Impact of chemical reaction on the Cattaneo-Christov heat flux model for viscoelastic flow over an exponentially stretching sheet.

In this article, the numerical solutions for the heat transfer flow of an upper-convected Maxwell fluid across an exponentially stretched sheet with a chemical reaction on the Cattaneo-Christov heat flux model have been investigated. Using similarity transformation, the controlling system of nonlinear partial differential equations was transformed into a system of ordinary differential equations. The resulting converted equations were solved numerically by a successive linearization method with the help of MATLAB software. A graphic representation was created to analyze the physical insights of the relevant flow characteristics. The findings were presented in the form of velocity, temperature, and concentration profiles. As the relaxation time parameter varied, the local Nusselt number increased. The thermal relaxation time was shown to have an inverse relationship with fluid temperature. Furthermore, the concentration boundary layer becomes thinner as the levels of the reaction rate parameter increase. The results of this model can be applicable in biological fluids and industrial situations. Excellent agreement exists between the analysis's findings and those of the previous studies.

MHD Maxwell dusty fluid in thermally stratified radiative flow with temperature-dependent thermal conductivity and Cattaneo-Christov model.

It might be very important for the polymer processing industries to comprehend how Maxwell fluids behave on a stretched cylinder. Optimizing the extrusion and drawing processes can ensure the desired product qualities while avoiding faults. The objective of this study is heat transfer analysis on a Maxwell dusty fluid flow cylindrical surface with the Cattaneo-Christov concept. We immerse the cylinder in porous media, with a two-dimensional fluid regulating the flow. Our mathematical model further considers the effects of variable thermal conductivity, radiation, viscous and joule heating, magnetic field, thermal stratification, and slip velocity. Based on the presumptions, partial differential equations (PDE's) have been used to evolve the mathematical model. Using similarity transformations, the PDE's for heat and momentum for both phases are transformed into highly nonlinear ODE's.The numerical results have been obtained on these ordinary differential equations by using the RKF-45 method. This issue's main characteristic is that it examines the scenario's liquid and dust phases throughout. Results are given both visually and tabularly for the major parameters over a velocity, temperature, skin friction coefficient, and Nusselt number. When we compared our method to a previously published paper, we discovered a decent match. The findings, which were obtained for our system, show that the velocity and thermal gradient of both the phases of fluid and dust behave in an opposite trend in favor of rising Maxwell parameter, where the curvature parameter makes the rise in the same manner. Furthermore, the thermal transport profiles for both phases decline for the rising thermal time relaxation parameter.

Comparative simulation of nonlinear radiative nano casson and maxwell fluids with periodic magnetic force and sensitivity analysis.

This study investigated cyclic magneto-hydrodynamic radiative effects in Casson and Maxwell fluids, including nonlinear radiation and Arrhenius activation energy. It promotes non-Newtonian fluid use in diverse fields like industry, manufacturing, sciences, medicine, and engineering. Using boundary layer approximations, non-dimensional equations are formulated. For numerical solutions, widely recognized explicit finite difference method (EFDM) has been utilized. To ensure the robustness of EFDM results, stability and convergence tests are performed. Exploration involve a detailed sensitivity analysis by using RSM, offering a thorough understanding of influential parameters. These analyses explore complex interactions among physical parameters, affecting Nusselt number, skin friction, and Sherwood number. Maxwell fluid's velocity is more affected by periodic magnetic force than Casson fluid, during the presence of nonlinear radiation. Additionally, nonlinear thermal radiation has a greater impact on temperature and concentration profiles compared to linear radiation for both fluids. Moreover, Casson fluid has a stronger influence on the average heat transfer rate compared to Maxwell fluid with nonlinear thermal radiation which is 8.6 % greater than the Maxwell fluid. On the other hand, at constant thermal radiation (Ra), due to decrease of Brownian motion (Nb), the rate of heat transfer is reduced by 1.2 % and 0.3 % respectively for Maxwell and Casson fluid. Also, for thermophoresis parameter (Nt), this rate is reduced by 2 % and 1.6 % respectively. The investigation also revealed that the Ra exhibits a positive sensitivity towards average Nusselt number, while Nb and Nt are displayed a negative sensitivity.

The significance of chemical reaction, thermal buoyancy, and external heat source to optimization of heat transfer across the dynamics of Maxwell nanofluid via stretched surface.

Energy loss during the transportation of energy is the main concern of researchers and industrialists. The primary cause of heat exchange gadget inefficiency during transportation was applied to traditional fluids with weak heat transfer characteristics. Instead, thermal devices worked much better when the fluids were changed to nanofluids that had good thermal transfer properties. A diverse range of nanoparticles were implemented on account of their elevated thermal conductivity. This research addresses the significance of MHD Maxwell nanofluid for heat transfer flow. The flow model comprised continuity, momentum, energy transport, and concentration equations in the form of PDEs. The developed model was converted into ODEs by using workable similarities. Numerical simulations in the MATLAB environment were employed to find the outcomes of velocity, thermal transportation, and concentration profiles. The effects of many parameters, such as Hartman, Deborah, buoyancy, the intensity of an external heat source, chemical reactions, and many others, were also evaluated. The presence of nanoparticles enhances temperature conduction. Also, the findings are compared with previously published research. In addition, the Nusselt number and skin friction increase as the variables associated with the Hartman number and buoyancy parameter grow. The respective transfer rates of heat are 28.26 % and 38.19 % respectively. As a result, the rate of heat transmission increased by 14.23 % . The velocity profiles enhanced while temperature profiles declined for higher values of the Maxwell fluid parameter. As the external heat source increases, the temperature profile rises. Conversely, buoyancy parameters increase as it descends. This type of problem is applicable in many fields such as heat exchangers, cooling of electronic devices, and automotive cooling systems.

Numerical modeling of a MHD non-linear radiative Maxwell nano fluid with activation energy.

The present research explores linear as well as nonlinear radiation patterns based on the MHD non-Newtonian (Maxwell) nanofluid flow having Arrhenius activation energy. This study's core focus is MHD properties in non-Newtonian fluid dynamics and boundary layer phenomena analysis. It initiates with time-dependent equations, employing boundary layer approximations. Extensive numerical computations, executed with custom Compact Visual Fortran code and the EFD method, provide profound insights into non-Newtonian fluid behavior, revealing intricate force interactions and fluid patterns. To check the stability of the solution, a convergence and stability analysis is performed. With the values of ΔY = 0.25, Δτ = 0.0005, and ΔX = 0.20; it is found that the model convergence occurs to the Lewis number, Le > 0.016 as well as the Prandtl number, Pr > 0.08. In this context, investigating non-dimensional results that depend on multiple physical factors. Explanation and visual representations of the effects of different physical characteristics and their resultant temperatures, concentrations, and velocity profiles are provided. As a result of the illustrations, the skin friction coefficient and Sherwood number, which are calculated, as well as Nusselt values, have all come up in discussion. Additionally, detailed representations of isothermal lines and streamlines are implemented, and it is pointed out that the development of these features occurs at the same time as Brownian motion. Furthermore, the temperature field for Maxwell fluid is modified due to the impression of chemical reaction as well as the Dufour number (Kr and Du). Our research demonstrates the superior performance of non-Newtonian solutions, notably in cases involving activation energy and nonlinear radiation. This paradigm shift carries significant implications. In another context, the interplay between Maxwell fluid and nonlinear radiation is notably affected by activation energy, offering promising applications in fields like medicine and industry, particularly in groundbreaking cancer treatment approaches.

A comparative study on the rheological properties of upper convected Maxwell fluid along a permeable stretched sheet.

The objective of this paper is to examine the flow of a non-Newtonian Maxwell fluid induced by a permeable stretching sheet in motion within a porous medium. The research incorporates the Cattaneo-Christov heat flux model to study the heat transfer process. The utilization of the Cattaneo-Christov heat flux approach becomes relevant in scenarios involving materials with high thermal conductivity or during short time intervals. Consequently, the current investigation holds significant importance. It is assumed that the viscosity of the Maxwell fluid changes exponentially as the temperature changes. The modeling of the physical phenomena being investigated takes into account the effects of a magnetic field, thermal radiation, velocity, and thermal slip conditions. In this study, the viscous dissipation phenomenon is taken into account because it can have notable impacts on the temperature and viscosity of the fluid, and is known to play a crucial role in fluid flow phenomena. The equations developed to model fluid flow are transformed into nonlinear ordinary differential equations through the use of appropriate similarity transformations. The focus of the research revolves around investigating the numerical solution of ordinary differential equations accompanied by boundary conditions using the shooting technique. The findings are then showcased via tables and graphs and scrutinized in order to arrive at conclusions. Furthermore, the precision of the present findings was evaluated by contrasting the heat transfer rate with outcomes that were previously published. Based on the obtained outcomes, it can be concluded that both the Eckert number and thermal radiation have a comparable enhancing influence, whereas the thermal relaxation parameter and thermal slip parameter exhibit opposing effects.

Impact of solid-fluid interfacial layer and nanoparticle diameter on Maxwell nanofluid flow subjected to variable thermal conductivity and uniform magnetic field.

The utilization of Maxwell fluid with nanoparticle suspension exhibits promising prospects in enhancing the efficacy of energy conversion and storage mechanisms. They have the potential to be utilized in sophisticated cooling systems for power generation facilities, thereby augmenting the overall energy efficacy. Keeping this in mind, the current research examines the Maxwell nanofluid flow over a rotating disk with the impact of a heat source/sink. The present study centers on the examination of flow characteristics in the existence of a uniform magnetic field. The conversion of governing equations into ordinary differential equations is achieved using appropriate similarity variables. To derive the Nusselt number (Nu) and skin friction (SF) model related to the flow and temperature parameters, the suggested back-propagation artificial neural networking (ANN) technique is used. The Runge-Kutta-Fehlberg fourth-fifth order (RKF-45) method is used to solve the reduced equations and produce the necessary data to create the Nu and SF model. Both the Nu and SF models require 1000 data for training the network, respectively. Graphs are utilized to communicate numerical outcomes. The results concluded that the upsurge in magnetic parameter drops the velocity profile but advances the heat transport. Rise in the thermal conductivity parameter, increases the heat transport.

Effectiveness of thermal radiations and homogeneous-heterogeneous reactions in Maxwell flow field across a rotating cylinder.

This paper investigates the impact of cubic autocatalysis on energy transport in Maxwell fluid flow induced into a rotating cylinder inspired by a solar radiative surface. The homogeneous-reaction is assumed to be furnished by the kinetics of isothermal cubic autocatalytic and the heterogeneous reaction by kinetics of first order. To prevent induced axial secondary flow, the cylinder's rotation is maintained at a constant rate. The characteristics of thermal radiation are also investigated to regulate the pace of heat transmission. A magnetic beam is projected in the upward radial direction to control the fluid momentum. A suitable flow ansatz is used to convert the entire physical problem of thermal energy transmission and fluid flow from partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). Results obtained numerically with the bvp4c approach are presented graphically and explained physically. It is observed that by flourishing the Reynolds parameter, the penetration depth decreases. Further, when the thermal relaxation period increases, the temperature field degrades. Moreover, when the homogeneous-heterogeneous reaction's strength is increased, a reduction in fluid concentration is shown.

Significance of improved heat conduction on unsteady axisymmetric flow of Maxwell fluid with cubic autocatalysis chemical reaction.

This paper investigates the effect of chemical reactions on the flow of magnetized Maxwell fluid generated by an unsteady stretching surface. The thermal transport phenomenon is analyzed by using the Cattaneo-Christov theory. By applying the appropriate similarity transformations, the governing equations of motion turn into a set of nonlinear differential equations. For the velocity, temperature, and concentration fields, the resultant equations are then solved as series solutions using the homotopy analysis approach. Using graphical representations, the physical behavior of significant factors is examined in depth. The analysis reveals that higher Maxwell parameter values reduce the flow field while increasing energy transportation in the fluid flow. Further, it is noted that thermal distribution declines for the higher values of the thermal relaxation parameter. Additionally, the solutal distribution bootup for the increasing values of Schmidt number while it shows a decreasing trend for homogeneous and heterogeneous reactions strength. In order to verify our findings, a comparison to earlier research is also included.

Numerical simulation of the fractional Maxwell fluid flow in locally narrow artery.

Research on hemorheology and blood flow behavior in non-uniform vessels is of extreme significance for diagnosis and treatment of many cardiovascular diseases. The aim of this study is to reveal the hemodynamics in stenotic vessels, and provide a reference for formulating a clinical operation plan. A set of rheological data of human blood at 37° is utilized in the paper to construct the fractional Maxwell constitutive equation of blood. Consequently, the continuity and momentum equations of a fractional Maxwell fluid passing through a stenosis artery in a two-dimensional cylindrical coordinate system are established. With the help of the vorticity and stream function, the finite difference method combined with the fractional order derivative L1 algorithm is applied to acquire the numerical solutions of the velocity, wall shear stress and intravascular pressure gradient, and the validity of the algorithm is verified. Furthermore, the effects of the stenosis degree, stenosis shoulder length, various Reynolds numbers and fractional parameter α on the blood flow characteristics in stenosis are analyzed.

Alternating Current Electroosmotic Flow of Maxwell Fluid in a Parallel Plate Microchannel with Sinusoidal Roughness.

The EOF of a viscoelastic Maxwell fluid driven by an alternating pressure gradient and electric field in a parallel plate microchannel with sinusoidal roughness has been investigated within the Debye-Hückel approximation based on boundary perturbation expansion and separation of variables. Perturbation solutions were obtained for the potential distribution, the velocity and the mean velocity, and the relation between the mean velocity and the roughness. There are significant differences in the velocity amplitudes of the Newtonian and Maxwell fluids. It is shown here that the velocity distribution of the viscoelastic fluid is significantly affected by the roughness of the walls, which leads to the appearance of fluctuations in the fluid. Also, the velocity is strongly dependent on the phase difference θ of the roughness of the upper and lower plates. As the oscillation Reynolds number ReΩ increases, the velocity profile and the average velocity um(t) of AC EOF oscillate rapidly but the velocity amplitude decreases. The Deborah number De plays a similar role to ReΩ, which makes the AC EOF velocity profile more likely to oscillate. Meanwhile, phase lag χ (representing the phase difference between the electric field and the mean velocity) decreases when G and θ are increased. However, for larger λ (e.g., λ > 3), it almost has no phase lag χ.

Analysis of variable mass diffusivity in Maxwell's fluid with Cattaneo-Christov and nonlinear stratification.

This investigation consists of Maxwell's fluid which describes rate type non-Newtonian fluid in best; it has great applications in engineering, technology and industry. Linear stretching sheet generates the flow in fluid. Flow momentum is measured with MHD effect. When Fourier's and Fick's laws are incorporated relaxation time factor then known as Cattaneo-Christov model which are implemented for heat and mass transport. The features of heat source or sink and non-linear type thermal stratification are employed with variable thermal conductivity. The features of chemical reaction and non-linear type solutal stratification are analyzed along with variable mass diffusivity. By the usage of boundary layer phenomenality in this problem, non-linear PDEs are achieved. These equations are transmuted into non-linear and non-homogeneous differential equations ramified with ordinary derivatives after applying similarity transformations. The most exclusive homotopic analysis method is used to get the analytic solutions of nonlinear and non-dimensional governing equations. The significant results of progressive parameters are dominant in this investigation. The arising parameters are examined in detail and results are shown graphically. It is found out that with the increment of time relaxation factor velocity, temperature and concentration profiles reduce. It increases the viscoelastic impacts related to stress relaxation time which makes viscoelastic materials more durable.

Modeling and Mathematical Investigation of Blood-Based Flow of Compressible Rate Type Fluid with Compressibility Effects in a Microchannel.

In this investigation, the compressibility effects are visualized on the flow of non-Newtonian fluid, which obeys the stress-strain relationship of an upper convected Maxwell model in a microchannel. The fundamental laws of momentum and mass conservation are used to formulate the problem. The governing nonlinear partial differential equations are reduced to a set of ordinary differential equations and solved with the help of the regular perturbation method assuming the amplitude ratio (wave amplitude/half width of channel) as a flow parameter. The axial component of velocity and flow rate is computed through numerical integration. Graphical results for the mean velocity perturbation function, net flow and axial velocity have been presented and discussed. It is concluded that the net flow rate and Dwall increase in case of the linear Maxwell model, while they decrease in case of the convected Maxwell model. The compressibility parameter shows the opposite results for linear and upper convected Maxwell fluid.

Insight into the Role of Nanoparticles Shape Factors and Diameter on the Dynamics of Rotating Water-Based Fluid.

This article addresses the dynamic of three-dimensional rotating flow of Maxwell nanofluid across a linearly stretched sheet subject to a water-based fluid containing copper nanoparticles. Nanoparticles are used due to their fascinating features, such as exceptional thermal conductivity, which is crucial in modern nanotechnology and electronics. The primary goal of this comprehensive study is to examine the nanoparticles size and shape factors effect on the base fluid temperature. The mathematical model contains the governing equations in three dimensional partial differential equations form, and these equations transformed into dimensionless ordinary dimensional equations via suitable similarity transformation. The bvp4c technique is harnessed and coded in Matlab script to obtain a numerical solution of the coupled non-linear ordinary differential problem. It is observed that the greater input of rotating, Deborah number, and magnetic parameters caused a decline in the fluid primary and secondary velocities, but the nanoparticles concentration enhanced the fluid temperature. Further, a substantial increment in the nanofluid temperature is achieved for the higher nanoparticle's diameter and shape factors.

On Thermal Distribution for Darcy-Forchheimer Flow of Maxwell Sutterby Nanofluids over a Radiated Extending Surface.

This study addresses thermal transportation associated with dissipated flow of a Maxwell Sutterby nanofluid caused by an elongating surface. The fluid passes across Darcy-Forchheimer sponge medium and it is affected by electromagnetic field applied along the normal surface. Appropriate similarity transforms are employed to convert the controlling partial differential equations into ordinary differential form, which are then resolved numerically with implementation of Runge-Kutta method and shooting approach. The computational analysis for physical insight is attempted for varying inputs of pertinent parameters. The output revealed that the velocity of fluid for shear thickening is slower than that of shear thinning. The fluid temperature increases directly with Eckert number, and parameters of Cattaneo-Christov diffusion, radiation, electric field, magnetic field, Brownian motion and thermophoresis. The Nusselt number explicitly elevated as the values of radiation and Hartmann number, as well as Brownian motion, improved. The nanoparticle volume fraction diminishes against Prandtl number and Lewis number.

Chemical Reaction and Internal Heating Effects on the Double Diffusive Convection in Porous Membrane Enclosures Soaked with Maxwell Fluid.

In this paper, the joint impact of the interior heating and chemical reaction on the double diffusive convective flow in porous membrane enclosures soaked by a non-Newtonian Maxwell fluid is investigated applying linear and nonlinear stability techniques. The porous enclosures are square, slender and rectangular. Using the linear stability analysis, the expression for the critical thermal Rayleigh-Darcy number, above which the convective movement occurs, is derived analytically in terms of associated physical parameters. A nonlinear stability examination reliant on the Fourier double series is executed to calculate the convective heat and mass transports of the arrangement. It is observed that the pattern of convective activity is oscillatory only in the occurrence of a relaxation parameter and the threshold value of the relaxation parameter for the occurrence of the oscillatory pattern depends on the other physical parameters. The onset of convective instability accelerates with the increasing chemical reacting parameter, the interior heating parameter, the solute Rayleigh-Darcy number, the Lewis number, the Vadasz number, and the relaxation parameter, while it delays with the heat capacity ratio. The convective heat and mass transfers increase with the solute Rayleigh-Darcy number, the Vadasz number, the relaxation parameter, and the aspect ratio (for rectangular enclosure), while it decreases with the heat capacity ratio and the aspect ratio (for slender enclosure). Additionally, the convective heat transfer enhances with the interior heating parameter, while the convective mass transfer enhances with the chemical reacting parameter and the Lewis number. The effects of Vadasz number, heat capacity ratio, and relaxation parameter are witnessed only on the oscillatory pattern of convection and unsteady convective heat and mass transfers. Further, some existing literature results are compared with the current findings.

Transient electroosmosis of a Maxwell fluid in a rotating microchannel.

The transient electroosmotic flow of Maxwell fluid in a rotating microchannel is investigated both analytically and numerically. We bring out the complex dynamics of the flow during the transience due to the combination of rotation and rheological effects. We show the regimes of operation under which our analysis holds the most significance. We also shed some light on the volumetric flow rate characteristics as dictated by the underlying flow physics. Mainly we show and analyze the various regimes of operation under which viscoelastic effects actuated by electroosmotic forcing dominate over Coriolis forces and vice versa, which has not been studied before. We also observe that the analytical solution compares well with the numerical solution. We believe that the results from the present study could potentially have far reaching applications in bio-fluidic microsystems where fluids such as blood, mucus and saliva may be involved.

Flow and heat transfer in a Maxwell liquid film over an unsteady stretching sheet in a porous medium with radiation.

A problem of flow and heat transfer in a non-Newtonian Maxwell liquid film over an unsteady stretching sheet embedded in a porous medium in the presence of a thermal radiation is investigated. The unsteady boundary layer equations describing the problem are transformed to a system of non-linear ordinary differential equations which is solved numerically using the shooting method. The effects of various parameters like the Darcy parameter, the radiation parameter, the Deborah number and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. It is observed that increasing values of the Darcy parameter and the Deborah number cause an increase of the local skin-friction coefficient values and decrease in the values of the local Nusselt number. Also, it is noticed that the local Nusselt number increases as the Prandtl number increases and it decreases with increasing the radiation parameter. However, it is found that the free surface temperature increases by increasing the Darcy parameter, the radiation parameter and the Deborah number whereas it decreases by increasing the Prandtl number.