Viscous Dissipation Effects Research Articles

Peristaltic transport of diethylene glycol-based magnesium aluminate nanofluid under the effects of viscous dissipation and Hall current

ABSTRACT The fundamental importance of peristaltic phenomena in numerous biological systems, including dialysis, heart-lung machines, urine transportation, invertebrate locomotion, and the passage of gallbladder bile into the intestines, persuaded scientists to investigate the different aspects of it over the past few years. In addition, peristaltic pumping is an important consideration in industrial processes including, roller pumps used for the transport of sanitary materials, finger pumps, cell separation, and endoscopes. Keeping such inspirational applications in mind, the present investigation is dedicated to exploring the peristaltic transport of a Cross-magneto nanofluid through a curved geometry in the presence of heat transfer. The inspection of the heat transfer is conducted by utilizing variable viscosity and ohmic heating aspects. This study also retains the characteristics of viscous dissipation, heat generation/absorption, and thermal conductivity of nanofluids. Modeling of the 2D, incompressible Cross nanofluid with peristaltic movement is carried out using a curvilinear coordinate system. The basic equations of the problem are mPodeled in the light of physical laws and then simplified by adopting the lubrication theory. The solutions of the resulting nonlinear system are computed numerically. The outcomes of the related flow parameters on the nanofluid’s temperature, pressure gradient, velocity distribution, heat transfer, streamlines pattern, and stresses at the wall are discussed through graphs. The graphical results depict that the rates of heat transfer are augmented by increasing the curvature parameter, Hartmann number, and nanoparticles’ volume fraction while decreasing the Hall parameter and temperature-dependent viscosity parameter. Moreover, the nanofluid’s temperature increases by improving the values of the heat generation parameter, whereas it decreases for the Hall parameter. Furthermore, a reduction in the axial velocity occurs near the center of the channel, when Hartmann number attains higher values.

Investigation of convective peristaltic flow of non-Newtonian fluids through a non-uniform tapered porous conduit with Ohmic heating and viscous dissipation

ABSTRACT The study of convective magnetohydrodynamic (MHD) biofluid transport through a non-uniform duct is of interest due to its applications to biomedical devices and equipment. Because of this, a comparative study of free convective peristaltic flow of non-Newtonian (Casson and Jeffrey) fluids in a tapered porous symmetric duct with Hall current and viscous dissipation effects is carried out. The proposed dimensional governing equations are converted into a system of non-dimensional partial differential equations by invoking adequate non-dimensional parameters. Furthermore, a long-wavelength approximation is used to reduce the complexity of the system. Then the reduced system of partial differential equations is solved analytically using the regular perturbation method. The fascinating features of the influential parameters on the flow characteristics are demonstrated and analyzed in depth through graphs and tables. The results demonstrate that the velocity and temperature in the Jeffrey fluid flow are larger compared to those in the Casson fluid flow. The thermal Grashof number and the Hall current parameter enhanced the pressure rise profile. This research has significant implications in biomedical devices (MRI, vitamins A and D injections, heart-lung machines, etc.) and pharmaceutical fluid preparation in biomedical sciences.

Thermal case study of magnetic radiative flow impacts on Newtonian nanofluid over a stretchable plate in absorbent: Box approach

Nanofluid technology represents a significant breakthrough in thermal engineering, with widespread applications spanning heat exchangers, cancer treatment, and heat storage systems. Despite its success in improving heat transfer rates in diverse devices, the challenge of enhancing thermal conductivity using nanoparticles looms large. This study aims to elucidate the 2D flow of nanofluid under suction/injection over a stretching wedge. It considers factors such as Brownian and thermophoretic diffusions, nonlinear heat generation, and thermal radiation. Additionally, it examines the effects of viscous dissipation and Joule heating. Through the conversion of governing nonlinear coupled partial differential equations into a system of coupled ordinary differential equations using similarity transformations, numerical solutions are obtained via the Keller-box method. The analysis delves into the significant impacts of relevant parameters on velocity, temperature, concentration, and microorganism fields, presented graphically. Notably, the findings underscore the role of solid particles in enhancing the thermal efficiency of base fluids. These investigation outcomes are vital for controlling heat transferal rates and fluid velocities throughout a variation of manufacturing processes and industrial sectors, guaranteeing the required quality of the ending product. The perceptions garnered from this research hold capacity for a broad range of industrial purposes and carry consequences through countless engineering disciplines, mostly within the range of nanotechnology.

Pulsating magnetohydrodynamic hybrid nanofluid flow with thermal radiation, viscous dissipation, and entropy generation: Application to bio-nanomedicine

The aim of this investigation is to explore the flow phenomena in two distinct hybrid nanofluids (with micropolar fluid as the base fluid) undergoing hydromagnetic pulsation between two vertical walls, accompanied by entropy generation. This study also explores the unique heat transfer characteristics of F e 3 O 4 − Ti O 2 and A l 2 O 3 − MgO hybrid nanofluids, with the effects of Ohmic heating, thermal radiation, and viscous dissipation. The goal of using hybrid nanofluids is to improve the performance of biological systems such as nano-drug delivery in arteries, magnetic bio-separation, artificial kidneys, pressure surges, magnetofection agents, biomedical engineering, cancer treatments, and brain tumor treatment. The governing partial differential equations are transformed into a system of ordinary differential equations, which are then solved numerically by a shooting technique with a fourth-order Runge-Kutta method using a bvp4c MATLAB solver. Graphical explanations are provided for the flow variables such as the velocity, the microrotation, the temperature, the entropy generation, and the Bejan number. The heat transfer rate is an increasing function of the thermal radiation parameter; when the thermal radiation parameter increases from 1 to 3 the increases in the heat transfer rates in micropolar fluid (the base fluid), first hybrid nanofluid ( F e 3 O 4 − Ti O 2 ), and second hybrid nanofluid ( A l 2 O 3 − MgO ) are respectively 55%, 51%, and 43.86%. However, while the heat transfer rate (the Nusselt number) is a diminishing function of the Hartmann number. Further, the outcomes reveal that the hybrid nanofluids with emerging physical effects are helpful to treat cancer patients, recovering the damaged tissues and cells in arteries, and various medical-related procedures.

Numerical analysis of velocity slip and magnetic Soret effect on dissipative Maxwell liquid motion about a stretching wall with heat source/sink

The main aim of present numerical analysis is to explore the effects of viscous dissipation and velocity slip on the two-dimensional steady-state viscous incompressible flow of Maxwell fluid over a stretching sheet under the infleunce of magnetic field. Novel collective effects of heat source/sink and Soret impacts have been included in the governing equations to explore the salient features of heat and mass transport mechanism. Further, the velocity slip is introduced into the boundary conditions to depict the momentum transport behavior in the flow region. A typical Maxwell fluid model is deployed to separate the non-Newtonian flow behavior from that of classical Newtonian fluids. However, the visco-elastic Maxwell fluid finds its abundant applications in various fields of engineering and medicine such as plastic sheet drawing, metallurgy, polymer sheet extrusion, chemical engineering, electronic cooling, injection molding and nuclear cooling and many others. Inspired by these applications, authors have made an attempt to disclose the magneto-thermo salient features of slip flow of Maxwell fluid over stretching wall under Soret effect. The current physical situation results the highly nonlinear coupled two-dimensional steady-state partial differential equations and which are not amenable to any of the direct techniques. Due to this, the suitable similarity transformations are deployed to reduce the dimensional complexity of the constructed partial differential equations. A robust Matlab-based bvp4c scheme is utilized as a basic tool to produce the similarity solutions of the governing equations. The computer generated numerical data is presented in view of flow, temperature and concentration profiles including physical quantities of interest like skin-friction coefficient, heat and mass transport rates for the various values of physical parameters range such as, 0 ≤ M ≤ 1 , 0 ≤ β ≤ 1 , − 0.3 ≤ λ ≤ 0.6 , − 0.2 ≤ Q ≤ 0.2 , 0 ≤ Ec ≤ 2.2 , 1.2 ≤ Pr ≤ 2.2 , 0 ≤ Sr ≤ 0.5 and 1.2 ≤ Sc ≤ 2.2 . Accordingly, it is noticed that, enhancing magnetic parameter decreases the Maxwell fluid flow and amplifies the temperature and concentration fields. Enlarging Maxwell fluid parameter decreases the velocity field and increases the temperature and concentration profiles. Amplified slip parameter diminished the Maxwell flow inside the flow regime. Increasing heat source/sink parameter amplifies the temperature field. Further, magnifying Soret number amplifies the concentration field. Magnitude of skin-friction coeffiecient enlarged with amplified magnetic and Maxwell fluid parameters. Heat and mass transport rates decayed with enhancement in heat source/sink and Soret parameters. Finally, it is described that, the present similarity solutions showing good agreement with the previously reported solutions in the literature and this fact confirms the accurateness of the used numerical method and the generated similarity solutions.

Finite difference analyses of bioconvective Williamson nanofluids stream over irregular plates with effects of nonlinear radiation and viscous dissipation

The purpose of this work is to provide a comprehensive analysis of the bioconvective Williamson nanofluid stream while considering the effects of radiation flux and viscous dissipation. The two-phase nanofluids model is applied where the impacts of the Brownian motion and thermophores are significant. This study starts with introducing the governing system in case of the irregular plane then it transforms to the regular plane. The solution methodology is based on the fully implicit finite difference method. The major results disclosed that maximizing the amplitude parameter causes a diminishing in the velocity and skin-friction coefficients. Also, lower behaviors are noted for the velocity in the case of Williamson nanofluids compared to a Newtonian nanofluid case (We = 0). Furthermore, the considered range of Biot number (1 ≤ Bi ≤ 5)causes an improvement in the surface temperature up to 71.59%.

Thermal analysis of electroosmotic flow in a vertical ciliated tube with viscous dissipation and heat source effects: implications for endoscopic applications

Thermal analysis of electroosmotic flow in a vertical ciliated tube with viscous dissipation and heat source effects: implications for endoscopic applications

Thermal performance appraisal of hybrid and nanofluid flow between a cone and a disk with variable thermal conductivity, viscous dissipation, and Joule heating

In many engineering systems, hybrid and nanofluids are influenced by their respective thermophysical characteristics. Lately, several models have been envisaged to foresee the hybrid and nanofluid attributes. The properties of hybrid nanofluids (HNFs) as potential heat transfer fluids are controlled by numerous aspects such as solid part size, volume fraction, and temperature. Considering the interesting facts of the hybrid and nanofluid flows, we in this exploration examined the thermal performance comparison of both types of fluid flows. The nanofluid and HNF are composed of molybdenum disulfide (MoS[Formula: see text]/kerosene oil and silicon dioxide–molybdenum disulfide (SiO2–MoS[Formula: see text]/kerosene oil, respectively. The flows are taken in a canonical gap between the cone and the disk. Both the cone and the disk may be rotating or stationary. The novelty of the computational model is enhanced by discussing the effects of viscous dissipation, Joule heating, and the variable thermal conductivity with convective condition. The Tawari and Das model is designed to analyze the heat transfer performance of the assumed fluid flows. The assumed fluid model is transmuted into the set of differential equations that are dealt numerically with the bvp4c MATLAB approach. The results are displayed in tables and graphical forms. For elevating estimations of the Eckert number, the heat transmission rate is found to be more significant in the disk than cone. It is also learned that hybrid nanoliquid heat transfer performance outperforms nanoliquid. The fluid velocity increases by raising the nanoparticle volume fraction [Formula: see text], and is decreasing for a higher magnetic field parameter. With the elevating estimates of thermal conductivity, it is shown that the cone transmits heat more quickly whereas the disc transmits heat more slowly. The thermal conductivity parameter increases the probability of collision of the liquid particles, that ultimately upsurges fluid heat transmission rate.

Numerical simulations of thermal heat conservation in hybrid nanofluids with chemical reaction, viscous dissipation, and inclination

In this work numerical solutions using finite difference method of hybrid nanofluids (TiO2–Cu/Water) over an inclined plate are obtained. The nanoparticles are taken of volume fraction of size less than or equal to 0.05. Heat and mass transfers are studied. Chemical reaction and viscous dissipation effect are also examined. The results are computed and plotted for various parameters such as radiation, chemical reactions, and magnetohydrodynamics. The results of skin friction, rate of heat and mass transfers are computed in tables for Prandtl number 6.2 which corresponds to water and discussed in details. The present results can be used for comparison in future research for other non-Newtonian fluids models.

Magnetized hybrid nanofluid flow across a wedge: A computational three-dimensional study

The boundary layer fluid flow past a wedge surface occurs in various industrial processes, including wire drawing, metal foaming, polymer extraction, fiber processing, and in determining the dynamic properties (shear stress, drag) of working fluids. Theoretically, the boundary layer three-dimensional flow of a magnetized hybrid nanoliquid over a wedge surface is studied with viscous dissipation and radiation effects. The flow is due to moving wedge surface and power-law free-stream velocities. The current study unifies three different classical flow problems, namely, the Blasius flow, the Hiemenz flow, and the Falkner-Skan flow. Single-phase description of hybrid nanofluid is considered, and the problem is kept realistic by considering the experimental thermophysical properties of the nanomaterial. The governing system consists of conservation of mass, momentum, and the energy equations for hybrid nanofluids. Prandtl’s boundary layer approximations are applied to study the viscous dominant fluid regimes. The entropy equation and the Bejan number are also derived. Numerical computations of self-similar equations are obtained to explore the rheological and the heat transport features against the physical parameters. The Nusselt number and the drag on the wedge surface are computed and analyzed. Of the three classical flow problems, the maximum thickness of the momentum layer occurs for the Blasius flow problem. A minimum drag force on the wedge surface occurs for lower Hartmann number values. Furthermore, an increase in the volume fraction of the hybrid nanoparticles leads to an enhanced heat transport. The use of carbon nanotubes which has exceptional characteristics are taken into consideration in this study. This study also demonstrates the comparison on three-different classical flow problems (Blasius flow, Hiemenz flow, and Falkner-Skan flow).

Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle

Abstract The thermo-diffusion applications of nanofluid subject to variable thermal sources have been presented. The significance of Darcy–Forchheimer effects is attributed. The flow comprises the mixed convection and viscous dissipation effects. Furthermore, the variable influence of viscosity, thermal conductivity, and mass diffusivity is treated to analyze the flow. The analysis of problem is referred to convective mass and thermal constraints. The analytical simulations are proceeded with homotopy analysis method. The convergence region is highlighted. Novel physical contribution of parameters is visualized and treated graphically. It is noted that larger Brinkman number leads to improvement in heat transfer. The concentration pattern boosted due to Soret number. The wall shear force enhances with Hartmann number and variable thermal conductivity coefficient.

Analytical analysis of water and engine oil base nanofluid flow with the influence of viscous dissipation and variable viscosity on stretching surface

AbstractIn this study, we will look at the analytical characterization of water and motor oil‐based nanofluid flow and the effects of viscous dissipation and variable viscosity on stretching surfaces. The primary goal of this research is to improve heat transfer efficiency in a range of systems, including cooling applications, refrigeration systems, and heat exchangers. The addition of nanoparticles to the base fluid increases its thermal conductivity, which boosts heat transfer rates. The flow system considers the impact of viscous dissipation. In addition, this methodology accounts for temperature and velocity slips during stretching. We utilized the proper transformations to convert a set of PDEs to NLODEs. To solve this system of equations, we use hybrid nanofluid. The impact of different parameters obtained from temperature and velocity equations involving the porosity parameter, power law number, ratio velocity, dynamic viscosity, Forchheimer parameter, and Eckert number input factors are shown in the form of graphs.

Numerical insights of fractal–fractional modeling of magnetohydrodynamic Casson hybrid nanofluid with heat transfer enhancement

Fractional calculus expands the idea of differentiation to fractional/non‐integer orders of the derivatives. It includes the memory‐dependent and non‐local system's behaviors while fractal–fractional derivatives is the generalization of fractional‐order derivatives which refers to a combination of fractional calculus and fractal geometry. In this article, we have considered the magnetohydrodynamic (MHD) flow of Casson hybrid nanofluid through a vertical open channel with the effect of viscous dissipation and Newtonian heating. The problem is modeled in terms of non‐linear and coupled integer‐order PDEs which is further generalized through fractal–fractional derivative of power law kernel. Due to non‐linearity and complexities, we have adopted the numerical procedure as it is used when the analytical solutions of PDEs are frequently difficult or impossible for complicated situations. We have established the numerical algorithms for both the classical and fractal–fractional‐order model and compared the results. The existence and uniqueness of the model's solution has been shown theoretically. The effect of various embedded parameters on the heat transfer and fluid flow has been simulated and presented through various figures while skin friction and Nusselt number are tabulated. The effect of fractional and fractal parameter is also shown. As the present model is taken for the hybrid nanofluid flow and for the heat transfer applications, we have considered mineral transformer oil as a base fluid while titania and cadmium telluride nanoparticles are dispersed in it. From the results, it is observed that hybrid nanofluid have a better heat transfer enhancement up to 19.71% while the unitary nanofluids are only capable to enhance the heat transfer up to 9%.

Modeling viscous dissipation in MHD boundary layer flow: A two-stage in time and compact in space finite difference approach

It is suggested that an explicit-implicit third-order in-time numerical scheme be used to solve time-dependent partial differential equations (PDEs). A fourth-order compact scheme in space is adopted for discretizing space variables. The work creatively blends a third-order explicit-implicit numerical scheme in time with a fourth-order compact scheme in space to solve time-dependent PDEs. Notably, the proposed numerical scheme demonstrates stability for scalar PDEs and exhibits convergence for both linear and nonlinear PDE systems. In addition, a mathematical model is given for the heat transfer of magnetohydrodynamic (MHD) flow over flat and oscillatory sheets, and the effect of viscous dissipation is also considered. For various governing parameters, features of the flow and heat transfer characteristics are discussed and examined. Some results are verified using an exact solution. We use an explicit-implicit finite difference method guaranteed to be stable and convergent under all conditions to solve the coupled nonlinear partial differential equations that describe this problem. Physical aspects of the problem are discussed in light of the system’s embedded parameters, and numerical and graphical results are presented. To sum up, progress in our knowledge of such systems relies heavily on creating an accurate and efficient numerical scheme for modeling MHD boundary layer flows while considering the influence of viscous dissipation. This study aims to improve the current state of MHD flow simulations and provide a useful resource for engineers and scientists engaged in developing and improving MHD-based technologies.

Time-dependent hydromagnetic convective transport upon a vertical perforated sheet with heat production and viscous dissipation effects

This research analysed the theoretical influences of viscous dissipation and heat production on an unstable hydromagnetic free convective transference upon a vertical porous sheet. The converted conservation equations are resolved numerically with suitable boundary conditions by exerting the similarity techniques. Then the coupled ODEs is resolved by inserting the finite difference method (FDM). The influences of the working dimensionless numbers or parameters on the flow, concentration and temperature fields, the mass transmission rate, the coefficient of local skin friction, and the heat transmission rate examined and discussed quantitatively with the aid of graphs. The findings show that as the Eckert number rises, the temperature and fluid velocity both advance along with the heat generation parameter. The f ′ ( 0 ) increases by around 8% and 12% due to uprising amounts of the heat generation parameter from 1.0 to 2.0, and the Eckert number from 0.5 to 2.5, respectively. Growing amounts of the heat generation parameter from 1.0 to 2.0 and Eckert number from 0.5 to 2.5, the heat transmission rate lessens by around 63% and 52%, respectively. The comparable outcomes are good coincided with a published article.

Entropy generation due to MHD Falkner–Skan flow of Casson fluid over a wedge: A numerical study

AbstractThis study highlights the significance of entropy generation in the Falkner–Skan flow of Casson fluid past a wedge. To investigate the energy analysis, the governing equations include the heat transport equation in the presence of internal heat source, and the energy transport accounts for heat dissipation using viscous dissipation and Joule heating effect. The mathematical formulation of the problem leads to a set of nonlinear coupled partial differential equations. To obtain a similarity solution, similarity variables are introduced. The resulting differential equations are solved numerically using the shooting technique in conjunction with the Runge–Kutta–Fehlberg 45 (RKF‐45) method. Graphical representations are utilized to demonstrate the physical significance of the relevant parameters. The study analyzes the impact of various parameters on the velocity, temperature, and entropy distributions for three wedge positions: stationary, forward‐moving, and backward‐moving. The results show that an increase in the wedge angle parameter and Casson parameter leads to an increase in fluid velocity, while fluid entropy increases rapidly with an increase in the Brinkmann number, power law Falkner–Skan parameter, and Reynolds number. Moreover, with an increment in the Prandtl and Eckert number, the Nusselt number coefficient decelerates for both static and moving wedge.

Linear stability analysis of MHD mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation

PurposeThis paper aims to investigate the hydrodynamic instability properties of a mixed convection flow of nanofluid in a porous channel.Design/methodology/approachThe treated single-phase nanofluid is a suspension consisting of water as the working fluid and alumina as a nanoparticle. The anisotropy of the porous medium and the effects of the inclination of the magnetic field are highlighted. The effects of viscous dissipation and thermal radiation are incorporated into the energy equation. The eigenvalue equation system resulting from the stability analysis is processed numerically by the spectral collocation method.FindingsAnalysis of the results in terms of growth rate reveals that increasing the volume fraction of nanoparticles increases the critical Reynolds number. Parameters such as the mechanical anisotropy parameter and Richardson number have a destabilizing effect. The Hartmann number, permeability parameter, magnetic field inclination, Prandtl number, wave number and thermal radiation parameter showed a stabilizing effect. The Eckert number has a negligible effect on the growth rate of the disturbances.Originality/valueLinear stability analysis of Magnetohydrodynamics (MHD) mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation.

Significance of shape factor on magnetohydrodynamic buoyancy thin film flow of nanofluid over inclined sheet with slip condition: Irreversibility analysis

This work aims to examine the entropy production, heat transport, and dynamics of the unsteady thin film magnetohydrodynamic (MHD) flow of a nanofluid composed of alumina (Al2O3) and water. The fluid flow is seen to pass over an inclined sheet, taking into account the effects of buoyancy force, viscous dissipation, and joule heating. The system of partial differential equations (PDEs) is optimized under the boundary layer assumptions. Appropriate transformations are used to convert the governing partial differential equations (PDEs) and boundary conditions into dimensionless forms. Using MATLAB’s bvp4c code and a local non-similarity technique with up to second-degree truncation, we can obtain the findings of the enhanced model. The effect of multi-shape Al2O3 nanoparticles on flow, heat, and entropy-generating features is also investigated after the calculated results have been successfully aligned with published data. Mixed convection, nanoparticle volume percent, inclination angle, magnetic field intensity, mass suction, Eckert number, and Biot number are only a few of the governing parameters whose effects are graphically shown for selected values. As a result, the local Nusselt number and skin friction coefficient may be calculated. The skin friction and Nusselt number profiles exhibit a decreasing trend as the values of nanoparticle volume fraction ([Formula: see text]) magnetic [Formula: see text] and unsteadiness (A) increase toward mixed convection ([Formula: see text]). On the other hand, Nusselt number profile increases with increasing values of mass suction parameter [Formula: see text] The profiles of entropy generation and Bejan number show an upsurge as the values of the magnetic parameter [Formula: see text] and Brinkman number (Br) increase. Conversely, the entropy generation reduces with an increase in the temperature difference parameter [Formula: see text] and Bejan number increases.

Influence of thermal radiation and shape factor on a hybrid nanofluid flow over a permeable flat plate with cross-diffusion effects: An irreversibility analysis

Understanding and controlling the shape factors of nanoparticles in fluid flow problems is crucial for optimizing heat transfer, fluid dynamics, and various applications such as nanofluids, drug delivery systems, catalysis, and nanocomposites. By tailoring the shape of nanoparticles, researchers can manipulate their behavior, dispersion, and interaction with the fluid, thereby optimizing the desired outcomes in various fluid flow problems. The meticulous investigation uncovers the integration of entropy analysis in the investigation of the flow of convective magnetohydrodynamic hybrid nanofluid via a permeable flat surface, by considering the effects of Dufour, viscous dissipation, Soret, and thermal radiation. The governing equations are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved using the bvp4c solver, a MATLAB in-built function. We display the outcomes for three different shape factors: platelet, cylinder, and brick. The skin friction coefficient increases at a rate of 1.5089 for the brick shape, 1.5163 for the cylindrical shape, and 1.5212 for the platelet shape when the mixed convection parameter lies between 1 and 5. In this regard, it is important to point out that there is a direct connection between the increase in temperature transmission rate and a decline in the Dufour number ( Du ). It has been found that when 1 ≤ Du ≤ 2.4 , the Nusselt number decreases by 0.4786, 0.4618, and 0.4512 for brick, cylinder, and platelet shapes, respectively. A decline in the Sherwood number is noticed with an upsurge in the Soret number ( Sr ). There is a noticeable increase of 0.0442 in the Sherwood number for brick shape, 0.0438 for cylinder form, and 0.0435 for platelet form when 1 ≤ Du ≤ 2.4 . Furthermore, we have detected that an increase in the radiation parameter amplifies both the Bejan number and the profiles of entropy formation.

Parametric simulations of fractal-fractional non-linear viscoelastic fluid model with finite difference scheme

Fractal-fractional derivatives are more general than the fractional derivative and classical derivative in terms of order. Fractal-fractional derivative is used in those models where the classical continuum hypothesis theory fails. More precisely, these derivative operators are used where the surface or space is discontinuous, e.g., porous medium. Fractal-fractional derivative is considered advance tool to analyze the fluid dynamic model more than fractional and classical model. Given the extensive applicability of fractal-fractional derivatives, the current analysis focuses on investigating the behavior of a non-linear Walter’s-B fluid model under the influence of time-varying temperature and concentration During the simulation process, we have also taken into account the effects of first-order chemical reactions, Soret numbers, thermal radiation, Joule heating, and viscous dissipation of energy. A magnetic field with a strength of B0 was applied to the left plate in the transverse direction. The classical mathematical model was first developed using relative constitutive equations and later generalized with the fractal-fractional derivative operator. Numerical solutions to the generalized model have been obtained using the finite difference method. Various graphs are drawn from the obtained numerical solutions to study the influence of physical parameters on the rheology of Walter’s-B fluid. It has been observed that by varying the fractional and fractal order of the generalized model, one can easily derive fractal, fractional, and classical models.