Impact of Cattaneo–Christov heat flux on MHD nanofluid flow and heat transfer between parallel plates considering thermal radiation effect

Cattaneo-Christov heat flow model at mixed impulse stagnation point past a Riga plate: Levenberg-Marquardt backpropagation method

Applications of artificial intelligence (AI) via soft computing procedures have attracted the attention of researchers due to their effective modeling, simulation procedures, and detailed analysis. In this article, the designing of intelligence computing through a neural network that is backpropagated with the Levenberg-Marquardt method (NN-BLMM) to study the Cattaneo-Christov heat flow model at the mixed impulse stagnation point (CCHFM-MISP) past a Riga plate is investigated. The original model CCHFM-MISP in terms of PDEs is converted into non-linear ODEs through suitable similarity variables. A data set is generated for all scenarios of CCHFM-MISP through Lobatto IIIA numerical solver by varying Hartman number, velocity ratio parameter, inverse Darcy number, mixed impulse variable, non-dimensional constraint, Eckert number, heat generation variable, Prandtl number, thermal relaxation variable. To find the physical impacts of parameters of interest associated with the presented fluidic system CCHFM-MISP, the approximate solution of NN-BLMM is carried out by performing training (80 %), testing (10 %), and validation (10 %), and then the results are equated with the reference data to ensure the perfection of the proposed model. Through MSE, state transition, error histogram, and regression analysis, the outcomes of NN-BLMM are presented and analyzed. The graphical illustration and numerical outcomes confirm the authentication and effectiveness of the solver. Moreover, mean square errors for validation, training and testing data points along with performance measures lie around 10-10 and the solution plots generated through deterministic (Lobatto IIIA) approach and stochastic numerical solver are matching up to 10-6, which surely validate the solver NN-BLMM. The outcomes of M and B on velocity present the similar impacts. The velocity of material particles decreases under D a while, it increases through velocity ratio and magnetic parameters.

Computational analysis of Darcy-Forchheimer relation, reduced gravity, and external applied magnetic field influence on radiative fluid flow and heat transfer past a sphere: Finite difference method

The study of radiation, Darcy-Forchheimer relation, and reduced gravity, effects on magnetohydrodynamic flow across a solid sphere immersed in porous material, is the focus of the current work. Coupled and nonlinear partial differential governing equations, are established to model the studied configuration. By using appropriate scaling variables, the resultant set of governing equations is converted to its dimensionless form. Based on these established equations, a numerical algorithm is written based on the finite element approach to solve the considered problem. A verification of the validity of the proposed model is done by comparing with already published results. Furthermore, to check the precision of solutions, a grid independence test has been accomplished. The unknown variables, such as fluid velocity and temperature, and their gradients are evaluated. This investigation's main objective is to demonstrate how the Darcy-Forchheimer law and reduced gravity due to density difference affect the natural convective heat transfer across a solid sphere immersed in a porous medium. Results show that the flow intensity decreases with the magnetic field parameter, local inertial coefficient, Prandtl number, and porosity parameter and becomes more important by increasing the reduced gravity and radiation parameters. In addition, the temperature increases with the inertial coefficient, porosity parameter, Prandtl number, radiation parameter, and magnetic field parameter and get declined with the reduced gravity parameter.

Linear and Quadratic Radiation of Dynamical Non-Fourier Flux in a Disk Flow with the Suspension of Hybrid Nanoparticles

Considering putting in diverse nanoparticles to the base fluid is the latest technique to increase the thermal accomplishment of ordinary fluids. for the present investigation, the flow and heat transfer of nanofluids over a spinning disk with an invariable stretching pace is observed. The non-Fourier flux, magnetic field, and radian heat have all been paid regard to. The nanoparticle used here is Graphene with water as a base fluid. The governing equations are reshaped by utilizing Von Karman transformation and worked it out numerically via boundary value problem solver (bvp5c). We also provided some of the results with magnetic field and beside magnetic field cases and found disparity in both circumstances. Results pointed out that with little proliferation in stretching force constant, the skin friction and the local Nusselt number, the velocity in radial and axial paths improved, when the velocity in the tangential trend and the thermal boundary layer thickness reduce, significantly.

A New Explicit Numerical Schemes for Time-Dependent PDEs with Application to Pressure Driven Fluid Flow in a Rectangular Duct

A modified class of temporal discretization schemes for partial differential equations (PDEs) is proposed, explicit and second to fifth-order accurate in time. In time, the stability region of the proposed modified second-order scheme is larger than the standard second-order Adams–Bashforth method constructed on two time levels. A modification made for the Du Fort–Frankel method was also implemented in the proposed second-order scheme, which permits the little larger stability region, but the scheme becomes first-order accurate. Since the Du Fort–Frankel method cannot be employed without a modification of averaging in time levels, the proposed second-order scheme can be used without any modification. The proposed modified scheme with different orders in space and second orders in time was implemented for heat and mass transfer of chemically reactive fluid flow in a rectangular duct. The flow is generated due to applying different pressure gradients. The contour plots of velocity, temperature, and concentration profiles are portrayed at different pressure gradients; Péclet number in heat transfer, Péclet number in mass transfer, reaction parameter, and at different times. In addition, stability and convergence conditions for the considered system of linear and non-linear PDEs consisting of non-dimensional momentum, energy, and concentration equations were found for two cases. The displayed graphs depict the transfer of heat in the fluid, which rises due to heated boundaries, and the transfer of mass in the fluid at various moments. Classical models can be solved using the proposed method, which has a faster convergence rate than the standard or classical approach. This approach is illustrated through computer simulations that demonstrate its key computational features. It is believed that the data presented in this study will serve as a useful source for future fluid flow investigations to be conducted in an industrial setting within an enclosed area.

Radiative MHD flow of Rivlin–Ericksen nanofluid of grade three through porous medium with uniform heat source

Background

The paper investigates the analytical and numerical solution of the radiation effect on MHD flow of Rivlin–Ericksen nanofluid of grade three through a porous medium with a uniform heat source between two vertical flat plates. The governing equations are solved analytically using multi-step differential transform method (MDTM) and numerically using finite difference method (FDM) and shooting method by designing MATLAB and Mathematica algorithms. The study discovered that the MDTM, FDM, and shooting methods are effective for solving nonlinear differential equations like this one.

Results

Graphs and tables show the influence of different parameters on velocity and temperature. Figures and tables show the comparisons between current outcomes and previous results that are accessible.

Conclusions

The present results showed that the analytical and numerical solutions agree well with previously published outcomes.

Darcy–Forchheimer Relation Influence on MHD Dissipative Third-Grade Fluid Flow and Heat Transfer in Porous Medium with Joule Heating Effects: A Numerical Approach

The current investigations are carried out to study the influence of the Darcy–Forchheimer relation on third-grade fluid flow and heat transfer over an angled exponentially stretching sheet embedded in a porous medium. In the current study, the applied magnetic field, Joule heating, thermaldiffusion, viscous dissipation, and diffusion-thermo effects are incorporated. The proposed model in terms of partial differential equations is transformed into ordinary differential equations using suitable similarity transformation. The reduced model is then solved numerically with the help of MATLAB built-in function bvp4c.The numerical solutions for velocity profile, temperature profile, and mass concentration under the effects of pertinent parameters involved in the model are determined and portrayed in graphical form. The graphical effects of the skin friction coefficient, the Nusselt number, and the Sherwood number are also shown. From the displayed results, we conclude that when the Joule heating parameter is enlarged, the velocity and the temperature of the fluid are increased. We observed that while enhancing the viscous dissipation parameter (Eckert number) the fluid’s velocity and temperature increase but decreases the mass concentration. By increasing the values of the thermal-diffusion parameter, the velocity distribution, the temperature field, and the mass concentration increase. When the diffusion–thermo parameter rises, the velocity field and the temperature distribution increase, and the reverse scenario is seen in the mass concentration. The results of the current study are compared with already published results, and a good agreement is noted to validate the current study.

Significance of Chemical Reaction and Lorentz Force on Third-Grade Fluid Flow and Heat Transfer with Darcy–Forchheimer Law over an Inclined Exponentially Stretching Sheet Embedded in a Porous Medium

The combined impact of a linear chemical reaction and Lorentz force on heat and mass transfer in a third-grade fluid with the Darcy–Forchheimer relation over an inclined, exponentially stretching surface embedded in a porous medium is investigated. The proposed process is mathematically expressed in terms of nonlinear and coupled partial differential equations, with the symmetry of the conditions normal to the surface. To solve the mathematical model of the proposed phenomenon, the partial differential equations are first reduced to ordinary differential equations; then, MATLAB built-in Numerical Solver bvp4c is used to obtain the numerical results of these equations. The influence of all the pertinent parameters that appeared in the flow model on the unknown material properties of interest is depicted in the forms of tables and graphs. The physical attitude of the unknown variables is discussed with physical reasoning. From the numerical solutions, it is inferred that, as Lorentz force parameter is increased, the velocity of the fluid decreases, but fluid temperature and mass concentration increase. Thisis due to the fact that Lorentz force retards the motion of fluid, and the increasing resistive force causes the rise in the temperature of the fluid. It is also noted that, owing to an increasein the magnitude of chemical reaction parameter , the velocity profile and the mass concentration decline as well, but the fluid temperature increases in a reasonable manner. It is noted that, by augmenting the values of the local inertial coefficient and the permeability parameter , the velocity field decreases, the temperature field increases, and mass concentration also increases with reasonable difference. Increasing values of Prandtl number results in a decrease in the profiles of velocity and temperature. All the numerical results are computed at the angle of inclination . The current results are compared with the available results in the existing literature for thisspecial case, and there is good agreement between them that shows the validation of the present study. All the numerical results show asymptotic behavior by satisfying the given boundary conditions.

The improved thermal efficiency of Prandtl-Eyring hybrid nanofluid via classical Keller box technique

Prandtl-Eyring hybrid nanofluid (P-EHNF) heat transfer and entropy generation were studied in this article. A slippery heated surface is used to test the flow and thermal transport properties of P-EHNF nanofluid. This investigation will also examine the effects of nano solid tubes morphologies, porosity materials, Cattaneo-Christov heat flow, and radiative flux. Predominant flow equations are written as partial differential equations (PDE). To find the solution, the PDEs were transformed into ordinary differential equations (ODEs), then the Keller box numerical approach was used to solve the ODEs. Single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) using Engine Oil (EO) as a base fluid are studied in this work. The flow, temperature, drag force, Nusselt amount, and entropy measurement visually show significant findings for various variables. Notably, the comparison of P-EHNF's (MWCNT-SWCNT/EO) heat transfer rate with conventional nanofluid (SWCNT-EO) results in ever more significant upsurges. Spherical-shaped nano solid particles have the highest heat transport, whereas lamina-shaped nano solid particles exhibit the lowest heat transport. The model's entropy increases as the size of the nanoparticles get larger. A similar effect is seen when the radiative flow and the Prandtl-Eyring variable-II are improved.

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%.

Thermal Transport Investigation in Magneto-Radiative GO-MoS2/H2O-C2H6O2 Hybrid Nanofluid Subject to Cattaneo-Christov Model

Currently, thermal investigation in hybrid colloidal liquids is noteworthy. It has applications in medical sciences, drug delivery, computer chips, electronics, the paint industry, mechanical engineering and to perceive the cancer cell in human body and many more. Therefore, the study is carried out for 3D magnetized hybrid nanofluid by plugging the novel Cattaneo–Christov model and thermal radiations. The dimensionless version of the model is successfully handled via an analytical technique. From the reported analysis, it is examined that Graphene Oxide-molybdenum disulfide/C₂H₆O₂-H₂O has better heat transport characteristics and is therefore reliable for industrial and technological purposes. The temperature of Graphene Oxide GO-molybdenum disulfide/C₂H₆O₂-H₂O enhances in the presence of thermal relaxation parameter and radiative effects. Also, it is noted that rotational velocity of the hybrid nanofluid rises for stronger magnetic parameter effects. Moreover, prevailed behavior of thermal conductivity of GO-molybdenum disulfide/C₂H₆O₂-H₂O is detected which shows that hybrid nanofluids are a better conductor as compared to that of a regular nanofluid.

Cattaneo-Christov (CC) heat flux model for nanomaterial stagnation point flow of Oldroyd-B fluid

Background Magnetohydrodynamic (MHD) stagnation point flow of Oldroyd-B nanoliquid is discussed in presence of Cattaneo-Christov mass and heat fluxes. Impacts of Brownian motion and thermophoresis are discussed. Convergent solution for nonlinear analysis are organized for velocity, temperature and concentration. Method Average residual error is calculated with the help of optimal homotopy analysis method (OHAM). Results Prominent features of interesting parameters on concentration, velocity and temperature are scrutinized. Velocity field has reverse trend for Deborah number against retardation and relaxation times. Temperature and concentration have similar results versus thermophoresis parameter. Conclusions: 1: Velocity has opposite impact for Deborah number for relaxation and retardation time. 2: Velocity boosts up for higher ratio parameter. 3: Velocity against magnetic parameter is decreased. 4: Thermal upsurges versus thermal relaxation time parameter. 5: Outcomes of thermophoretic parameter and Brownian motion parameter on temperature are quantitatively similar. 6: Concentration boosts up via Brownian parameter. 7: Concentration have similar characteristics for both Prandtl number and thermophoretic parameter.

On the numerical simulation of stagnation point flow of non-Newtonian fluid (Carreau fluid) with Cattaneo-Christov heat flux

BACKGROUND

This research article is devoted to evaluating the impact of Cattaneo-Christov heat in MHD stagnation point flow over a stretched and shrinking surface of the cylinder. MHD liquid of Carreau fluid is considered. Flow is generated due to stretching and shrinking aspects. The energy equation is developed in the presence of Cattaneo-Christov heat flux, where thermal relaxation time plays an important role in the heat transport.

METHOD

The appropriate transformations are employed to solve a differential system via shooting method (bvp4c).

RESULTS

The velocity, skin friction coefficient, temperature and Nusselt number are discussed versus different pertinent flow variable graphically. Over results indicate that the velocity distribution decreases against larger magnetic power law index and Weissenberg number. Temperature field diminishes via Prandtl number and thermal relaxation variable. Engineering quantities are discussed graphically. Magnitude of skin friction or velocity gradient upsurges versus magnetic parameter. Moreover, temperature gradient or Nusselt number shows the increasing impact via Prandtl number. Main observations of the considered flow problem are listed as concluding remarks.

Theoretical and mathematical analysis of entropy generation in fluid flow subject to aluminum and ethylene glycol nanoparticles

BACKGROUND

Here we have conducted a magnetohydrodynamic (MHD) flow of viscous material with alumina water and ethylene glycol over a stretched surface. The flow is discussed with and without effective Prandtl number. MHD liquid is considered. Electric field is absent. Effect of uniform magnetic field is taken in the vertical direction to the surface. Influence of thermal radiation as well as Joule heating are taken into account for both aluminum oxide-water and aluminum oxide-Ethylene glycol nanofluids. Velocity slip and melting heat effects are considered.

METHODS

The nonlinear flow expressions are numerically solved via ND-solve technique (built-in-Shooting).

RESULTS

The physical impacts of flow variables like mixed convection parameter, magnetic parameter, Reynold number, Eckert number, melting parameter and heat source/sink parameter are graphically discussed. Moreover, entropy generation (irreversibility) and Bejan number are discussed graphically through various flow variables. Physical quantities like skin friction coefficient and Sherwood and Nusselt numbers are numerically calculated and discussed through Tables.

CONCLUSIONS

Impact of magnetic and slip parameters on the velocity field show decreasing behavior for both effective and without effective Prandtl number. Temperature field increases for both effective and without effective Prandtl number for higher values of magnetic and radiative parameters. Entropy number is an increasing function of Reynolds number while Bejan number shows opposite impact against Reynolds number. Moreover, heat transfer rate upsurges versus larger melting and radiative parameter.

Impact of generalized Fourier’s law and Fick’s law for MHD flow of Ag‒H2O and TiO2‒H2O nanomaterials

Purpose

The purpose of this paper is to investigate the effect of inclined magnetic field, variable viscosity and Cattaneo–Christov heat and mass flux theories on the steady MHD free convective boundary layer flow of viscous, incompressible and electrically conducting water-driven silver and titanium-oxide nanofluids over a vertical stretching sheet.

Design/methodology/approach

The boundary layer equations of momentum, energy and nanoparticle concentration are partial differential equations in nature, which are reduced to nonlinear ordinary differential equations by means of similarity transformations. The resulting nonlinear equations are solved analytically by means of optimal homotopy analysis method.

Findings

Assessments with numerical results are performed and are found to be in an excellent agreement. Numerical results of the skin friction factor, the local Nusselt number and the local Sherwood number are obtained through tables. The effects of various physical parameters on the velocity, temperature and nanoparticles fraction are incorporated through graphs. The study analyzes the efficiency of heat transfer of nanofluids in cooling plants and rubber sheets.

Originality/value

No research works have been conducted to evaluate the effects of various physical phenomena on the copper and titanium nanofluids flow.

Darcy-Forchheimer nanofluidic flow manifested with Cattaneo-Christov theory of heat and mass flux over non-linearly stretching surface

This research article aims to disclose the features of nanofluidic flow manifested with Cattaneo-Christov model of heat and mass flux over non-linearly stretching surface. An incompressible visco-elastic nanofluid saturates the given porous medium through Darcy-Forchheimer relation. A non-uniformly induced magnetic effect is considered to accentuate the electro-magnetic and thermal conductivity of the base fluid. The model is restricted to small magnetic Reynolds. Boundary layer assumptions are incorporated for the given flow model. Governing equations are remodeled into non-linear ordinary differential equations through transformations. So formulated nonlinear system is solved through homotopy analysis method (HAM) to achieve series solutions for velocity field, concentration of nanoparticles and temperature distribution. It is noticed that the temperature distribution and corresponding thermal boundary layer pattern shows declination for Cattaneo-Christov model of heat and mass flux as compared to classical Fourier's law of heat flux/conduction. Furthermore, the intensive resistance offered by the addition of porosity factor in the flow model results in rise of temperature profile, however, opposite behavior is noticed in concentration of nanoparticles. The wall-drag intensity, the heat flux and the mass flux are discussed on the premise of numerical information obtained upon simulation of the problem.

Entropy Analysis of 3D Non-Newtonian MHD Nanofluid Flow with Nonlinear Thermal Radiation Past over Exponential Stretched Surface

The present study characterizes the flow of three-dimensional viscoelastic magnetohydrodynamic (MHD) nanofluids flow with entropy generation analysis past an exponentially permeable stretched surface with simultaneous impacts of chemical reaction and heat generation/absorption. The analysis was conducted with additional effects nonlinear thermal radiation and convective heat and mass boundary conditions. Apposite transformations were considered to transform the presented mathematical model to a system of differential equations. Analytical solutions of the proposed model were developed via a well-known homotopy analysis scheme. The numerically calculated values of the dimensionless drag coefficient, local Nusselt number, and mass transfer Nusselt number are presented, with physical insights. The graphs depicting the consequences of numerous parameters on involved distributions with requisite deliberations were also a part of this model. It is seen that the Bejan number is an increasing function of the thermal radiation parameter.

Magnetohydrodynamic Nanofluid Natural Convection in a Cavity under Thermal Radiation and Shape Factor of Nanoparticles Impacts: A Numerical Study Using CVFEM

In this study, the natural convection of a magnetohydrodynamic nanofluid in an enclosure under the effects of thermal radiation and the shape factor of nanoparticles was analyzed numerically using the control-volume-based finite element method (CVFEM). Columns, spheres, and lamina are examples of the nanoparticle shapes used in the investigation. The study of nanofluid flow and heat transfer was accomplished with an extensive range of nanofluid volume fractions, radiation parameters, Hartmann numbers, Rayleigh numbers, and nanoparticle shape factors. Also, the correlation between the average Nusselt number and the influencing parameters of the current study was determined. The findings demonstrate that laminar nanoparticles have a more notable impact on the average and local Nusselt numbers than the other nanoparticle shapes.