Transportation of heat generation/absorption and radiative heat flux in homogeneous-heterogeneous catalytic reactions of non-Newtonian fluid (Oldroyd-B model)

Viscoelastic hybrid nanofluid flow over a vertical plate with sinusoidal surface temperature variations

Natural convection of a viscoelastic hybrid nanofluid along a vertically heated plate with sinusoidal surface temperature variations is investigated. The current investigation explores the non-similar boundary layer flow patterns and heat transfer of second-grade viscoelastic flow of hybrid nanofluid. Effects of magnetic field and thermal radiation are considered. The governing dimensional equations are converted into a non-dimensional form taking suitable transformations. Resulting equations are solved with the aid of finite difference method. It is discovered that the momentum boundary layer lessens while the thermal boundary layer grows for higher radiation parameters, surface temperature parameters, Eckert numbers, magnetic field parameters and amount of nanoparticles. For larger Deborah numbers (De₁), shear stress (τ) and heat transfer rate (q) accelerate, but momentum and thermal boundary decline near the leading edge of the vertical plate. However, the effects of Deborah number (De₂) show opposite results. Increase in magnetic field parameters causes a reduction in shear stress. The higher volume fraction of nanoparticles (φ₁, φ₂) enhances q as it was expected. Moreover, τ and q were increased with larger surface temperature parameters and decrease with higher Eckert numbers. This is because higher surface temperature boost up the fluid temperature, but higher Eckert numbers admit the fluid to spread over the surface. An increase in the amplitude of surface temperature oscillation enhances the shear stress and heat transfer rate.

Thermal Performance on Radiative and Ohmic Dissipative Magneto-Nanoliquid Over Moving Flat Porous Plate Suspended by Single Wall Carbon Nanotubes and Multi Wall Carbon Nanotubes

This investigation examines heat transport in the flow of magnetized Blasius flow suspended by carbon nanotubes (CNTs) on an accelerated by moving flat porous plate that contains water and ethylene glycol as base fluids. The transfer of heat has been contemplated in the company of suspended CNTs above a plane plate. The flow simulations are carried by utilizing the impact of magnetic field and uniform porous medium. The transport of thermal is controlled by the significant influence of thermal radiation, heat source, heat and Joule dissipation. Utilizing scaling analysis flow governing problem is converted into a set of higher order nonlinear ordinary differential equations which afterwards are tackled numerically by employing Runge-Kutta Fehlberg 45 method with shooting quadrature. Quantities of flow physical significance are portrayed through graphically. Verification of attained numerical results with available literature under certain limitations are presented and found excellent agreement. With elevation in convective term flow profiles of SWCNTs and MWCNTs are reduced. A reduction of flow characteristic dimensions is observed with increasing magnetic field and porosity terms. Finally, SWCNTs and MWCNTs are positively influenced by Joule dissipation and negatively by thermal radiation.

MHD Casson fluid flow with Navier's and second order slip due to a perforated stretching or shrinking sheet

The present work discusses the laminar boundary layer flow of an electrically conducting Casson fluid due to a horizontal perforated sheet undergoing linear shrinking/stretching with mass transpiration. Navier’s slip and second-order slip conditions are also imposed on the flow. The system is subjected to a transverse magnetic field. The non-Newtonian flow under consideration obeys the rheological equation of state due to the Casson model. The PDEs governing the bounder layer flow is reduced to a nonlinear boundary value problem in ODEs by utilizing appropriate similarity transformations and are expressed analytically. The similarity solution is found to be a function of the Casson parameter, magnetic parameter, mass suction/injection parameter, and the first/second-order slip parameters. Such a solution is either unique, or dual solutions exist in a region defined by the mass transfer induced slip parameter. The results of the present work are found to be an increase of the magnetic effects resulting in expansion of the unique solution region and contraction of the dual solution region for the flow due to the induced Lorentz force. In the unique solution region, an increase in magnitudes of mass suction induced slip and the first/second-order slip parameters result in a reduction of the wall shear stress in the shrinking sheet, while the wall shear stress with mass suction increases with the Casson and the magnetic effects. Similar results exist for the stretching sheet case with mass suction. However, only unique similarity solutions exist only for the case of stretching sheets with mass injection. The current work is a generalization of the classical works of Crane (1970) and Pavlov (1974) for a stretching sheet. Mass suction/injection induced slip enhances and achieves a dominant flow driven by reversing the flow direction of the moving sheet, which allows an adjacent flow against the sheet. The findings have possible industrial applications in fluid-based systems including stretchable/shrinkable things, automated cooling systems, power generation, microelectronics, and present new results to the problem.

A semi-analytical passive strategy to examine the water-ethylene glycol (50:50)-based hybrid nanofluid flow over a spinning disk with homogeneous-heterogeneous reactions

Scientists and researchers are much interested in studying graphene and silver nanoparticles for the enhancement of heat transport due to their extensive variety of applications in different areas of industrial and engineering such as drug delivery, medical devices, ultra-light, excellent electrical conductivity, strong medical strength, health care, consumer, food, etc. Therefore, in the existing investigation, the MHD flow of a mixed convective hybrid nanoliquid with graphene and silver nanoparticles past a rotating disk is considered. Water and ethylene glycol (50:50) is used as a base liquid in the existing model. The mechanism for heat transport is computed with the existence of thermal radiation and thermal convective condition. Homogeneous and heterogeneous chemical reactions are assumed in the flow behavior. The mathematical formulation of the proposed problem is based on the nonlinear PDEs which are then transformed to nonlinear ODEs by manipulating the appropriate similarity transformation. The simulation of the existing problem has been performed with the help of the homotopy analysis technique. The outcomes of the different flow parameters on the velocities, temperature, concentration, skin friction coefficient, and Nusselt number of the hybrid nanofluid are attained via graphs and tables. Some significant results from the existing problem demonstrate that the rate of heat transport is greater for the thermal Biot number and nanoparticles volume fraction. Further, it is noticed that the velocity of the liquid particles becomes lower for a higher magnetic field parameter.

Heat Transfer of Magnetohydrodynamic Stratified Dusty Fluid Flow through an Inclined Irregular Porous Channel

The primary objective of the study is to explore the phenomena of dusty fluid flow through an inclined irregular channel under the impact of the transversely applied magnetic field of fixed strength. The density and viscosity of the working fluid are assumed to vary along with the height of the channel as it behaves as a replica of many real world mechanisms. Hence, a stratified dusty fluid through a channel that tilts to an angle θ is the main objective of the present study. The prescribed flow is mathematically modeled and it is approached numerically under two distinct boundary conditions. The finite difference technique is employed to discretize the system of equations and solved using the Thomas algorithm. The velocity and temperature fields are discussed for different pertinent parameters which influence the flow. The friction factor and heat transfer rate are discussed as it has been a subject of interest in recent decades. The results show that the stratification decay parameter leads to enhancement in the momentum of the fluid flow. The temperature field is found to be higher in the convective boundary than the Navier slip boundary.

Pulsatile flow of thixotropic blood in artery under external body acceleration

This work presents a numerical technique for simulating non-Newtonian blood flow in human's arteries driven by an oscillating pressure gradient. The blood is considered as a thixotropic fluid and its structural properties are considered to obey Moore's thixotropic model as a constitutive equation. The equations of motion are simplified considering the flow laminar, axisymmetric and the fluid incompressible. A numerical solution is presented using finite difference method in order to compute the velocity field and wall shear stress distribution. The numerical results obtained have been validated with the analytical solution available in the literature. Furthermore, the effect of the structural properties, the average of the pressure gradient and the external acceleration on the velocity and wall shear stress distribution is investigated. These results reveal the influence of the different parameters studied on the pipe flow response of the thixotropic fluid.

Entropy Generation and Statistical Analysis of MHD Hybrid Nanofluid Unsteady Squeezing Flow between Two Parallel Rotating Plates with Activation Energy

Squeezing flow is a flow where the material is squeezed out or disfigured within two parallel plates. Such flow is beneficial in various fields, for instance, in welding engineering and rheometry. The current study investigates the squeezing flow of a hybrid nanofluid (propylene glycol–water mixture combined with paraffin wax–sand) between two parallel plates with activation energy and entropy generation. The governing equations are converted into ordinary differential equations using appropriate similarity transformations. The shooting strategy (combined with Runge–Kutta fourth order method) is applied to solve these transformed equations. The results of the conducted parametric study are explained and revealed in graphs. This study uses a statistical tool (correlation coefficient) to illustrate the impact of the relevant parameters on the engineering parameters of interest, such as the surface friction factor at both plates. This study concludes that the squeezing number intensifies the velocity profiles, and the rotating parameter decreases the fluid velocity. In addition, the magnetic field, rotation parameter, and nanoparticle volumetric parameter have a strong negative relationship with the friction factor at the lower plate. Furthermore, heat source has a strong negative relationship with heat transfer rate near the lower plate, and a strong positive correlation with the same phenomena near the upper plate. In conclusion, the current study reveals that the entropy generation is increased with the Brinkman number and reduced with the squeezing parameter. Moreover, the results of the current study verify and show a decent agreement with the data from earlier published research outcomes.

ABC Fractional Order Vaccination Model for Covid-19 with Self-Protective Measures

A mathematical model delineating the control strategies in transference of Covid-19 pandemic is examined through Atangana–Baleanu Caputo type fractional derivatives. The total count of people under observation is classified into Susceptible, Vaccinated, Infected and Protected groups (SVIP). The designed model studies the efficiency of vaccination and personal precautions incorporated qualitatively by every individual via fixed point theorem. Stability of the system has been investigated with spectral characterisation of Ulam Hyer’s kind. Numerical interpolation has been derived by Adam’s semi-analytical technique and we have approximated the solution. We have proved the theoretical analysis through graphical simulations that vaccination and self protective interventions are the significant role to decrease the contagious expansion of the virus among the people in process.

Fractional boundary element solution of three-temperature thermoelectric problems

The primary goal of this article is to propose a new fractional boundary element technique for solving nonlinear three-temperature (3 T) thermoelectric problems. Analytical solution of the current problem is extremely difficult to obtain. To overcome this difficulty, a new numerical technique must be developed to solve such problem. As a result, we propose a novel fractional boundary element method (BEM) to solve the governing equations of our considered problem. Because of the advantages of the BEM solution, such as the ability to treat problems with complicated geometries that were difficult to solve using previous numerical methods, and the fact that the internal domain does not need to be discretized. As a result, the BEM can be used in a wide variety of thermoelectric applications. The numerical results show the effects of the magnetic field and the graded parameter on thermal stresses. The numerical results also validate the validity and accuracy of the proposed technique.

MHD Laminar Boundary Layer Flow of a Jeffrey Fluid Past a Vertical Plate Influenced by Viscous Dissipation and a Heat Source/Sink

This study investigates the effects of viscous dissipation and a heat source or sink on the magneto-hydrodynamic laminar boundary layer flow of a Jeffrey fluid past a vertical plate. The governing boundary layer non-linear partial differential equations are reduced to non-linear ordinary differential equations using suitable similarity transformations. The resulting system of dimensionless differential equations is then solved numerically using the bivariate spectral quasi-linearisation method. The effects of some physical parameters that include the Schmidt number, Eckert number, radiation parameter, magnetic field parameter, heat generation parameter, and the ratio of relaxation to retardation times on the velocity, temperature, and concentration profiles are presented graphically. Additionally, the influence of some physical parameters on the skin friction coefficient, local Nusselt number, and the local Sherwood number are displayed in tabular form.

Impact of two-phase hybrid nanofluid approach on mixed convection inside wavy lid-driven cavity having localized solid block

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Flow, heat, and mass transfer of hybrid nanofluids in a wavy chamber were addressed.

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A two-phase approach, including the Brownian motion and thermophoresis forces, was introduced.

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The drift flux of composite hybrid nanoparticles was computed.

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The concentration distribution of composite nanoparticles was investigated.

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The location of the solid block and undulation of surfaces are investigated.

Introduction:

Mixed convection flow and heat transfer within various cavities including lid-driven walls has many engineering applications. Investigation of such a problem is important in enhancing the performance of the cooling of electric, electronic and nuclear devices and controlling the fluid flow and heat exchange of the solar thermal operations and thermal storage.

Objectives:

The main aim of this fundamental investigation is to examine the influence of a two-phase hybrid nanofluid approach on mixed convection characteristics including the consequences of varying Richardson number, number of oscillations, nanoparticle volume fraction, and dimensionless length and dimensionless position of the solid obstacle.

Methods:

The migration of composite hybrid nanoparticles due to the nano-scale forces of the Brownian motion and thermophoresis was taken into account. There is an inner block near the middle of the enclosure, which contributes toward the flow, heat, and mass transfer. The top lid cover wall of the enclosure is allowed to move which induces a mixed convection flow. The impact of the migration of hybrid nanoparticles with regard to heat transfer is also conveyed in the conservation of energy. The governing equations are molded into the non-dimensional pattern and then explained using the finite element technique. The effect of various non-dimensional parameters such as the volume fraction of nanoparticles, the wave number of walls, and the Richardson number on the heat transfer and the concentration distribution of nanoparticles are examined. Various case studies for Al₂O₃-Cu/water hybrid nanofluids are performed.

Results:

The results reveal that the temperature gradient could induce a notable concentration variation in the enclosure.

Conclusion:

The location of the solid block and undulation of surfaces are valuable in the control of the heat transfer and the concentration distribution of the composite nanoparticles.

Analytical Assessment of (Al2O3–Ag/H2O) Hybrid Nanofluid Influenced by Induced Magnetic Field for Second Law Analysis with Mixed Convection, Viscous Dissipation and Heat Generation

The current study is an attempt to analytically characterize the second law analysis and mixed convective rheology of the (Al2O3–Ag/H2O) hybrid nanofluid flow influenced by magnetic induction effects towards a stretching sheet. Viscous dissipation and internal heat generation effects are encountered in the analysis as well. The mathematical model of partial differential equations is fabricated by employing boundary-layer approximation. The transformed system of nonlinear ordinary differential equations is solved using the homotopy analysis method. The entropy generation number is formulated in terms of fluid friction, heat transfer and Joule heating. The effects of dimensionless parameters on flow variables and entropy generation number are examined using graphs and tables. Further, the convergence of HAM solutions is examined in terms of defined physical quantities up to 20th iterations, and confirmed. It is observed that large λ1 upgrades velocity, entropy generation and heat transfer rate, and drops the temperature. High values of δ enlarge velocity and temperature while reducing heat transport and entropy generation number. Viscous dissipation strongly influences an increase in flow and heat transfer rate caused by a no-slip condition on the sheet.

Irreversibility minimization analysis of ferromagnetic Oldroyd-B nanofluid flow under the influence of a magnetic dipole

Studies highlighting nanoparticles suspensions and flow attributes in the context of their application are the subject of current research. In particular, the utilization of these materials in biomedical rheological models has gained great attention. Magneto nanoparticles have a decisive role in the ferrofluid flows to regulate their viscoelastic physiognomies. Having such substantial interest in the flow of ferrofluids our objective is to elaborate the melting heat transfer impact in a stretched Oldroyd-B flow owing to a magnetic dipole in the presence of entropy generation optimization. Buongiorno nanofluid model expounding thermophoretic and Brownian features are considered. Moreover, activation energy with chemical reaction is also considered. The Cattaneo-Christov heat flux model is affianced instead of conventional Fourier law. The renowned bvp4c function of MATLAB is utilized to handle the nonlinearity of the system. Impacts of miscellaneous parameters are portrayed through graphical fallouts and numeric statistics. Results divulge that the velocity and temperature profiles show the opposite trend for growing estimates of the ferromagnetic parameter. It is also noticed that the temperature ratio parameter diminishes the entropy profile. Moreover, it is seen that the concentration profile displays a dwindling trend for the Brownian motion parameter and the opposite trend is witnessed for the thermophoretic parameter.

Electroosmotically driven flow of micropolar bingham viscoplastic fluid in a wavy microchannel: application of computational biology stomach anatomy

A comprehensive mathematical model is presented to study the peristaltic flow of Bingham viscoplastic micropolar fluid flow inside a microlength channel with electro-osmotic effects. The electro-osmotic effects are produced due to an axially applied electric field. The circulation of this electric potential is calculated by utilizing Poisson Boltzmann equation. The dimensionless form of mathematical equations is obtained by using lubrication theory and Debye-Huckel approximation. We have obtained analytical solutions for the final dimensionless governing equations. Finally, the graphical results are added to further discuss the physical aspects of the problem. Electro-osmotic is mainly helping to control the flow and axial velocity decreases with an increase in the electric field but micro-angular velocity increases with an increase in electric field.

On Criticality for a Generalized Couette Flow of a Branch-Chain Thermal Reactive Third-Grade Fluid with Reynold's Viscosity Model

This research considers the third-grade liquid flow and criticality branched-chain of a thermal reaction in a Couette generalized medium with a nonlinear viscosity model. A dimensionless transformation of the system momentum and heat equations are carried out. Compared with the diffusion coefficient, the flow is stimulated by initiation reaction rate, reaction branch-chain order, non-Newtonian term, thermal Grashof number, and pressure gradient. The reactive fluid is fully exothermic with consumption of the material, and the heat exchange in the system is greater than the exchange of heat with the ambient. A semianalytical collocation weighted residual scheme is employed for the branch-chain slice bifurcation, dimensionless energy, and momentum solutions. The results show that exponential decreases in the thermal fluid viscosity can help in controlling the boundless heat produced by the Frank-Kamenetskii term and initiation reaction rate. Therefore, the results will help in stimulating positive combustion processes.

Hydromagnetic Dissipative and Radiative Graphene Maxwell Nanofluid Flow Past a Stretched Sheet-Numerical and Statistical Analysis

The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations (PDE) of mathematical model in the form of nonlinear ordinary differential equations (ODE). Further, these transformed equations are numerically solved by making use of Runge-Kutta-Fehlberg algorithm along with the shooting scheme. The significance of pertinent physical parameters on the flow of graphene Maxwell nanofluid velocity and temperature are enumerated via different graphs whereas skin friction coefficients and Nusselt numbers are illustrated in numeric data form and are reported in different tables. In addition, a statistical approach is used for multiple quadratic regression analysis on the numerical figures of wall velocity gradient and local Nusselt number to demonstrate the relationship amongst heat transfer rate and physical parameters. Our results reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. Finally, we have compared our numerical results with those of earlier published articles under the restricted conditions to validate our solution. The comparison of results shows an excellent conformity among the results.

Analytical evaluation of Oldroyd-B nanoliquid under thermo-solutal Robin conditions and stratifications

Chilling systems are important in the improved technological thermal mechanisms which are considered continuously in passive along with active heat-transference improvement procedures. Engineers recommended several approaches to upsurge heat transference of thermal structures. The pulsating flow, corrugated tube, magnetic field aspect and nanoliquids are the heat-transference improvement procedures delved continuously. In present research work, we addressed the heat-transference characteristics of non-Newtonian (Oldroyd-B) liquid towards heated stratified surface. Thermally radiative laminar flow is modeled. In addition, we accounted Buongiorno's nanoliquid model which includes Brownian along with thermophoretic diffusions. Modeling is further based on heat source, magnetohydrodynamics, dual stratification, thermal radiation and convective conditions. Mathematical system is simplified through boundary-layer idea. Similarity variables are reported with the aim to simplify complex mathematical system. Homotopy algorithm yields convergent results of non-dimensional expressions. Our study unveils diminution of thermal along with solutal fields when stratification factors are increased.

Mathematical Analysis of Pseudoplastic Polymers during Reverse Roll-Coating

This article presents a mathematical model and theoretical analysis of coating of a thin film of non-Newtonian polymers as they travel through a small space between two reverse-rotating rolls. The dimensionless forms of the governing equations are simplified with the help of the lubrication approximation theory (LAT). By using the perturbation technique, the analytical solutions for velocity, flow rate and pressure gradient were obtained. From an engineering point of view, some significant results such as thickness of the coated web, pressure distribution, separation points, separation force and power input were computed numerically. The effect of velocities ratio k and Weissenberg number We on these physical quantities is presented graphically; others are shown in tabular form. It is noted that the involved material parameters provide a mechanism to control the flow rate, pressure distribution, the thickness of coating, separation force and power input. Moreover, the separation point is shifted toward the nip region by increasing velocities ratio k.