Optimal Homotopic Exploration of Features of Cattaneo-Christov Model in Second Grade Nanofluid Flow via Darcy-Forchheimer Medium Subject to Viscous Dissipation and Thermal Radiation

Entropy analysis of MHD hybrid nanoparticles with OHAM considering viscous dissipation and thermal radiation

This research explores the 3-D flow characteristics, entropy generation and heat transmission behavior of nanofluids consisting of copper and titanium in water as they flow across a bidirectional apparent, while considering the influence of magneto-hydrodynamics. The thermophysical properties of nanofluids are taken advantage of utilizing the Tiwari and Das demonstrate. The concept of the boundary layer has facilitated the comprehension of the physical ideas derived from it. By applying requisite transformations, the connected intricate sets of partial differential equation have been converted into ordinary differential equation. The modified model is calculated employing the widely recognized technique known as OHAM by using Mathematica program BVPh2.0 Software. For different dimensionless parameters computational and graphical investigations have been performed. It is notice that as fluid parameters change, they exhibit distinct responses in comparison to the temperature, velocity profiles and entropy generation. The results show that velocity profile rise with greater estimates of the magnetic parameter and the rate of entropy formation. Furthermore, thermal profiles become less significant as Eckert and Prandtl numbers increase.

Oblique stagnation point flow of magnetized Maxwell fluid over a stretchable Riga plate with Cattaneo-Christov heat flux and convective conditions

The current work deals with the oblique stagnation point flow phenomenon of a rate-type Maxwell fluid with the significance of the Cattaneo-Christov double diffusion theory. The Cattaneo-Christov theory is illustrated through the modified form of Fourier's and Fick's laws. The steady magnetized flow mechanism is observed in two dimensions through a stretchable convective Riga plate. In the mass and heat transfer analysis, the consequences of chemical reactions and thermal radiation are also incorporated. With the contribution of relevant dimensionless quantities, the setup of dimensionless equations is acquired which further takes the form of nonlinear equations. The physical significance of the numerous parameters on different features of the flow phenomenon is graphically exhibited. The interesting physical quantities are computed and numerically evaluated relative to the pertinent parameters. This study reveals that the thermal relaxation time parameter lowers the rate of heat transfer, and the thermal Biot number enhances the rate of heat transport. Moreover, the Deborah number minimizes the flow field of both tangential and axial velocities.

Variable Fluid Characteristics’ Impacts on the Dissipative and Chemically Reactive Fluid Flow across a Stretched Surface

This article’s goal was to explain how chemical reaction and viscous dissipation affect a non-Newtonian Cross-fluid in a boundary layer flow due to a stretching sheet with variable fluid properties. The results were obtained after assuming laminar, steady, and viscous flow characteristics. In this study, the analysis took into account the characteristics of the fluid variable diffusivity and slip velocity. It was considered that fluid viscosity and thermal conductivity are temperaturedependent variables. Because of their mobility, non-Newtonian fluid particles are thought to interact chemically. The physical problem is governed by a set of partial differential equations that are not linear. Anumerical solution was reached usingNewton’s shooting methodology and the Runge–Kutta integration technique. A set of figures displays the distributions of the temperature, concentration, and velocity at various physical parameter values. The influence of all physical parameters is shown in tabular form together with the local Sherwood number, drag force, and local Nusselt number. A key conclusion was that the temperature profile of the nanofluid increases as the mixed convection parameter and Eckert number rise. Furthermore, both the Sherwood number and the Nusselt number decreased as the slip velocity parameter increased. Last but not least, the results proved that the suggested numerical approach, which offers a reliable description of the flow and heat mass transfer mechanism, is effective.

A study of triple-mass diffusion species and energy transfer in Carreau-Yasuda material influenced by activation energy and heat source

The mechanism of thermal transport can be enhanced by mixing the nanoparticles in the base liquid. This research discusses the utilization of nanoparticles (tri-hybrid) mixture into Carreau-Yasuda material. The flow is assumed to be produced due to the stretching of vertical heated surface. The phenomena of thermal transport are modeled by considering Joule heating and heat generation or absorption involvement. Additionally, activation energy is engaged to enhance heat transfer rate. The mathematical model composing transport of momentum, heat and mass species is developed in Cartesian coordinate system under boundary layer investigation in the form of coupled nonlinear partial differential equations. The complex partial differential equations are converted into coupled nonlinear ordinary differential equations by using the appropriate similarity transformation. The conversion of PDEs into ODEs make the problem easy to handle and it overcome the difficulties to solve the PDEs. The transformed ordinary differential equations are solved with the help of help of finite element scheme. The obtained solution is plotted against numerous involved parameters and comparative study is established for the reliability of method and accuracy of obtained results. An enhancement in fluid temperature is recorded against magnetic parameter and Eckert number. Also, decline in velocity is recorded for Weissenberg number and concentration is controlled against higher values of Schmidt number. Furthermore, it is recommended that the finite element scheme can be implemented to handle complex coupled nonlinear differential equation arising in modeling of several phenomena occurs in mathematical physics.

Significance of Rosseland’s Radiative Process on Reactive Maxwell Nanofluid Flows over an Isothermally Heated Stretching Sheet in the Presence of Darcy–Forchheimer and Lorentz Forces: Towards a New Perspective on Buongiorno’s Model

This study aimed to investigate the consequences of the Darcy–Forchheimer medium and thermal radiation in the magnetohydrodynamic (MHD) Maxwell nanofluid flow subject to a stretching surface. The involvement of the Maxwell model provided more relaxation time to the momentum boundary layer formulation. The thermal radiation appearing from the famous Rosseland approximation was involved in the energy equation. The significant features arising from Buongiorno’s model, i.e., thermophoresis and Brownian diffusion, were retained. Governing equations, the two-dimensional partial differential equations based on symmetric components of non-Newtonian fluids in the Navier–Stokes model, were converted into one-dimensional ordinary differential equations using transformations. For fixed values of physical parameters, the solutions of the governing ODEs were obtained using the homotopy analysis method. The appearance of non-dimensional coefficients in velocity, temperature, and concentration were physical parameters. The critical parameters included thermal radiation, chemical reaction, the porosity factor, the Forchheimer number, the Deborah number, the Prandtl number, thermophoresis, and Brownian diffusion. Results were plotted in graphical form. The variation in boundary layers and corresponding profiles was discussed, followed by the concluding remarks. A comparison of the Nusselt number (heat flux rate) was also framed in graphical form for convective and non-convective/simple boundary conditions at the surface. The outcomes indicated that the thermal radiation increased the temperature profile, whereas the chemical reaction showed a reduction in the concentration profile. The drag force (skin friction) showed sufficient enhancement for the augmented values of the porosity factor. The rates of heat and mass flux also fluctuated for various values of the physical parameters. The results can help model oil reservoirs, geothermal engineering, groundwater management systems, and many others.

Modification of Cellulose Nanocrystals With 2-Carboxyethyl Acrylate in the Presence of Epoxy Resin for Enhancing its Adhesive Properties

Cellulose nanocrystals (CNCs) have unparalleled advantages in the preparation of nanocomposites for various applications. However, a major challenge associated with CNCs in nanocomposite preparation is the lack of compatibility with hydrophobic polymers. The hydrophobic modification of CNCs has attracted increasing interest in the modern era standing with long challenges and being environmentally friendly. Here, we synthesized CNCs by using cotton as raw material and then modified them with 2-carboxyethyl acrylate to improve their corresponding mechanical, adhesive, contact angle, and thermal properties. Different concentrations (1-5 wt%) of CNCs were used as modifiers to improve the interfacial adhesion between the reinforced CNCs and E-51 (Bisphenol A diglycidyl ether) epoxy resin system. CNCs offered a better modulus of elasticity, a lower coefficient of energy, and thermal expansion. Compared with the standard sample, the modified CNCs (MCNCs) showed high shear stress, high toughness, efficient degradation, thermal stability, and recycling due to the combined effect of the hyperbranched topological structure of epoxy with good compatibility. The native CNCs lost their hydrophilicity after modification with epoxy, and MCNCs showed good hydrophobic behavior (CA = 105 ± 2°). The findings of this study indicate that modification of CNCs with 2-carboxyethyl acrylate in the presence of epoxy resin and the enhancement of the features would further expand their applications to different sectors.

Methods for Predicting Ethylene/Cyclic Olefin Copolymerization Rates Promoted by Single-Site Metallocene: Kinetics Is the Key

In toluene at 50 °C, the vinyl addition polymerization of 4-vinyl-cyclohexene (VCH) comonomers with ethylene is investigated using symmetrical metallocene (rac-Et(Ind)2ZrCl2) combined with borate/TIBA. To demonstrate the polymerizations' living character, cyclic VCH with linear-exocyclicπ and endocyclicπ bonds produces monomodal polymers, but the dispersity (Ɖ) was broader. The copolymers obtained can be dissolved in conventional organic solvent and have excellent thermal stability and crystalline temperature (ΔHm), and their melting temperature (Tm) varies from 109 to 126 °C, and ΔHm ranges from 80 to 128 (J/g). Secondly, the distribution of polymeric catalysts engaged in polymer chain synthesis and the nature of the dormant state are two of the most essential yet fundamentally unknown aspects. Comprehensive and exhaustive kinetics of E/VCH have shown numerous different kinetic aspects that are interpreted as manifestations of polymeric catalysts or of the instability of several types of active center [Zr]/[C*] fluctuations and formation rates of chain propagation RpE, RpVCH, and propagation rate constants kpE and kpVCH, the quantitative relationship between RpE, RpVCH and kpE, kpVCH and catalyst structures, their constituent polymer Mw, and their reactivity response to the endocyclic and exocyclic bonds of VCH. The kinetic parameters RpE, RpVCH, kpE, and kpVCH, which are the apparent rates for the metallocene-catalyzed E/VCH, RpE, and kpE values, are much more significant than RpVCH and kpVCH at 120 s, RpE and RpVCH 39.63 and 0.78, and the kpE and kpVCH values are 6461 and 93 L/mol·s, respectively, and minor diffusion barriers are recommended in the early stages. Compared with previously reported PE, RpE and kpE values are 34.2 and 7080 L/mol·s. VCH increases the RpE in the initial stage, as we are expecting; this means that the exocyclic bond of VCH is more active at the initial level, and that the chain transfer reaction of cyclic internal π double is increased with the reaction time. The tp versus Rp, kp, and [Zr]/[C*] fraction count may be fitted to a model that invokes deactivation of growing polymer chains. At tp 120-360 s higher, the incorporation rate of VCH suppresses E insertion, resulting in reduced molecular weight.

An MHD Fluid Flow over a Porous Stretching/Shrinking Sheet with Slips and Mass Transpiration

In the present paper, an MHD three-dimensional non-Newtonian fluid flow over a porous stretching/shrinking sheet in the presence of mass transpiration and thermal radiation is examined. This problem mainly focusses on an analytical solution; graphene water is immersed in the flow of a fluid to enhance the thermal efficiency. The given non-linear PDEs are mapped into ODEs via suitable transformations, then the solution is obtained in terms of incomplete gamma function. The momentum equation is analyzed, and to derive the mass transpiration analytically, this mass transpiration is used in the heat transfer analysis and to find the analytical results with a Biot number. Physical significance parameters, including volume fraction, skin friction, mass transpiration, and thermal radiation, can be analyzed with the help of graphical representations. We indicate the unique solution at stretching sheet and multiple solution at shrinking sheet. The physical scenario can be understood with the help of different physical parameters, namely a Biot number, magnetic parameter, inverse Darcy number, Prandtl number, and thermal radiation; these physical parameters control the analytical results. Graphene nanoparticles are used to analyze the present study, and the value of the Prandtl number is fixed to 6.2. The graphical representations help to discuss the results of the present work. This problem is used in many industrial applications such as Polymer extrusion, paper production, metal cooling, glass blowing, etc. At the end of this work, we found that the velocity and temperature profile increases with the increasing values of the viscoelastic parameter and solid volume fraction; additionally, efficiency is increased for higher values of thermal radiation.