Cattaneo-Christov Double Diffusion Research Articles

Chebyshev spectral Newton iterative analysis on unsteady oblique stagnation flow of Maxwell fluids over an oscillating-rotating disk with Cattaneo–Christov double diffusion

Oblique stagnation flow on a rotating disk is commonly observed in processes such as spinning coating and thin film deposition techniques. The investigation of the unsteady oblique stagnation point flow for Maxwell fluid over an oscillating-rotating disk embedded in a porous medium is meticulously conducted by employing the Darcy–Maxwell framework in conjunction with Cattaneo–Christov double diffusion model. A transformation of similarity is applied to reframe the governing equations into a system of non-dimensional coupled partial differential equations, whose numerical solutions are secured by the Chebyshev Spectral Newton Iterative Scheme. The outcomes underscore that an escalation in the Darcy parameter escalates the resistance within the porous medium, consequently leading to a reduction in velocity. Both the first-order slip and the second-order slip mitigate the fluid's interaction with the disk wall, leading to a retardation in flow velocity. Additionally, the presence of augmented thermal radiation parameters is observed to enhance heat transfer efficiency, resulting in a more homogenized temperature distribution. The two-dimensional and three-dimensional streamlines provide a precise depiction of the flow characteristics at the oblique stagnation point on the oscillating-rotating disk. These findings offer a theoretical foundation that can be instrumental for forthcoming research in analogous fields.

Cattaneo–Christov double diffusion model for the entropy analysis of a non-Darcian MHD Williamson nanofluid

This research is carried out to observe the fluid flow across a stratified sheet in the presence of non-linear thermal radiation. Through the process of similarity transformations, the partial differential equations (PDEs) governing the flow model are transformed into ordinary differential equations (ODEs), which are then numerically solved using the shooting method. This study comprehensively examines the influence of various flow parameters, including the inertial coefficient, magnetic parameter, Brownian motion parameter, radiation parameter, Prandtl number, thermophoresis parameter, and Brinkman number, on key thermophysical characteristics, such as the skin friction coefficient, and the rates of heat, mass, and entropy generation. Notably, the relative difference in the skin-friction coefficient increases with the Weissenberg number, ranging from approximately 1.8 to 2.5. The results indicate that reducing the Cattaneo–Christov temperature parameter decreases the temperature profile while increasing the concentration profile, whereas entropy generation initially rises with increasing Weissenberg number, but decreases near the surface.

A study of electro-magneto Darcy-Forchheimer Casson nanofluid flow under the effects of Cattaneo-Christov double diffusive model over linear vs nonlinear stretching sheets

The present study reveals that the two-dimensional incompressible Casson nanofluid saturated the porous media in the presence of Darcy-Forchheimer medium over a non-linear sheet stretching. It has immense practical applications in engineering, like paper production, solar receivers, aluminous plate cooling, plastic sheet extrusions, petroleum resources, soil physics, etc. Here, non-linear stretching is supposed to be the driving force. The electro-magnetized Cattaneo-Christov double diffusion model was imposed to enhance the heat and mass transfer along with the influences of ist order chemical reactions, Brownian diffusion, thermophoresis motion, internal heat source viscous-ohmic dissipation, and thermal radiation. The electro-magnetic impacts are uniformly normal to the direction of flow. The governing flow model, a system of highly coupled and non-linear partial differential equations, is converted into ordinary differential equations imposing appropriate similarity transformations, and solved analytically (differential transformation method via MAPLE) and numerically (Bvp4c via MATLAB). The final results are tabulated and demonstrated graphically for different control parameters. In addition, the contour graphs have been prepared. For engineering and industrial importance, a significant difference can be observed in the enhancement of heat and mass transfer through temperature and concentration profiles and tables of Nusselt as well as Sherwood numbers. Through histograms, it is concluded that the nonlinear stretching sheet provides a better heat and mass transfer rate as compared to the linear stretching sheet. The rate of heat transfer in the linear vs nonlinear stretching sheet is 25–75%, but the rate of mass transfer is 30–70%.

Magnetohydrodynamic Casson SWCNT-MWCNT/EG hybrid nanofluid flow over a stretching cylinder with Cattaneo-Christov double diffusion model

The present problem examines the flow features of a two-dimensional time-independent Casson hybrid nanofluid on a stretching cylinder with dual stratification and MHD effects. Heat and mass transfer effects are analyzed by utilizing the Cattaneo-Christov double diffusion scheme with entropy generation. Further, the energy losses due to viscous and Joulian dissipation are also considered in the problem. Due to the high thermal conductivity nature of the carbon nanotubes, which plays a crucial role in cooling systems, material sciences, electrical components and treatment of cancer cells, single and multi-walled carbon nanotube particles (SWCNT, MWCNT) are considered in the hybrid nanofluid. The carbon nanotubes are mixed with base fluid ethylene glycol (EG) to form the required hybrid nanofluid. Suitable transformations are adopted for transforming the non-linear PDEs to non-linear ODEs of the mathematical model. Then, the system of ODEs are resolved by utilizing bvp4c numerical approach in MATLAB software. The impact of the various flow pertinent parameters on the flow model are disclosed through graphs and tables and then explained elaborately. The important findings of the study reveal a reduction in the absolute value of coefficient of surface friction with the Casson and velocity slip parameters. The entropy generation rate (NG ) is diminished due to slip parameters, whereas the opposite effect is observed due to the SWCNT nanoparticle volume fraction. The thermal and mass relaxation parameters induce a significant amplification in the rates of heat and mass transport, respectively. Furthermore, it is observed that the heat and mass transfer rates of EG-based SWCNT – MWCNT hybrid nanofluid perform better than those of EG-based SWCNT nanofluid. The outcomes of the investigation exhibit an excellent agreement with the previously published results. The present analysis has applications in cancer therapy, microelectronics cooling, industrial heat generators, nuclear reactor maintenance, electrolytic condensers, and many more.

Unsteady MHD oblique stagnation point slip flow of maxwell fluid over an oscillating–stretching cylinder with Cattaneo–Christov double diffusion model

The unsteady oblique stagnation point slip flow of a Maxwell fluid over an oscillating–stretching cylinder with convective heat transfer is investigated. The evaluation of this phenomenon is facilitated by employing the Cattaneo–Christov double diffusion model. According to the oblique stagnation point flow characteristics, an ordinary differential equation about pressure is derived, and pressure terms can be corrected by solving this equation. The equations are subjected to the similarity transformation, resulting in a set of dimensionless equations. The homotopy analysis method (HAM) is subsequently utilized to obtain their solutions. The effects of various parameters on the velocity, temperature, and concentration are analyzed. It is observed that slip boundary conditions accelerate fluid flow by reducing resistance. Elevating the Schmidt number means a reduction in the mass diffusion, leading to a diminished concentration. The temperature distributions of different thermal relaxation time parameters intersect at a thermal equilibrium point. Moreover, three-dimensional plots depicting the evolution of velocity and temperature over time demonstrate excellent agreement with the flow behavior and boundary conditions. They contribute to the comprehension and prediction of time-dependent flow and heat transfer phenomena.

Heat and mass transfer analysis of a Maxwell-power-law fluid in a laminar planar jet flow with Cattaneo–Christov double diffusion theory

This paper focuses on the heat and mass transfer characteristics of a steady laminar planar jet flow of a Maxwell-power-law (MPL) fluid. MPL is a renowned fluid model with shear thinning and viscoelastic characteristics that can accurately exhibit the rheological features of polymer liquids. In the envisioned study, the MPL constitutive equation is introduced based on an experiment utilizing the Xanthan gum solution. The heat and mass equations are supported by the Cattaneo–Christov double diffusion (CCDD) concept with unique characteristics of thermal conductivity, mass diffusion, and chemical reaction. Thermal conductivity and mass diffusion coefficient are considered to be velocity gradient-dependent. The problem is addressed numerically by the bvp4c method in Matlab after applying the similarity transformations to the governing equations. The impacts of related parameters on velocity, temperature, and concentration are analyzed. Results show that an upsurge in the power-law index hinders momentum, energy, and mass transmission. An interesting phenomenon is that the variation in relaxation time can hinder or promote the heat and mass transfer of a Maxwell-power-law fluid jet before or after the intersection point, respectively. The study can provide a theoretical reference for engineering applications of jets.

MHD Darcy–Forchheimer flow and double-diffusive modeling of Maxwell fluid over rotating stretchable surface: A computational study

In this work, the Cattaneo–Christov double diffusion model is used to analyze the three-dimensional boundary layer flow of an upper-convected Maxwell fluid flowing over a bi-directional stretching surface. The model assumes that the fluid’s diffusivity is concentration-dependent, whereas dynamic viscosity and thermal conductivity are temperature-dependent; and the model takes into account the influence of the magnetic field of uniform strength. The problem is formulated using the conservation rules of mass, momentum, and energy as well as the boundary layer approximation. The resulting nonlinear system is then numerically solved using the bvp4c procedure in MATLAB. The obtained results are set forth graphically to illustrate the variations of different parameters. It is contemplated that the increase in thermal relaxation parameter results in a drop in fluid temperature while there is an enhancement in the concentration profile. Also, the temperature field has a direct relationship with the temperature-dependent viscosity. This research has proven its utility in industries where there is a need to analyze fluid flow over surfaces that can stretch in two directions.

Effect of inclined magnetic field and chemical reaction on Casson fluid flow over a stretching surface with Cattaneo–Christov double diffusion

This investigation discusses the significance of studying the behavior of non-Newtonian fluids, specifically the Casson fluid, subjected to an electrically conducting and stretching sheet. The study also explores the effects of an aligned magnetic field, Cattaneo–Christov double diffusion, viscous dissipation and chemical reactions on heat and mass transfer, respectively. The partial differential equations governing the flow problem are transformed into ordinary differential equations through the utilization of similarity transformations. Furthermore, the shooting technique is implemented in MATLAB to solve the ODEs. The influence of physical parameters, such as the magnetic field parameter, Eckert number, Prandtl number and chemical reaction parameter, on the velocity profile, temperature distribution, concentration profile, skin friction coefficient, Nusselt number and Sherwood number is studied and presented in graphical and tabular forms. It is found that increasing the Prandtl number causes a drop in the temperature profile. Moreover, the presence of thermal radiation and the Eckert number significantly amplifies the temperature distribution. When the magnetic number undergoes a substantial increase, there is a notable decrease in the velocity profile, and simultaneously, the temperature profile experiences a noticeable rise. Additionally, increase in the chemical reaction parameters leads to a decrease in the concentration profile. The skin friction coefficient, local Nusselt number and Sherwood number exhibit significant reductions as the Casson parameter increases. Additionally, a MATLAB built-in function named bvp4c is incorporated to verify the computed results. The practical implications of the Cattaneo–Christov heat flux model include microelectronics, microfluidic devices, processes involving rapid heating or cooling, such as laser welding or pulsed laser ablation and heat transfer in biological tissues.

Numerical treatment for double diffusion phenomenon with generalized heat flux effects in 3d nanomaterial flow over bi-directional stretched wall

Current study aims to numerically investigate the bi-directional flow of nanofluids in the presence of Cattaneo–Christov double diffusion for two heat sources, namely, prescribed surface temperature (PST) along with prescribed heat flux (PHF). The conventional mathematical model in partial differential equations (PDEs) of the system have been reduced into an equivalent set of ordinary differential equations (ODEs). The system dynamics in the form of approximate solutions of the ODEs is presented by Adams and Explicit Runge Kutta numerical solvers. For better understanding the influence of physical parameter of interest including Brownian movement parameter, thermophoresis parameter, concentration relaxation parameter, Schmidt number, Prandtl number, thermal relaxation parameter, temperature ratio parameter, stretching ratio parameter and Deborah number on temperature, as well as concentration profiles are presented exhaustively. Appropriateness of the scheme is ascertained through close resemblance of results for different state of the art counterparts with negligible error around 10–05 to 10–09.

Impact of motile microorganisms on a Sutterby nanofluid flow over a rotating disk with Hall current and ion slip

The dynamics of partly ionized fluid flow, when subjected to a magnetic field, differ considerably from that of typical fluid flow. The main applications of the partially ionized fluids including thermal arc plasma cutting, gas discharge lamps, lighting, and plasma medicine have made them vital when discussed under the effects of the applied magnetic field. This study discusses the flow of the Sutterby nanofluid over a stretching disk with Hall and ion slip effects amalgamated with Cattaneo–Christov double diffusion. The uniqueness of the envisaged model is enriched by considering the gyrotactic microorganisms. The system of governing equations is normalized and addressed numerically by applying the bvp4c package of MATLAB software. The outcomes are depicted via graphs and in tabularized form. It is perceived that fluid velocity is affected by the Hall current parameter. For the bioconvection Lewis number, a decline in the microorganism distribution is also observed. In addition, it is also perceived that the fluid concentration is enhanced against mass diffusion relaxation stress. The validity of the envisioned model by comparing it with a published study is also a part of this exploration.

Utilization of variable thermal conductivity and diffusion coefficient on non-Newtonian Prandtl model with modified heat and mass fluxes

PurposeThis study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.Design/methodology/approachThe governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.FindingsGraphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.Originality/valueThe reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.

3D flow of variable properties viscoelastic nanofluids with impacts of Arrhenius energy and Cattaneo–Christov double-diffusion

In several situations, particularly, flow of viscoelastic nanofluids, the dynamic viscosity and thermal conductivity should be considered as variables due to their roles in various practical applications. Therefore, this article aims applying the Cattaneo–Christov double-diffusion theory to investigate the three-dimensional (3D) forced flow of second-grade viscoelastic nanofluids over a permeable stretching surface. The properties of the mixture are considered to be variables where the dynamic viscosity is exponentially varied with temperature and the thermal conductivity and Brownian motion are linearly dependent on temperature and concentration, respectively. The included medium is isotropic porous, and both heat generation and thermal radiation impacts are assumed. At the surface, the nanoparticles are either active or passively controlled, and the convective boundary conditions are considered for the surface temperature. The solution methodology is based on similarity transformations, and the numerical technique is based on 4th-order Runge-Kutta method. The major outcomes revealed that the growth in thermal relaxation time δ e and viscoelastic parameter K causes gradually decreases in temperature and nanoparticles features. Also, constant dynamic viscosity gives higher velocity features compared to the variable case. Furthermore, the considered range of thermal conductivity coefficient ε 1 gives an enhancement in rate of the heat transfer by 5.26%.

Blasius–Rayleigh–Stokes nanofluid dusty flow influenced by Cattaneo–Christov double diffusion and melting heat transfer — application of response surface methodology

This paper focuses on the study of Blasius–Rayleigh–Stokes nanofluid dusty flow with generalized Fourier and Fick laws under the influence of a transitive magnetic field. The Blasius–Rayleigh–Stokes nanofluid dusty flow has significant applications in various fields, including the design of heat exchangers, microfluidic devices and industrial processes involving the transportation of suspended particles in fluids. This paper considers the impact of melting heat transfer at the surface boundary. By employing relevant transformations, the mathematical model is transformed into a system of self-similar equations. The solution to this set of highly nonlinear equations is obtained using the bvp4c numerical method in combination with the response surface methodology (RSM) statistical approach. The results are presented through graphical illustrations and numerically calculated tabulated values. It is observed that the fitted model for the skin friction coefficient [Formula: see text] optimal. Moreover, the model parameters [Formula: see text], Q, [Formula: see text], M and L are linearly and quadratically significant in explaining the variation presented for skin friction coefficient [Formula: see text]. This indicates the response skin friction coefficient [Formula: see text] is minimized to 0.005 at [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] and is maximized to 1.387 at [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

Cattaneo–Christov double diffusive non-Newtonian nanofluid flow over a rotating disk of variable thickness influenced by swimming microorganisms and velocity slip condition

This exploration examines the effects of the Cattaneo–Christov double diffusion in the Ostwald-de-Waele nanofluid flow on a rotating disk with varying thicknesses. The incorporation of the impacts of the bioconvection microorganisms increases the stability of the nanofluids. The slip boundary constraint is taken at the disk. The flow system is based on the Buongiorno nanofluid model. The envisioned fluid flow model incorporates heat transmission properties that are affected by nanoparticle volume fraction, Brownian motion, and thermophoresis. The numerical software bvp4c method is affianced. The presented diagrams portray the correlation of the protuberant parameters with the associated profiles given with cogent arguments. It is heeded that higher estimates of the thermal and solutal relaxation parameters dwindled the thermal and mass profiles. Furthermore, the motile microorganism distribution is diminished for larger counts of the Peclet number. A comparison table is also included to justify the truthfulness of the proposed model.

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.

Microrotating chemically reactive hybrid nanomaterial in a high porous medium influenced by Cattaneo-Christov double diffusion and non-linear slip

ABSTRACT A simultaneous heat and mass transfer due to microrotating Darcy-Forchheimer flow of hybrid nanofluid over a moving thin needle is investigated. Darcy-Forchheimer medium accommodating hybrid nanofluid flow yields greater heat transfer rate, thereby leading to greater mass transfer rate over thin needle in industrial applications such as blood flow problems, aerodynamics, transportation, coating of wires, lubrication, and geothermal power generation. The thermophoresis and Brownian motion phenomena are introduced to enrich thermal treatment. Heat and mass transfer are accompanied by Cattaneo-Christov heat and mass flux. The hybrid nanofluid is radiative and dissipative in nature. Arrhenius pre-exponential factor law is introduced. Entropy generation analysis is carried out. The 4th order Runge-Kutta method along with shooting technique is devised to get requisite numerical solution of the transformed non-dimensional system of equations. Darcy-Forchheimer effect to simultaneous heat and mass transfer of microrotating hybrid nanofluid flow over thin needle subject to non-linear slip is the novelty of present study which is beyond of previous investigations. Rise in Forchheimer number (strengthening Darcy Forchheimer medium) leads to surface viscous drag decreases by 11.11% for hybrid nanofluid and 10.78% for pure nanofluid indicating the control of momentum transfer, thereby regulating heat transfer rate effectively.

Significance of Cattaneo-Christov double diffusion and induced magnetic field on Maxwell ternary nanofluid flow with magnetic response boundary

The present study delves into the significance of Cattaneo-Christov double diffusion and the induced magnetic field (IMF) on a stagnation-point flow of Maxwell ternary nanofluids. A new boundary condition with the magnetic response is designed to study superior heat and mass transfer of Maxwell ternary nanofluid combined with double diffusion and IMF. The governing equations are formulated by mathematically modeling of the current flow in a Cartesian coordinate system and solved using an improved shooting method and the Runge-Kutta method. Through the application of similarity transformations, the governing equations are transformed into a system of initial boundary value ordinary differential equations. These equations are further transformed into linear equations with initial value problems using the shooting method and subsequently solved using the Runge-Kutta method and Newton's iterative techniques. The numerical results and correlation analysis vividly demonstrate the profound influence of double diffusion and IMF on thermal and concentration patterns via graphical representations. It is found that the double diffusion and the induced magnetic field always helps to achieve lower temperature and concentration. The magnetic response boundary leads to higher heat and mass transfer efficiency for the suction case. The magnetically responsive boundary is verified to be effective for regulating the heat and mass transfer of ternary nanofluid.

Thermodynamic properties of Second-grade micropolar nanofluid flow past an exponential curved Riga stretching surface with Cattaneo–Christov double diffusion

In the current study, second-grade micropolar nanofluid flow past an exponential curved Riga sheet in the presence of Cattaneo–Christov double diffusion is studied. The slip impacts are considered. The model of governing equations in PDE’s (Partial Differential Equations) form is formulated because of the boundary layer approximation. The suitable transformations of similarity variables are defined to implement the approach of Lie symmetry method to change the set of formulated PDE’s into ODE’s. Then bvp4c scheme is adopted to numerically describe the dimensionless expressions of ODE’s. The influences of involving physical factors on the velocity, microrotation, temperature, and concentration distributions are plotted with the help of graphical figures. Numerical findings of involved parametric impacts against physically interested quantities which are skin friction, couple stress, Nusselt number, and Sherwood number are comprehensively described in tabular format. A comparison with the literature work is also conducted to check the validity of modeled problem. The values of velocity are found to be diminishing by an increment of second-grade parameter. The values of shear thickening increased and fluid viscosity enlarged but the increment of second-grade parameter ultimately fluid velocity reduced at Riga stretching curved sheet.

Active and passive control of Casson nanofluid flow on a convectively heated nonlinear stretching permeable surface with the Cattaneo–Christov double diffusion theory

The 3-D Casson nanofluid flow over a nonlinear permeable stretching surface is examined in the present work. The generalized form of Fourier’s heat flux and Fick’s mass flux are incorporated with the additional impacts of the magnetic field, chemical reaction, thermal radiation, and convective conditions for heat transfer. Buongiorno’s model is used for the analysis of Brownian motion and molecular diffusion. The flow mechanism has been formulated in the form of a nonlinear system of partial differential equations, which are converted to the nondimensional form of the system of ordinary differential equations, using the similarity substitution. The homotopy analysis method has been applied for the solution of a derived nondimensional set of differential equations. The consequences of flow constraints on the energy, mass, and velocity fields are presented. It has been noted that the mass and energy curves are the increasing functions of the Forchheimer number, porosity factor, Hartman number, and thermophoresis parameters. Furthermore, it is found that compared to passive control, active control of nanoparticles gives a higher rate of energy transmission.

Analyses of entropy generation and Hall influence in the Cattaneo–Christov double diffusive radiative Non-Darcy flow of a Casson nanofluid within rotating disks

The present research work interprets the entropy generation in the magnetohydrodynamic multiple slip flow of Casson nanofluid initiated due to stretching and coaxially rotating surfaces of two disks inside a non-Darcy porous medium under the dominance of the diacritic Hall current and heat generation. The energy field is explored by incorporating the consequences of distinctive thermal radiation, viscous dissipation, and Joule heating. The present study overcomes the barrier of heat and mass transport by annexing Cattaneo–Christov double diffusion effects. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with multiple slip boundary conditions. A compatible similarity transformation comprised in the current study is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via dispensing the successive linearization method. The present article deals with an in-depth exploration of diagnostic flow parameters’ attributes against the flow field and efficient physical quantities with the help of distinctive graphs and tables. As per regression analysis, the maximum relative error for the regression model on the skin friction coefficient in the radial direction ranging from .0097236 to .017225% is less than that of the other physical quantities. Besides, augmenting the thermophoretic diffusion boosts diluting the concentration of nanoparticles.