Narrow Results

Squeezing flow of Casson liquid between two disks is a practical application in compression, polymer processing and injection molding. In this paper, the Casson liquid flow between two convectively heated disks is analyzed using Buongiorno model. Further, the heat and mass transport analysis is done by considering the impact of heat source/sink and activation energy. The continuity and momentum equations governing the unsteady two-dimensional flow are derived using conservative laws. The equations are reformulated using the similarity transformations and the reformulated equations are solved numerically with MATLAB routine bvp4c. The effect of embedding different physical parameters on the flow is analyzed through the graphs for both suction and blowing cases along with comprehensive solutions and equal Biot numbers. Results are validated with the existing literature. For both suction and blowing cases, squeezing number decreases the velocity near the lower disk but increases the velocity near the upper disk. Increasing magnetic field strength slightly increases velocity near the lower disk for equal Biot numbers.

This model is designed to provide clarity on how blood travels through tiny veins in physiological systems with heat and mass transfer characteristics. Further, the purpose of this paper is to examine the Ohmic heating and heat source/sink effects on peristaltic transport of radiative Casson nanofluid in a nonuniform porous inclined channel in the presence of a normal/inclined magnetic field. We also considered the sway of chemical reaction, Soret and Dufour effects. The momentum, temperature and mass equations for Casson fluid model are obtained with the utilization of the lubrication approach. The exact solutions have been acquired for stream function and axial velocity. Further, the temperature and concentration equations are solved numerically by using the R–K based shooting method. We also tabulated the Nusselt and Sherwood numbers for various relevant parameters. Finally, the impacts of all major factors on the physical properties of the flow for both normal and inclined magnetic fields are explored and discussed in depth using graphs. The Casson fluid velocity is more for an inclined magnetic field than a normal magnetic field. The nonuniform parameter of the channel boosts the trapped fluid bolus size. The heat source/sink parameter improves the temperature field but the opposite trend is observed in the field of concentration. Moreover, the findings are validated with the existing works for some special circumstances.

This investigation articulately addresses the role of gold nanoparticles in medical sciences from a different perspective. Aiming to highlight the significant usage of nanoparticles, four different types such as spherical, platelets, cylindrical and brick-like nanoparticles are brought into consideration with the main focus to achieve maximum heat enhancement. This motivation leads to mathematically formulating an electroosmosis blood flow. Casson fluid is treated as physiological fluid through an asymmetric microchannel. The nonlinear term of radiative heat flux is added on the right-hand side of the heat equation to report the impact of radiation which is beneficial in skin diseases. A closed-form solution is achieved with the help of physical approximation. Moreover, analytical expressions for velocity distribution, temperature field, shear stress, heat transfer rate and pressure gradient have been provided. The expression of stream function is also presented and the trapping phenomena are discussed. Besides studying the tremendous capacity of gold particles to enhance the heat transfer rate for targeting the maligned tissues as a prime objective, the current survey will also assist readers to explore the other similar metallic particles which can effectively be used as an alternative.

This paper discusses the impacts of velocity, temperature, and solutal slip on the mass and heat transfer characterization of MHD mixed convection Casson fluid flow along an exponential permeable stretching surface with chemical reaction, Dufour and Soret effects. The Casson fluid is supposed to flow across an exponentially stretched sheet, together with the exponential temperature and concentration fluctuations of the fluid. As governing equations, the momentum, energy and species concentration equations are constructed and represented as PDEs. Following that, these equations were converted via the similarity transformation into ODEs. Finally, the ODEs are numerically solved using the Keller-box method with MATLAB software’s algorithm. Expressions are produced for the fluid flow, temperature and concentration gradients. We also determined the physical variables from which the friction factor, rate of mass and heat transfer are attained for engineering purposes. Using graphs and tables, the impacts of altered physical characteristics on flow amounts are explored. The consistency and validity of our outcomes revealed a significant degree of agreement when comparing them to previously published studies. The findings reveal that raising the Soret and Dufour parameter enhances the velocity profile at the wall, but the converse is true for increasing the velocity slip factor.

This paper addresses the problem of steady two-dimensional magnetohydrodynamics (MHD) migration of dusty fluid across a stretching sheet with the inclusion of Darcy–Forchheimer porosity and Brownian dispersion. The most significant aspect of the ongoing problem is elaborating the entire context with dusty and fluid phases. The governing partial differential equations (PDEs) are transmuted into non-dimensional ordinary differential equations (ODEs) by implementing similarity transformations. The MATLAB script has used the bvp4c strategy to accumulate a visualization of the computational observations. Also, this study illustrates an assessment of the effects of significant parameters on non-Newtonian fluids and fluids with a dusty phase. It is observed that the thermal boundary layer is enhanced with the increasing strength of the mass concentration of dusty granules (${\mathrm{\Gamma }}_{\nu }$) and Eckert number (Ec) for both scenarios, while in the case of fluid interaction temperature parameter (${\beta }_t$) the scenario is opposite for dusty and fluid phases. Moreover, the heat transfer rate intensifies with the increasing effect of thermal radiation, and magnetic field. The significant variations in the various physical quantities are represented through tabular and graphs.

In this paper, the self-propelled movement on gyrotactic swimming microorganisms into this generalized slip flow by nanoliquid over the stretching cylinder with strong magnetic field is discussed. Constant wall temperature was pretended as well as the Nield conditions of boundary. The intuitive non-Newtonian particulate suspension was included into applying Casson fluid by the base liquid and nanoparticles. This formation on the bio-mathematical model gives the boundary value problem by the nonlinear partial differential equations. Primly, modeled numerical system was converted to nondimensional against this help on acceptable scaling variables and the bvp4c technique was used to acquire the mathematical outcomes on the governing system. This graphical description by significant parameters and their physical performance was widely studied. The Prandtl number has the maximum contribution (112.595%) along the selected physical parameters, whereas the Brownian motion has the least (0.00165%) heat transfer rate. Anyhow, Casson fluid was established for much helpful suspension of this method on fabrication and coatings, etc. Therefore, this magnetic field performs like the resistive force of that fluid motion, and higher energy was enlarged into the structure exhibiting strong thermal radiation.

In this paper, the effect of heat and mass transfer on particle–fluid suspension due to peristaltic motion is examined with of slip effects. The governing equations of fluid phase and particulate phase for Casson fluid model with embedded particles are interpreted under the approximation of long wavelength and neglecting the inertial forces. The obtained coupled resulting partial differential equations are solved analytically and an exact form of solutions are conferred. The impact of various sundry parameters are plotted and discussed for velocity, temperature and concentration distribution for both fluid and particle phase. Numerical solution is evaluated for pressure rise along the whole channel. The present analysis reveals various interesting behavior that warrant further analysis on various Newtonian and non-Newtonian fluids. In the present flow problem, the influence of slip represents opposite attitude on the walls of the channel whereas due to the impact of particle volume fractions, the velocity of the fluid diminishes along the whole length of the channel.

In this paper, the two-phase flow of non-Newtonian fluid is investigated. The main source of the flow is metachronal waves which are caused by the back and forth motion of cilia attached to the opposite walls of the channel. Magnetohydrodynamics (MHD) of Casson fluid experience the effects of transverse magnetic fields incorporated with the slippery walls of the channel. Thermal effects are examined by taking Roseland’s approximation and application of thermal radiation into account. The heat transfer through the multiphase flow of non-Newtonian fluid is further, compared with Newtonian bi-phase flow. Since the main objective of the current study is to analyze heat transfer through an MHD multiphase flow of Casson fluid. The two-phase heated flow of non-Newtonian fluid is driven by cilia motion results in nonlinear and coupled differential equations which are transformed and subsequently, integrated subject to slip boundary conditions. A closed-form solution is eventually obtained form that effectively describes the flow dynamics of multiphase flow. A comprehensive parametric study is carried out which highlights the significant contribution of pertinent parameters of the heat transfer of Casson multiphase flow. It is inferred that lubricated walls and magnetic fields hamper the movement of multiphase flow. It is noted that a sufficient amount of additional thermal energy moves into the system, due to the Eckert number and Prandtl number. While thermal radiation acts differently by expunging the heat transfer. Moreover, Casson multiphase flow is a more suitable source of heat transfer than Newtonian multiphase flow.

The use of nanoparticles in heat transmission is an interesting research subject and many scholars have shown an interest in this topic. In accordance with the motivating relevance of nanomaterials, the current research advocates for an evaluation of Casson nanofluid using porous medium thermal analysis in conjunction with vibrant implementations of mixed convection through a chemical reaction. Additionally, a nonlinear suction/injection phenomenon is taken into consideration. A consistent flow pattern is created by the stretched porous structure. The extended Casson nanofluid model is used to identify the heat production of non-Newtonian fluids. The essential incentives for choosing the Casson nanofluid model are validated as it simultaneously achieves Casson fluid, nanofluid and porous medium outcomes. The convective transport of nanofluid has been addressed using convective temperature boundary conditions and convective flow. A dimensionless form with similarity variables is used to simplify the fundamental equations for the provided flow model. The fourth-order Runge–Kutta (RK) strategy is deployed to arrive at a numerical solution for simulated flow. The physical conveyance of flow variables is accessed visually. It is calculated from engineering quantities (i.e., skin friction, Nusselt number and Sherwood number) to generate the numerical values. The velocity declines with increasing porosity and material factors while opposite outcomes are witnessed for buoyancy factors (mixed convection and buoyancy ratio) and injection factor.

This paper addresses a hybrid nanoflow of Casson fluid. The theoretical formulation is derived by considering spherical and, as well as, platelet shape nanoparticles. Electro-osmotic flow (EOF) through an asymmetric channel endures the simultaneous effects of Joule heating, viscous dissipation and magnetic fields. Lubrication effects have also been taken into account to subdue the skin friction. Moreover, the contribution of thermal slip boundary conditions and laser radiation articulately devises a theoretical remedy for rheumatoid arthritis. Detailed parametric reveals the promising results for the application of spherical shape nanoparticles to curb autoimmune diseases.

In this work, we investigate the time-dependent MHD free convection of Casson fluid across a vertical semi-infinite plate fitted inside a permeable medium, along with viscous dissipation, radiation absorption, and Soret effect by using several non-dimensional variables. The characteristics of a variety of elements influencing the flow phenomenon are examined using the Casson fluid model. The governing dimensional partial differential equations are transformed into an ordinary differential equation set by introducing the similarity variables. The reduced model is numerically solved via the Galerkin finite element method. The non-dimensional equations with suitable boundary conditions can be mathematically simplified using the efficient Galerkin finite element approach. The restrictions are shown numerically and graphically, and their effects on temperature, velocity, species concentration, and rate coefficients are all shown. This study is to present the influence of radiation absorption along with viscous dissipation on the heat transfer phenomenon. For different flow parameter estimations, graphs are generated for various flow profiles as well as skin friction coefficients. The Nusselt (Nu) and Sherwood (Sh) quantities are also demonstrated via graphs.

The particular exploration includes the two-dimensional Casson nanoliquid motion predicaments, adjacent to the boundary level over the stretching sheet via non-Darcian porous medium. A particular computational description is given for the governing boundary value problem pertaining to nonlinear partial differential equations relating to momentum, thermal and mass transfer which are computed by fourth-order Runge–Kutta and shooting approaches. The brunt of several parameters like viscous dissipations, magnetic field, porous parameter, thermal diffusivity, Brownian diffusion coefficient and Casson fluid parameter on momentum, heat as well as mass transfer is explored. Moreover, it was noticed that liquid motion is repelled by the Forchheimerr parametric quantity resulting in a reduction in velocity magnitude, within the boundary layer, whereas in the thermic boundary layer, there is an increase in the thermal profile. Furthermore, when the value of the Brownian motion parameter increases, the axial velocity drops, but the thermophoresis parameter is said to have the opposite effect.

The streamline boundary layer Casson liquid flow via wedge inspired by magnetic field effects is considered in this study. The governing laws of Casson fluid are modified by adding the effects of radiative heat flux, viscous dissipation and the surface permeability. Afterward, the model is transformed into simplified form using similarity variables and then analyzed via numerical scheme. The significant influence of the physical parameters appeared due to acting magnetic field, radiative heat flux, dissipation function and Prandtl number is specially treated for the flow behavior and thermal transfer mechanism plotted and discussed in detail. Further, tabulated results are also provided to replicate the study in future and this model is validated with the date published in open literature and it is found that these results are accurate and aligned with existing results.

In this work, an approximate analytical solution for the problem of non-Newtonian Casson fluid flow past a porous exponentially stretching sheet with Joule heating and convective boundary condition is obtained using a relatively new technique; He’s homotopy perturbation (HPM). The major feature of HPM is that it does not need the small parameters in the equations, and hence the determination of classical perturbation can be discarded. Due to the complete efficiency of the HPM, it becomes practically well suited for use in this field of study. Also, the obtained solutions for both the velocity and temperature field are graphically sketched. The results reveal that the method is very effective, convenient and quite accurate to systems of nonlinear equations.

Recently, in various biological processes such as endoscopic medication, blood pumping from the heart to different parts of the body, food supply, and in maintaining heat transfer phenomenon, slip plays a significant part in all aspects. Therefore, a study is aimed to enlighten the significance of multiple slips with Joule heating in a mixed convective Casson fluid. The flow regime is induced by the thermal radiation, chemical reaction and nonuniform heat source/sink in order to accomplish the heat and mass transportation. The modeled equations generated from the physical problem are transmuted into ordinary differential frameworks. The transformed system of equations was solved by means of numerical technique named Runge–Kutta Fehlberg method. The numerical results for involved engineering parameters like Joule heating, Eckert number, thermal, mass and velocity slip parameters for temperature, velocity and fluid concentration are analyzed by graphs using MATLAB. The numerical values for the drag force and Nusselt number are keenly observed and concluded that slip controls the flow closer to the boundary layer. Furthermore, magnetic factor decreases the velocity field and Eckert number enhances the temperature filed.

In recent years, the research for enhanced thermal transportation is centered around the utilization of nanostructures to avail the prospective benefits in areas of biomedical, metallurgy, polymer processing, mechanical and electrical engineering applications, food processing, ventilation, heat storage devices, nuclear systems cooling, electronic devices, solar preoccupation, magnetic sticking, bioengineering applications, etc. The thermal aspects of nanoliquids and associated dynamics properties are still necessary to be explored. In this thermal contribution, the flow of Casson nanofluid configured by an infinite disk is analyzed. The significance of Marangoni flow with activation energy, thermal and exponential space-dependent heat source, nonlinear thermal radiation and Joule heating impacts is also incorporated. Similarly, variables are affianced to recast the governing flow expressions into highly coupled nonlinear ODEs. The numerical simulation for the prevailing model is elucidated by applying the bvp4c built-in function of computational commercial software MATLAB. Consequences of sundry parameters, namely, magnetic parameter, Prandtl number, radiation parameter, exponential space-dependent heat source parameter, thermal-dependent heat source parameter, Eckert number, Dufour parameter, Soret number, Schmidt number, Marangoni number and Marangoni ratio parameter, mixed convection parameter, buoyancy ratio parameter, bioconvection Rayleigh number, activation energy parameter, thermophoresis parameter, Brownian motion parameter, bioconvection Lewis number, Peclet number microorganisms difference variable versus involved flow profiles like velocity, temperature, concentration of nanoparticles and microorganism field are obtained and displayed through graphs and tabular data.

This work focused on slip flow over a non-Newtonian nanofluid fluid flow past a stretching sheet with particles–liquid suspension. The convective boundary condition is taken into account. Similarity transformations are utilized to reduce the nonlinear partial differential equations into a set of nonlinear ordinary differential equations. Runge–Kutta–Fehlberg scheme is used to get the numerical solution. Important parameters are analyzed through graphs and skin friction coefficient. Nusselt numbers are presented in tables. Investigation reveals that slip parameter decreases the velocity field and Biot number increases the temperature field.

In this paper, magnetohydrodynamics of a Casson fluid flow is inspected with the presence of thermal radiation and chemical reaction. Employing the perturbation procedure, the modeling equations are tenacious; the graphs are acquired to illustrate the results. The Casson fluid velocity increases as the perturbation parameter increases. Grashof values for heat and mass transport enhanced Casson fluid velocity. Increasing Casson, magnetic, heat source, and radiation parameters reduce the flow velocity. Prandtl number, heat source, and radiation parameter all reduced the temperature profiles. Chemical reaction parameters lowered the concentration profiles. The skin friction enhances with Casson parameter impact. However, the skin-friction coefficient, Sherwood and Nusselt numbers reduce with an increment in the perturbation parameter. In certain cases, this study’s answers agreed well with the previous literature. Casson liquid with a magnetic region using mixed convection by an exponential vertical boundary layer is the novelty of the work.

This paper presents a numerical solution for the nonlinear thermal radiation effect of magnetohydrodynamic flow of Casson nanofluid over a stretching wall through a porous channel. As the linear thermal radiation leads to a significant difference between the highest and lowest possible temperatures, the nonlinear thermal radiation is used in this work. The governing partial differential equations are changed into nonlinear ordinary differential equations using similarity transformation and then solved using the Runge–Kutta method together with the shooting technique. The graphical representation of the temperature and the velocity profiles is presented for different values of the parameters involved in the problem. The obtained results of the skin friction and the heat transfer are compared with the results in the literature and achieved an excellent agreement.

The study explores the velocity of Casson fluid that is time-independent over an exponentially infinite isotherm vertical permeable sheet. The impact of magnetohydrodynamic (MHD) with Casson flow over the permeability sheet is examined. In contrast, thermal radiation and heat sink parameters have been incorporated. This study’s primary goal is to determine the significance of thermal radiation on Casson flow with MHD using an analytical solution over a permeable sheet. The flow of the fluid occurs above the sheet when $y$ is greater than zero, and the sheet extends far away in the $x$-direction. The model of governing equations is reduced by applying a suitable set of dimensionless parameters. These dimensionless systems of equations are solved through the Laplace transformation method. The impacts of various variables over velocity, temperature, concentration, skin friction, and Nuseelt number are scrutinized. These variables contain magnetic field $M$, Casson fluid parameter $\beta$, Ghroshof number $\mathrm{\text{Gr}}$, modified Grashof number $\mathrm{\text{Gc}}$, Prandtl number $\mathrm{\text{Pr}}$, thermal radiation $\mathrm{\text{Rd}}$ and Scimdth number $\mathrm{\text{Sc}}$. These plots are sketched for the considerable magnitude of these variables through the Mathematica Software, and these plots are discussed in detail. Results show that the increasing value of $M$ reduces the fluid velocity but velocity of fluid is enhanced with larger values of $\mathrm{\text{Gr}}$, $\mathrm{\text{Gc}}$ and $\beta$. The impact of Skin friction and Nusselt number is elaborated by tabular outlined.