of a Casson nanoliquid over an elongated surface. The flow equations are modelled by using Tiwari-Das nanofluid model. Sodium alginate (SA) is considered as the base fluid together with Ferromagnetic oxide (Fe3O4) nanoparticles. The governing flow equations are changed into a system of ODEs with the aid of similarity variables and are then addressed computationally. Influence of various pertinent parameters on different physical quantities is examined graphically. The outcomes of present investigation is validated through comparison study and is found to be in good arrangement. It is noticed that the coefficient of heat transfer rises with growing radiation and Biot numbers. Also the mass transfer coefficient surges for higher values of Schmidt number and generative chemical reaction parameter.

Radiative MHD unsteady Casson fluid flow with heat source/sink through a vertical channel suspended in porous medium subject to generalized boundary conditions

Unsteady, incompressible flow of Casson fluid between two infinitely long upward heated walls nested in a porous medium is analyzed in this work. The mass diffusion and heat transfer phenomena are also studied in the presence of thermal radiation, magnetic field, and heat source/sink. The generalized boundary conditions in terms of continuous time-dependent functions are considered for mass, energy, and momentum fields. Fick’s law, Fourier’s law, and momentum conservation principle are adopted to formulate the mathematical equations. Analytic solution for the concentration equation is established first by adding certain unit-less quantities and then by using the Laplace method of transformation. Semi-analytic solutions are calculated by means of Stehfest’s numerical Laplace inversion algorithm for energy and velocity equations. To demonstrate the verification of those solutions, a tabular comparison is drawn. Graphical illustrations along with physical descriptions are provided to discuss the essential contribution of thermo-physical parameters in heat and mass transfer and flow of the Casson fluid. The numerical computations of Sherwood number, Nusselt number, and skin friction for various inputs of related parameters are organized in tables to investigate mass transfer rate, heat transfer rate, and shear stress respectively. It is observed that porosity of the medium and buoyancy force tend to accelerate the flow. The heat and mass transfer rates are appreciated by Prandtl and Schmidt numbers respectively. Furthermore, radiation parameter and Grashof number significantly minimize the shear stress.

Finite Element Study of Bio-Convective Stefan Blowing Ag-MgO/Water Hybrid Nanofluid Induced by Stretching Cylinder Utilizing Non-Fourier and Non-Fick's Laws

In the present framework, an analysis on nanofluid magneto-transport phenomena over an extending cylinder influenced by gyrotactic behavior of algal suspension, is made using the Cattaneo–Christov heat flux (non-Fourier) and mass flux (non-Fick’s) concept in modified Buongiorno’s model. Two dimensional incompressible MHD hybrid nanofluid which comprises chemically reactive hybrid nanomaterials (Ag-MgO NPs) and Stefan blowing effect along with multiple slips is considered. The experimental correlations with their dependency on initial nanoparticle volume fraction are used for viscosity and thermal conductivity of nanofluids. Similarity transformation is used to convert the governing PDE’s into non-linear ODE’s along with boundary conditions, which are solved using the Galerkin Finite Element Method (GFEM). The mesh independent test with different boundary layer thickness (ξ∞) has been conducted by taking both linear and quadratic shape functions to achieve a optimal desired value. The results are calculated for a realistic range of physical parameters. The validation of FEM results shows an excellent correlation with MATLAB bvp5c subroutine. The warmth exhibitions are assessed through modified version of Buongiorno’s model which effectively reflects the significant highlights of Stefan blowing, slip, curvature, free stream, thermophoresis, Brownian motion and bio-convection parameters. The present study in cylindrical domain is relevant to novel microbial fuel cell technologies utilizing hybrid nanoparticles and concept of Stefan blowing with bioconvection phenomena.