Computational fluid dynamics analysis on endoscopy of main left coronary artery: An application of applied mathematics.

The endoscopy of a coronary arterial segment having a symmetric emergence of plaque at its innermost region is numerically modeled via computational fluid dynamics toolbox Open-FOAM. The considered left coronary artery for this model has a radius of 2 mm and span of 10 mm. The formation of plaque inside the artery that is a stenosis has length 2 mm and height 0.82 mm. The catheter used for this analysis has a diameter of 1 mm with a balloon over it with a height of 0.53 mm. The blood flow rate considered for this analysis has a range 2.00 ml/s to 2.50 ml/s. The fluid under consideration for this endoscopy review is the non-Newtonian Casson model. The mesh illustrations are arranged for the proposed model with numerical simulations of velocity, pressure profile and streamlines. The narrow channel formed due to assembly of stenosis and balloon over catheter inside this arterial segment has developed some swirling flow profile with turbulence effects just after the flow leaves the stenosis plus balloon region. Although this disturbance caused due to narrowing of channel has made the flow slightly turbulent, the flow eventually leaves the arterial segment again as a laminar flow. To cure coronary artery disease, catheterization, and balloon dilation of stenosed arteries is performed to locate the position and shape of stenosis. A catheter is inserted inside the body through a minor cut and then it is moved inside arteries to place it exactly at the stenosis location. A balloon is placed at front of that catheter and the stenosed region can be opened wide by using balloon dilation.

Instability analysis for MHD boundary layer flow of nanofluid over a rotating disk with anisotropic and isotropic roughness.

The study focuses on the instability of local linear convective flow in an incompressible boundary layer caused by a rough rotating disk in a steady MHD flow of viscous nanofluid. Miklavcic and Wang's (Miklavcic and Wang, 2004) [9] MW roughness model are utilized in the presence of MHD of Cu-water nanofluid with enforcement of axial flows. This study will investigate the instability characteristics with the MHD boundary layer flow of nanofluid over a rotating disk and incorporate the effects of axial flow with anisotropic and isotropic surface roughness. The resulting ordinary differential equations (ODEs) are obtained by using von Kàrmàn (Kármán, 1921) [3] similarity transformation on partial differential equations (PDEs). Subsequently, numerical solutions are obtained using the shooting method, specifically the Runge-Kutta technique. Steady-flow profiles for MHD and volume fractions of nanoparticles are analyzed by the partial-slip conditions with surface roughness. Convective instability for stationary modes and neutral stability curves are also obtained and investigated by the formulation of linear stability equations with the MHD of nanofluid. Linear convective growth rates are utilized to analyze the stability of magnetic fields and nanoparticles and to confirm the outcomes of this analysis. Stationary disturbances are also considered in the energy analysis. The investigation indicates the correlation between instability modes Type I and Type II, in the presence of MHD, nanoparticles, and the growth rates of the critical Reynolds number. An integral energy equation enhances comprehension of the fundamental physical mechanisms. The factors contributing to convective instability in the system are clarified using this approach.

Entropy generation for exact irreversibility analysis in the MHD channel flow of Williamson fluid with combined convective-radiative boundary conditions.

The scrutinization of entropy optimization in the various flow mechanisms of non-Newtonian fluids with heat transfer has been incredibly enhanced. Through the investigation of irreversibility sources in the steady flow of a non-Newtonian Willaimson fluid, an analysis of entropy generation is carried out in this current work. The current study has an essential aspect of investigating the heat transfer mechanism with flow phenomenon by considering convective-radiative boundary conditions. A horizontal MHD channel is assumed with two parallel plates to develop a mathematical model for the flow phenomenon by considering the variable viscosity of the fluid. The contribution of physical impacts of thermal radiation, Joule heating, and viscous dissipation is interpolated in the constitutive energy equation. The complete flow of the current analysis is established in the form of ordinary differential equations which further take the form of the dimensionless system through the contribution of the similarity variables. A graphical scrutinization of the physical features of the flow phenomenon in relation to the pertinent parameters is proposed. This study reveals that the higher magnitude of radiation parameter and Brinkman number dominates the system's entropy. Moreover, the temperature distribution experiences an increasing mechanism with improved conduction-radiation parameter at the lower plate.

Exact soliton solutions and the significance of time-dependent coefficients in the Boussinesq equation: theory and application in mathematical physics.

This article effectively establishes the exact soliton solutions for the Boussinesq model, characterized by time-dependent coefficients, employing the advanced modified simple equation, generalized Kudryashov and modified sine-Gordon expansion methods. The adaptive applicability of the Boussinesq system  to coastal dynamics, fluid behavior, and wave propagation enriches interdisciplinary research across hydrodynamics and oceanography. The solutions of the system obtained through these significant techniques make a path to understanding nonlinear phenomena in various fields, surpassing traditional barriers and further motivating research and application. Significant impacts of the coefficients of the equation, wave velocity, and related parameters are evident in the profiles of soliton-shaped waves in both 3D and 2D configurations when all these factors are treated as variables, which are not seen in the case for constant coefficients. This study enhances the understanding of the significant role played by nonlinear evolution equations with time-dependent coefficients through careful dynamic explanations and detailed analyses. This revelation opens up an interesting and challenging field of study, with promising insights that resonate across diverse scientific disciplines.

The flow of an Eyring Powell Nanofluid in a porous peristaltic channel through a porous medium.

In a porous medium, we have examined sinusoidal two-dimensional transport enclosed porous peristaltic boundaries having an Eyring Powell fluid with a water containing [Formula: see text]. The determining momentum and temperature equations are solved semi-analytically by using regular perturbation method and Mathematica. In present research only free pumping case and small amplitude ratio is studied. Mathematical and pictorial consequences are investigated for distinct physical parameters of interest like porosity, viscosity, volume fraction and permeability to check the effects of flow velocity and temperature.

Comparative appraisal of mono and hybrid nanofluid flows comprising carbon nanotubes over a three-dimensional surface impacted by Cattaneo-Christov heat flux.

Carbon nanotubes (CNTs) are nanoscale tubes made of carbon atoms with unique mechanical, electrical, and thermal properties. They have a variety of promising applications in electronics, energy storage, and composite materials and are found as single-wall carbon nanotubes (SWCNTs) and double-wall carbon nanotubes (DWCNTs). Considering such alluring attributes of nanotubes, the motive of the presented flow model is to compare the thermal performance of magnetohydrodynamic (MHD) mono (SWCNTs)/Ethylene glycol) and hybrid (DWCNTs- SWCNTs/Ethylene glycol) nanofluids over a bidirectional stretching surface. The thermal efficiency of the proposed model is gauged while considering the effects of Cattaneo-Christov heat flux with prescribed heat flux (PHF) and prescribed surface temperature (PST). The flow is assisted by the anisotropic slip at the boundary of the surface. The system of partial differential equations (PDEs) is converted into a nonlinear ordinary differential system by the use of similarity transformations and handled using the bvp4c numerical technique. To depict the relationship between the profiles and the parameters, graphs, and tables are illustrated. The significant outcome revealed that the fluid temperature rises in the scenario of both PST and PHF cases. In addition, the heat transfer efficiency of the hybrid nanoliquid is far ahead of the nanofluid flow. The truthfulness of the envisioned model in the limiting scenario is also given.

Reynolds nano fluid model for Casson fluid flow conveying exponential nanoparticles through a slandering sheet.

Nanofluids with their augmented thermal characteristics exhibit numerous implementations in engineering and industrial fields such as heat exchangers, microelectronics, chiller, pharmaceutical procedures, etc. Due to such properties of nanofluids, a mathematical model of non-Newtonian Casson nanofluid is analyzed in this current study to explore the steady flow mechanism with the contribution of water-based Aluminum oxide nanoparticles. A stretchable surface incorporating variable thickness is considered to be the source of the concerning fluid flow in two-dimension. An exponential viscosity of the nanofluid is proposed to observe the fluid flow phenomenon. Different models of viscosity including Brinkman and Einstein are also incorporated in the flow analysis and compared with the present exponential model. The physical flow problem is organized in the boundary layer equations which are further tackled by the execution of the relevant similarity transformations and appear in the form of ordinary nonlinear differential equations. The different three models of nanofluid viscosity exhibit strong graphical and tabulated relations with each other relative to the various aspects of the flow problem. In all concerned models of the viscosity, the deteriorating nature of the velocity field corresponding to the Casson fluid and surface thickness parameters is observed.

Entropy analysis for a novel peristaltic flow in a curved heated endoscope: an application of applied sciences.

Entropy interpretation with a descriptive heat generation analysis is carried out for the heated flow between two homocentric and sinusoidally fluctuating curved tubes. A novel peristaltic endoscope is considered for the first time inside a curved tube with evaluation of heat transfer and entropy. This flexible and novel endoscope with peristaltic locomotion is more efficient for endoscopy of complex mechanical structures and it is more comfortable for patients undergoing the endoscopy of a human organs. A comprehensive mathematical model is developed that also completely evaluates the heat transfer analysis for this novel endoscope. Certain and systematic computations are performed with the help of Mathematica software and exact mathematical as well as graphical solutions are obtained. Entropy has a lower rate that is almost zero entropy in the central region of these two curved tubes, but maximum entropy is noted near the sinusoidally deformable walls of both the endoscope and channel.

Numerical study for bioconvection peristaltic flow of Sisko nanofluid with Joule heating and thermal radiation.

Present work describes the peristaltic flow of Sisko nanomaterial with bioconvection and gyrotactic microorganisms. Slip conditions are incorporated through elastic channel walls. Additionally, we considered the aspects of thermal radiation and viscous dissipation. Further ohmic heating features are also present in the thermal field. Buongiorno's nanofluid model comprising thermophoresis and Brownian movement is taken. The lubrication approach is utilized for the simplification of the problem. Being highly coupled and nonlinear, the resulting system of equations must be solved numerically using the NDSolve technique and bvp4c via Matlab. Velocity, concentration, thermal field and motile microorganisms. are addressed graphically.

Magnetic Dipole and Thermophoretic Particle Deposition Impact on Bioconvective Oldroyd-B Fluid Flow over a Stretching Surface with Cattaneo-Christov Heat Flux.

This study emphasizes the performance of two-dimensional electrically non-conducting Oldroyd-B fluid flowing across a stretching sheet with thermophoretic particle deposition. The heat and mass transfer mechanisms are elaborated in the presence of a magnetic dipole, which acts as an external magnetic field. The fluid possesses magnetic characteristics due to the presence of ferrite particles. The gyrotactic microorganisms are considered to keep the suspended ferromagnetic particles stable. Cattaneo-Christov heat flux is cogitated instead of the conventional Fourier law. Further, to strengthen the heat transfer and mass transfer processes, thermal stratification and chemical reaction are employed. Appropriate similarity transformations are applied to convert highly nonlinear coupled partial differential equations into non-linear ordinary differential equations (ODEs). To numerically solve these ODEs, an excellent MATLAB bvp4c approach is used. The physical behavior of important parameters and their graphical representations are thoroughly examined. The tables are presented to address the thermophoretic particle velocity deposition, rate of heat flux, and motile microorganisms' density number. The results show that the rate of heat transfer decreases as the value of the thermal relaxation time parameter surges. Furthermore, when the thermophoretic coefficient increases, the velocity of thermophoretic deposition decreases.

Analytical solutions of PDEs by unique polynomials for peristaltic flow of heated Rabinowitsch fluid through an elliptic duct.

In this research, we have considered the convective heat transfer analysis on peristaltic flow of Rabinowitsch fluid through an elliptical cross section duct. The Pseudoplastic and Dilatant characteristics of non-Newtonian fluid flow are analyzed in detail. The Rabinowitsch fluid model shows Pseudoplastic fluid nature for [Formula: see text] and Dilatant fluid behaviour for [Formula: see text] The governing equations are transformed to dimensionless form after substituting pertinent parameters and by applying the long wavelength approximation. The non-dimensional momentum and energy equations are solved analytically to obtain the exact velocity and exact temperature solutions of the flow. A novel polynomial of order six having ten constants is introduced first time in this study to solve the energy equation exactly for Rabinowitsch fluid flow through an elliptic domain. The analytically acquired solutions are studied graphically for the effective analysis of the flow. The flow is found to diminish quickly in the surrounding conduit boundary for Dilatant fluid as compared to the Pseudoplastic fluid. The temperature depicted the opposite nature for Pseudoplastic and Dilatant fluids. The flow is examined to plot the streamlines for both Pseudoplastic and Dilatant fluids by rising the flow rate.

Hybrid Nanofluid Flow Induced by an Oscillating Disk Considering Surface Catalyzed Reaction and Nanoparticles Shape Factor.

Lately, a new class of nanofluids, namely hybrid nanofluids, has been introduced that performs much better compared with the nanofluids when a healthier heat transfer rate is the objective of the study. Heading in the same direction, the present investigation accentuates the unsteady hybrid nanofluid flow involving CuO, Al2O3/C2H6O2 achieved by an oscillating disk immersed in the porous media. In a study of the homogeneous and heterogeneous reactions, the surface catalyzed reaction was also considered to minimize the reaction time. The shape factors of the nanoparticles were also taken into account, as these play a vital role in assessing the thermal conductivity and heat transfer rate of the system. The assumed model is presented mathematically in the form of partial differential equations. The system is transformed by invoking special similarity transformations. The Keller Box scheme was used to obtain numerical and graphical results. It is inferred that the blade-shaped nanoparticles have the best thermal conductivity that boosts the heat transfer efficiency. The oscillation and surface-catalyzed chemical reactions have opposite impacts on the concentration profile. This analysis also includes a comparison of the proposed model with a published result in a limiting case to check the authenticity of the presented model.

Significance of induced hybridized metallic and non-metallic nanoparticles in single-phase nano liquid flow between permeable disks by analyzing shape factor.

The current communication is designed by keeping in the mind high heat transfer capabilities of nanoliquids with the dispersion of diversified-natured nanoparticles in poorly conducting base liquids. Here, an amalgamation of metallic (Cu) and hybridization of metallic and non-metallic oxide (Cu-TiO2) nanoparticles to uplift thermophysical attributes of water is deliberated. The magnetically affected flow between rotating disks under the impact and permeability aspect is assumed. Empirical relations for effective dynamic viscosity, density, and heat capacitance to show mesmerizing features of obliged nanoparticles are also expressed. In addition, mathematical relations also depend on morphological factors like shape, size, and diameter of inducted nanoparticles. The mathematical formulation of the problem is conceded in the form of a system of ODEs after using similarity transformation on dimensional PDEs. Simulations of the complex coupled differential structure are solved by using a numerical approach by employing shooting and Runge-Kutta procedures jointly. The impact of flow concerning variables on associated distributions is revealed through tabular and graphical manner. Quantities of engineering interest associated with work like wall friction and thermal flux coefficients at walls of the disk are also calculated. It is deduced from an examination that the addition of metallic particles raises heat transfer more than non-metallic particles. A significant impression of magnetic field on shear stress is executed by hybrid nanoparticles along the surface of disks. In addition, elevation in Nusselt number and depreciation in skin friction coefficient is revealed against increasing magnitude of nanoparticle volume fraction. A positive trend in skin friction coefficient is manifested against the increasing magnitude of Reynold number. It is also observed that by increasing the size and shape of hybrid nanoparticles thermal conductivity and viscosity of the base fluid increases.

Hydrodynamic and heat transfer analysis of dissimilar shaped nanoparticles-based hybrid nanofluids in a rotating frame with convective boundary condition.

Solar thermal systems have low efficiency due to the working fluid's weak thermophysical characteristics. Thermo-physical characteristics of base fluid depend on particle concentration, diameter, and shapes. To assess a nanofluid's thermal performance in a solar collector, it is important to first understand the thermophysical changes that occur when nanoparticles are introduced to the base fluid. The aim of this study is, therefore, to analyze the hydrodynamic and heat characteristics of two different water-based hybrid nanofluids (used as a solar energy absorber) with varied particle shapes in a porous medium. As the heat transfer surface is exposed to the surrounding environment, the convective boundary condition is employed. Additionally, the flow of nanoliquid between two plates (in parallel) is observed influenced by velocity slip, non-uniform heat source-sink, linear thermal radiation. To make two targeted hybrid nanofluids, graphene is added as a cylindrical particle to water to make a nanofluid, and then silver is added as a platelet particle to the graphene/water nanofluid. For the second hybrid nanofluid, CuO spherical shape particles are introduced to the graphene/water nanofluid. The entropy of the system is also assessed. The Tiwari-Das nanofluid model is used. The translated mathematical formulations are then solved numerically. The physical and graphical behavior of significant parameters is studied.

Performance-based comparison of Yamada-Ota and Hamilton-Crosser hybrid nanofluid flow models with magnetic dipole impact past a stretched surface.

The nanofluid flows play a vital role in many engineering processes owing to their notable industrial usage and excessive heat transfer abilities. Lately, an advanced form of nanofluids namely "hybrid nanofluids" has swapped the usual nanofluid flows to further augment the heat transfer capabilities. The objective of this envisaged model is to compare the performance of two renowned hybrid nanofluid models namely Hamilton-Crosser and Yamada-Ota. The hybrid nanoliquid (TiO2-SiC/DO) flow model is comprised of Titanium oxide (TiO2) and Silicon carbide (SiC) nanoparticles submerged into Diathermic oil (DO). The subject flow is considered over a stretched surface and is influenced by the magnetic dipole. The uniqueness of the fluid model is augmented by considering the modified Fourier law instead of the traditional Fourier law and slip conditions at the boundary. By applying the suitable similarity transformations, the system of ordinary differential equations obtained from the leading partial differential equations is handled by the MATLAB solver bvp4c package to determine the numerical solution. It is divulged that the Yamada-Ota model performs considerably better than the Hamilton-Crosser flow model as far as heat transfer capabilities are concerned. Further, the velocity reduces on increasing hydrodynamic interaction and slip parameters. It is also noted that both temperature profiles increase for higher hydrodynamic interaction and viscous dissipation parameters. The envisioned model is authenticated when compared with an already published result in a limiting case.

Significance low oscillating magnetic field and Hall current in the nano-ferrofluid flow past a rotating stretchable disk.

The present investigation involves the Hall current effects past a low oscillating stretchable rotating disk with Joule heating and the viscous dissipation impacts on a Ferro-nanofluid flow. The entropy generation analysis is carried out to study the impact of rotational viscosity by applying a low oscillating magnetic field. The model gives the continuity, momentum, temperature, magnetization, and rotational partial differential equations. These equations are transformed into the ODEs and solved by using bvp4c MATLAB. The graphical representation of arising parameters such as effective magnetization and nanoparticle concentration on thermal profile, velocity profile, and rate of disorder along with Bejan number is presented. Drag force and the heat transfer rate are given in the tabular form. It is comprehended that for increasing nanoparticle volume fraction and magnetization parameter, the radial, and tangential velocity reduce while thermal profile surges. The comparison of present results for radial and axial velocity profiles with the existing literature shows approximately the same results.