Narrow Results

This research discusses the investigation of heat and mass transfer in a magnetohydrodynamic (MHD) Casson fluid (CF) flow over an exponentially porous stretching sheet. The analysis takes into account the existence of thermal radiation, viscous dissipation, chemical reactions, and the influence of velocity and thermal slips. A recognized Casson model is taken into account in order to distinguish the characteristics of Casson fluid from those of Newtonian fluids. Using the geometry under consideration, the current physical problem is modeled. Appropriate similarity conversions are implemented to reduce the resultant set of coupled nonlinear PDEs to a set of nonlinear ODEs. By implementing the Keller-Box technique, numerical solutions to these reduced non-dimensional governing flow field equations are obtained. Tables and diagrams are utilized to illustrate the physical behavior of various control parameters. The temperature profile is enhanced and velocity profile diminished as the CF parameter value increased, according to this study. An increase in the velocity slip factor resulted in a diminution in the velocity field, while a gain in the thermal and concentration contours. With growing amounts of the chemical reaction factor, the concentration profile exhibited a decline. Indeed, the similar outcomes elucidated in this paper exhibit a remarkable correspondence with solutions that have been previously documented in the academic literature. This research may be motivated by a desire to improve the comprehension of fluid flow in different engineering and environmental situations, where these conditions are common, such as geothermal energy extraction, thermal management, chemical processing industries, and environmental control technologies.

Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid.

This paper examines the three-dimensional flow of a bio-hybrid nanofluid through a porous rotating disk while considering the effects of linear thermal radiation and quadratic thermal radiation and examining entropy generation. The fluid enclosure with blood is taken as base fluid and silver–gold is considered as nanoparticles. The fluid flow phenomenon is characterized by nonlinear coupled differential equations involving two or more independent variables. A suitable numerical technique is used to handle the set of governing equations along with a stability and convergence analysis, followed by applying the homotopy perturbation method for solving stated equations. Through graphical illustrations, the radial and tangential velocity distributions, temperature distributions, entropy production and Bejan number are discussed graphically. The Nusselt number and friction factor results are presented and analyzed. The current finding is validated using the available data in both the numerical and homotopy perturbation methods. The results show that when heat absorption increases on blood/gold–silver hybrid nanofluid, a large heat flux develops on the revolving disk, accelerating the heat-transfer mechanism from that surface in both linear thermal radiation and quadratic thermal radiation cases. Moreover, we have seen that the entropy generation is increasing as the magnetic interaction parameter and heat absorption/generation coefficient in quadratic thermal radiation grow, in comparison with linear thermal radiation. The application of thermal radiation and entropy generation analysis is significantly used in the study of renal artery stenosis (RAS) systems and is an active area of research in the field of biomedical engineering. The model is utilized to compute entropy in physiological systems, such as cancer treatment, heat transfer in tissues, dialysis blood pump, and the efficacy of medical apparatus.

This study is to illustrate the thermometric exchange of Casson fluid’s double diffusive nonlinear radiative heat flux over vertical plate associated with convective boundary conditions, incorporating artificial intelligence (AI)-based neural network computation technique. The AI analysis provides enhanced and optimized results with predictive modeling. The analysis utilizes a dataset generated through Mathematica environment and then embedded the filtered matrix dataset in MATLAB employs AI analysis using the Neural Auto Regressive Exogenous (NARX) method for optimized solutions. Levenberg–Marquard algorithm is used to train neural network. The model’s importance and applications span nuclear reactors, aerodynamics, hydrodynamics, transportation and radiating processes of energy transfer. The physical problem is governed by PDEs that is transformed into a set of ODEs by using similarity transformation. The flow is analyzed against the variation in significant influencing parameter like Prandtl number (Pr), velocity ratio ($\lambda$), convective coefficient ($\gamma$), Rayleigh number (Ra), buoyancy ratio parameter ($N$), radiation parameter ($R$) and Casson fluid parameter ($\beta$). Findings of this paper are significant for various industrial, engineering and research-based activities.

The main motivation of this study is to examine the effects and behavior of Casson nanofluid mainly in reference to oblique stagnation points across a stretching surface. Oblique stagnation point (OSP) motions have so many applications, like artificial fibers, sticky materials, drying paper, and freezing electrical equipment, and numerous applications for endothermic and exothermic processes exist, including in heat exchangers, cooking, and drying damp clothes. Because of these applications on various domains, the Casson nanofluid OSP motion via a stretching sheet is studied with endothermic/exothermic chemical processes and convective boundary conditions (CBC). Similarity transformations are employed to convert partial differential equations (PDEs) into a collection of ordinary differential equations (ODEs). Furthermore, some significant engineering coefficients are discussed and also evaluated the behaviors of several nondimensional factors using the Runge–Kutta–Fehlberg-45 numeric method with a shooting scheme and graphical representations. The outcomes signify that temperature and concentration both rise with a rise in the Casson parameter and activation energy (AE) respectively. A higher Biot value leads to a higher temperature profile. A temperature profile increases with an enhance in the Casson parameter. The addition of a solid fraction will enrich the mass transmission rate in combination with AE.

This work analyzed numerically the impacts of viscous dissipation, Joule heating and inclined magnetic field on reactive-diffusion magneto-hydrodynamic radiative mixed convection oscillatory non-Newtonian Casson fluid (CF) fluxing across a slanted semi-infinite vertical plate inserted in a porous medium. The framed dimensional flow controlling partial differential equations were modified to dimensionless partial differential equations by bringing in applicable scaling variables and then numerically solved by imposing the finite difference scheme. The outcomes are established with graphical representations to inspect the flow fields’ performance for diverse flow parameters. At the same time, numerical data of skin friction and heat and mass transferal rates near the surface area are presented in a tabular format. This research study discovered that the viscous dissipation and radiation effects intensify the temperature and velocity fields while heat ingestion has a contrary effect. Both velocity and concentration distributions are diminished by the chemical reaction and Schmidt number while the converse trend was noted with thermo-diffusion effect. The velocity distribution was narrowed by the angled magnetic field, Casson parameter, and magnetic field but the porosity parameter exposed the opposite impact. The influence of the magnetic field and Casson parameters incited to decline the friction. Heat absorption in the flow makes the Nusselt number rise but improving viscous dissipation and radiation effects have pointed to an opposite trend. The chemical reaction parameter increases the Sherwood number but thermo-diffusion decreases it. Further, validation with already published results is accomplished and an excellent agreement is realized.

This paper investigates the effects of radiation, internal heat source and magnetohydrodynamics (MHD) on the mixed convective boundary layer flow of a Casson nanofluid within a porous medium that is saturated and subject to an exponentially stretching sheet. The nanofluid model incorporates Brownian motion and thermophoresis, and the Darcy model is employed for the porous medium. By applying an appropriate similarity transformation, the nonlinear governing boundary layer equations are converted into a set of nonlinear coupled ordinary differential equations. These equations are then solved numerically using the Hermite wavelet method, with simulations conducted through the MATHEMATICA programming language. The analysis covers various aspects including temperature distribution, velocity, solute concentration and several engineering parameters such as skin friction coefficients, the Nusselt number (rate of heat transfer) and the Sherwood number (rate of mass transfer), all evaluated based on dimensionless physical parameters. The results indicate that elevated radiation intensifies temperatures and leads to thicker thermal boundary layers. As the Casson parameter increases, both the velocity and the momentum boundary layer become narrower. Additionally, a more pronounced chemical reaction rate reduces the thickness of the solutal boundary layer. The accuracy and reliability of the numerical Hermite wavelet method are validated through a comparative analysis with previous studies, demonstrating excellent concordance and confirming the robustness of the computational approach.

The purpose of this investigation is to examine the impacts of fractional calculus on fluid dynamics and heat transfer of a nanofluid in drilling applications. More specifically, the study explores how free convection and electrical conductivity impact clay nanoparticles dispersed in engine oil—which is modeled as a Casson fluid—as they pass over a flat vertical plate. The key objectives are to: (1) determine the effects of memory effects at different timescales on temperature and momentum profiles via the Caputo–Fabrizio fractional derivative; and (2) analyze the consequences of varying different physical parameters such as magnetic field, Grashof number, nanoparticle volume fraction and Prandtl number. The objective of the investigation is to provide insight into controlling these parameters to optimize drilling processes. The Laplace method is applied to find solutions to the governing equations, and MathCad15 is utilized for illustrating the physical results. The results expose that the temperature and momentum fields are enhanced (at large times) when the fractional parameter is increased and both profiles show opposite behavior at small times. The heat transmission is enlarged with growing estimations of the volume fraction for clay nanoparticles, whereas the momentum field is declined by growing estimations of the volume fraction of nanoparticles. Further, the nanofluid motion declines by growing the magnetic field but accelerates by increasing the Grashof number. Further, this model has applications in engineering to optimize drilling operations, where performance and efficiency in refining depend upon controlling fluid flow and heat transmission. It can also be applied in fields where nanofluids are utilized to enhance heat transfer and fluid dynamics, such as petrochemicals, manufacturing and material engineering. Overall, this study establishes a vigorous foundation for further research and delivers a structure for exploring non-Newtonian NF systems from the perspective of magnetized-driven free convection flow.

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement.

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.

The aim of this paper is to study the combined effects of induced magnetic field and chemical reaction on MHD nonlinear mixed convective flow of Casson fluid over an inclined vertical porous plate embedded in a porous medium. The influence of viscous dissipation, heat source/ sink, and slip phenomena is taken into consideration. The effect of thermal radiation is also considered in the energy equation. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. The main objective here is to analyze the induced magnetic field in a nonlinear mixed convective flow. At first, the appropriate similarity transformation is used to transform the governing nonlinear coupled partial differential equations into nonlinear coupled ordinary differential equations. The nonlinear ordinary differential equations are solved by a shooting technique with the help of bvp4c Matlab package. For the validation of the obtained results through the bvp4c Matlab solver, we have also solved this problem via R-K fourth-order method in Matlab and a good agreement is noted in both the results. The results of different physical parameters involved in the problem on the velocity, temperature, induced magnetic field and concentration are discussed by using graphs. It is noticed that the increasing values of the inclination angle cause rising of the induced magnetic field while induced magnetic field has opposite nature with magnetic parameter and magnetic Prandtl number. With increasing values of the thermal radiation parameter, the temperature profile diminishes. Apart from this, the numerical values of skin friction coefficient, Nusselt number and Sherwood number for the various values of parameters are displayed in tabular form.

This study explores heat and mass transport in natural convection of Casson fluid in a vertical annulus via porous medium. Impacts of thermal radiation, heat source and chemical reaction are taken into consideration. The equations representing the model reduced into nondimensional ordinary differential equations under adequate transformations are solved analytically. Closed form solutions are obtained for the problem in terms of Bessel’s functions. Influences of various arising parameters such as porous medium parameter, heat generation, thermal radiation, thermal Grashof number, solutal Grashof number, etc. on flow, temperature and concentration fields are exhibited by graphs and discussed. Also, we have solved the problem numerically on MATLAB software employing the bvp4c technique along with shooting technique. The exact and numerical solutions compared found a good match. Moreover, the effects of numerous parameters on quantities of physical importance such as skin-friction coefficient, Nusselt number and Sherwood number are also portrayed and discussed. Heat exchangers, energy storage systems such as batteries and inverters, thermal storage and thermal protection systems are some examples of applications of the study.

In this study, we investigate the effect of entropy generation on a Casson hybrid nanofluid over a stretching cylinder in the presence of linear thermal radiation and Cattaneo–Christov heat flux. We assumed ${\mathrm{\text{Fe}}}_2{\mathrm{\text{O}}}_3$ and ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$ to be the nanoparticles suspended in the blood’s basic fluid for our model. Targeted drug delivery is one of the most proficient ways to diagnose and treat cancer. This is because attractive nanoparticles can be used as beneficial agents in the occurrence of both heat and an angled magnetic field. In addition, several form aspects have been taken into account. By making sure that the self-similarity transformations are accurate, the fundamental Partial Differential Equations (PDEs) are converted into Ordinary Differential Equations (ODEs). The Runge–Kutta fourth-order and firing approach are used to solve the ODEs. For the situations of cylinder and plate, homotopy perturbation method (HPM) and numerical method (NM) solutions on behalf of the nonlinear structure are obtained to compare one another. In this model, we compared the shapes of the sphere, the cylinder, the blade, the platelet and the lamina, which are all graphically represented. Additionally, the results are compared to those that have already been published and are found to be in great agreement. The performance of biological applications, particularly Radio-Frequency Identification (RFA), cancer therapy, MRI, tumor therapy and malaria disease, is improved by this kind of theoretical research.

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.

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 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 analysis inspects an unsteady and incompressible Casson-type fluid moving on a poured inclined oscillating plane with a ramped thermal profile. The physical effects of flow parameters cannot be investigated and studied using a memory effect, just like with regular PDEs. In this study, we have confabulated the solution of magnetised Casson-type fluid with the help of the best and most modified fractional definition, known as the Prabhakar-like thermal fractional derivative. An integral transforms scheme, namely Laplace transformation (LT) solves the dimensionless governed equations. The physical impacts of significant and fractional constraints are examined graphically and mathematically. As a result, we have confabulated that both thermal and momentum dynamics of flowing Casson fluid slow down with the increment in fractional constraint. Additionally, because of the thickness of the boundary layer, the Casson fluid parameter emphasises the dual character of flowing fluid dynamics.

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.

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.

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.