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This paper intends to discuss the hybrid nanofluid flow through a cone in a Darcy–Forchheimer porous media, containing base fluid Methanol (CH3OH), nanoparticles of titanium oxide (TiO2) and copper (Cu). We have examined the flow under the influences of mixed convection, viscous dissipation, chemical reaction, and nonlinear heat source. In hybrid nanofluid flow, viscous dissipation and mixed convection play a crucial role in heat exchangers. By accounting for both mixed convection and viscous dissipation, the addition of nanoparticles into a base fluid improves the transfer of heat and optimizes the performance of the cooling system. Using the laws of conservation, governing equations have been constructed. The flow model is converted using the appropriate similarity transformations from partial differential equations to ordinary differential equations. The homotopy analysis method is used to solve the updated system of equations. When Forchheimer inertial drag parameter is increased, the velocity profile decreases, but it rises when the Darcy number is increased. As the value of exponential heat source parameter rises, the temperature profile increases as well. The result exposes that with an increment in nanoparticle volume fraction, temperature profile also rises but velocity profile decreases. [ABSTRACT FROM AUTHOR]

This study investigates analytically the stability analysis of a nonlinear convective boundary layer (BL) flow of the nanofluids GO-EG and GO-W on a shrinking surface in the presence of a magnetic field and viscous dissipation. We provide a second-order nonlinear ordinary differential equation (NODE) for temperature distribution (TD) and a third-order NODE for velocity profile (VP) coupling based on the thermophysical characteristics of the base fluid and nanofluid as well as similarity transformations (STs) in the fundamental governing equations of momentum and energy. The analytical method HAM is used to answer the equations that have been gathered. In many different industries, such as manufacturing, automotive, microelectronics, and defense, cooling of various types of equipment and devices has very important challenges. To fulfill the demands of the engineering and industrial industries, it is hoped that this issue would significantly improve the heat transformation ratio. [ABSTRACT FROM AUTHOR]

This study examines the effects of viscous dissipation, thermal radiation, nanofluid over a stretched surface, and viscous dissipation on a two-dimensional couple stress blood base for the enhancement of heat transfer rate. Gold and multiwall carbon nanotubes are two forms of nanoparticles that are taken into consideration, with blood serving as the base fluid. The NLPDE controls the considering problem. The NLPDE was converted to NODEs using the mentioned similarity transformation. The analytical method known as HAM was used to analyze the transform NODE analytically. Graphs are used to illustrate the effects of many parameters, such as magnetic factors, nanoparticle volume friction, velocity power index, PN, thermal radiation factors, and EN, which are derived from TE and VE. The current research work highlights how important it is to include viscous dissipation in nanofluid dynamics. The results show complex interactions among stretching, thermal properties, and micro-scale effects. The results may have an impact on the development and enhancement of biomedical devices and treatments that use nanofluidic systems, especially those that deal with blood. [ABSTRACT FROM AUTHOR]

The proposed study examines the effect of inclined magnetic field on a ternary hybrid nanofluid flow that is axisymmetric thermo-solutal Marangoni convective over an infinite disc. Some well-known uses of Marangoni convection include semiconductor production, atomic reactors, crystal growth, fine art mechanisms, melting, thin-film stretching and welding processes. The non-uniform heat generation and viscous dissipation are taken into account. The thermal conductivity and diffusivity coefficient are presumed to vary inversely with linear function of temperature and concentration. The ternary hybrid nanofluid, which consists of silicon dioxide ( SiO 2 ), iron oxide ( Fe 3 O 4 ), molybdenum disulfide ( MoS 2 ) and ethylene glycol as base liquid, undergoes an energy transition to improve heat transfer. The system of PDEs is transformed into nonlinear ordinary differential equations (ODEs) by using the appropriate transformations. Using the BVP4C method, this problem is numerically solved. The heat and mass phenomena rates on flow behavior are investigated using tables and graphs to address the impact of several physical and flow parameters on velocity, concentration, and thermal profiles. By increasing the Marangoni convection parameter, the surface tension gradient gets stronger, leading to more efficient heat and mass transfer inside the liquid as well as stronger induced flows. As the temperature and concentration profiles decrease, the outcome is a more consistent dispersion of these properties throughout the liquid. [ABSTRACT FROM AUTHOR]

The motivation of this paper is to explore an oscillatory flow of a magnetohydrodynamics (MHD) couple stress fluid with heat and mass transfer analyses through a porous medium. The modified Darcy–Brinkman couple stress fluid model is employed. There could be many potential applications of this study, such as thermal system, solidification of liquid crystals, cooling of metallic plates in a bath, exotic lubricants and colloidal solutions. In the wake of these potential applications, the study of MHD couple stress fluid flow with additional diffusing components has been found to be innovative and very interesting in the analysis of the influence of combined magnetic effects, couple stress fluid and two solutes. A governing coupled nonlinear partial differential equation with boundary constraints represents the modeled flow problem. In addition, these equations are converted into nondimensional form by employing the suitable nondimensionalizing quantities. It is possible to attain analytic solutions to the dimensionless equations that control the liquid flow, and the consequences of the flow's confines on velocity, temperature, concentration and skin friction profile are examined and also the results are discussed through graphs. It is noteworthy that when the injection level on the heated plate is increased, the skin friction on each channel plate also increases. [ABSTRACT FROM AUTHOR]

The purpose of this research is to discuss a two-dimensional (2D), laminar, continuous flow of Casson liquid through a stretched porous wedge in the presence of chemical reaction and buoyancy effects over wedge. This research is aimed at analyzing chemically reacting flow of Casson model over a heated porous wedge in order to understand the features of dynamic wedge. The governing equations and involved parameters are nondimensionalized using transformations. Bvp4c, a numerical tool in Matlab is employed to assess the solution. Significant findings of the major dimensionless parameters on state profiles of velocity, temperature and concentration are drawn graphically. The principal results indicate the impacts of Casson parameter, Eckert and Prandtl number, R stretching parameter, K 1 chemical parameter, Sc Schmidt number, C mass transfer parameter, m wedge angle parameter on concentration, velocity and temperature field. The Sherwood, Nusselt number and skin friction numerical values are presented in tabular form. Major findings show that drag force at wedge declines for greater K 1 . Nusselt number shrinks for larger behavior for K 1 . Sherwood number upsurges for greater performance for chemical reaction parameter K 1 . Moreover, K 1 upsurges the temperature slowly but the impacts of K 1 on concentration show a decreasing behavior. [ABSTRACT FROM AUTHOR]

In this research work, we will carry out analytical investigation of MgO–CuO∖H2O, hybrid nanofluid magnetohydrodynamics (MHD) stagnation point flow with the influence of viscous dissipation for enhancement of heat transfer ratio. The flow system takes into account the impact viscous dissipation and transport dependence on the shape factor. Furthermore, velocity and temperature at the stretching surface are also considered in this study. To convert a collection of PDEs to nonlinear ODEs, we applied appropriate transformations. We utilize the Homotopy analysis method (HAM) to solve this set of equations. A physical description is used to simulate and evaluate the structures of flow features such as velocity, skin friction, Nusselt number and temperature profiles in response to changes in developing factors, the effects of different factors on temperature and velocities are shown in the form of graphs. It is hoped that this theoretical approach would contribute positively to improve the heat transformation ratio to satisfy the demands of the manufacturing and engineering sectors. [ABSTRACT FROM AUTHOR]

The combined heat and mass transfer, the so-called thermosolutal convective problem, has become an attractive field of research in many diversified areas. In this paper, for the first time, oscillatory flow analysis has been carried out for triple diffusive viscoelastic fluid flow in a porous medium. A comprehensive model is developed for the modified Darcy–Brinkman–Oldroyd-B fluid, porous medium, Boussinesq approximation, heat and mass transfer across a finite temperature and concentration difference in the chemical potential of two salts. Triple diffusive viscoelastic fluid flows through porous media have grown significantly as this situation occurs in more than a few applications such as improved oil recovery filtration, liquid complex molding, solidification of liquid crystals, cooling of metallic plate in a bath, exotic lubricants and colloidal solutions, polymer processing, chemical and bioengineering industries, among others. The governing coupled nonlinear partial differential equations with boundary constraints represent the modeled flow problem. In addition, these equations are converted into non-dimensional form by employing suitable non-dimensionalizing quantities. The impacts of the pertinent parameters and related dimensionless numbers on the dimensionless velocity, temperature, concentrations, shear stress, heat and mass transfer are examined for both suction and injection cases. It has been found that when the injection level on the heated plate is increased, the shear rate increases for each channel plate. Furthermore, we recognized that the viscoelastic parameters exhibit an opposite kind of behavior on the velocity, temperature, and concentrations fields. [ABSTRACT FROM AUTHOR]

This work objective focuses on studying the combined influences of variable thermal conductivity, chemical reaction, and magnetohydrodynamics (MHD) on the flow of a tangent hyperbolic nanofluid flow over an exponentially stretching surface, considering a first-order velocity slip condition. Additionally, thermophoresis and Brownian motion impacts are taken into account. The phenomena of heat transfer are analyzed considering several factors such as thermal radiation, Joule heating and nonlinear heat source. On the other hand, mass transfer is explored under the effect of chemical reaction. Tangent hyperbolic fluid is an important branch of non-Newtonian fluids known for its ability to describe shear thinning effects. Understanding fluid flow on exponentially stretched surfaces is of great significance due to its applications in various industrial processes. These applications include fluid film condensing methods, plastic production for making plastic covers, fiber manufacturing (where it is used to spin fibers), glass blowing, metallurgical procedures, and the paper industry. The concept of magnetohydrodynamics (MHD) is significant due to its various engineering applications, such as MHD generators, flow meters, heat reservoirs, small components in different devices, and cooling systems for nuclear reactors. To analyze the system, using similarity transformations, the governing equations of continuity, velocity, and concentration are transformed into non-dimensional differential equations. The numerical solution is obtained using the shooting technique. The study presents the physical significance of all the fluid parameters involved, focusing on the velocity, temperature, and concentration profiles. These profiles are presented graphically and discussed in detail. The results show that the fluid velocity profile increases with enhancing values of the We and the magnetic number M. The thermal profile increases with higher Nt and Rd The concentration profile decreases with higher values of Q t and Nb. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to analytically investigate graphene oxide blood base nanofluid with the impact of dynamic viscosity and viscous dissipation. The increased thermal conductivity of nanofluids over regular fluids motivates this research. The basic flow equations are used to model the flow problem in nonlinear partial differential equations (NLPDEs). The dimensionless parameters, classical lie group, and thermo-physical properties are applied to transform the developed NLPDEs into dimensionless ordinary differential equations (ODEs). The resultant ODEs are resolved using the homotopy analysis method (HAM), and graphical and tabular interpretations are used to note the effects of contributing parameters including magnetic parameter, dynamic viscosity, nanoparticle volume friction, Eckert number, and Prandtl number on the velocity profile and temperature distribution. From the obtained results, we see that the velocity profile is decreasing by increasing magnetic parameter, dynamic viscosity, nanoparticle volume friction, and the temperature profile is increasing by increasing dynamic viscosity and Eckert number. The tabular descriptions of convergence of the presented fluid flow are also provided. [ABSTRACT FROM AUTHOR]

This work considers the analytical analysis of silver-water, silver-blood base nanofluid flow over fluctuating disk with the influence of viscous dissipation over fluctuating disk. The primary goal of this study is an effort to improve the heat transfer ratio, which is a core part of the engineering and industrial sectors. Following a continuity check, the problem is modeled using the conservation rules of momentum and energy. Nonlinear PDEs are produced through modeling, which are then transformed into ODEs using a similarity transformation and thermophysical characteristics. The resultant ODEs are resolved using the Optimal Homotopy Asymptotic Method (HAM). The outcomes of this method are compared to authenticate the outcomes of the obtained results. The Mathematica software is used to run HAM methods, and graphical interpretations are given to highlight the influence of dissimilar contributing factors on the velocity profile and temperature distribution. Nusselt's number, and the skin friction are examined through graphical representation. Convergence of the problem is checked with the help of graphs and tables by using dual solution of the problem. [ABSTRACT FROM AUTHOR]

This work considers the analytical analysis of graphene oxide ethylene glycol and graphene oxide blood base nanofluid over a vertical sheet. The principal objective of this study is to make an effort to improve the heat transfer ratio, which is the core part of the engineering and industrial sectors. Following a continuity check, the problem is modeled using the conservation rules of momentum and energy. Nonlinear PDEs are produced through modeling, which are then transformed into ODEs using the similarity transformation and thermophysical characteristics. The resultant ODEs are resolved using the Homotopy Asymptotic Method, and graphical interpretations are given to highlight the influence of different contributing parameters such as unsteady parameter, nanoparticle volume fraction, mixed convection parameter, Grashof number and Prandtl number on the velocity profile and temperature distribution. It is noted that increasing the values of nanoparticle volume fraction and stretching parameter slow down the velocity profile. Also, increasing the values of mixed convection parameter and Grashof number (Gr) enhance the velocity profile, and increasing values of Prandtl number and Graship number reduce the temperature distribution. The Nusselt number and the skin friction are examined through graphical representation. It is noted that increasing the value of mixed convection parameter decreases the skin friction of the fluids, and the Nusselt number decreases with the growing value of Prandtl number. [ABSTRACT FROM AUTHOR]

This research paper examines the Darcy–Forchheimer flow of second-grade hybrid nanofluid with thermophoretic particle deposition on a solar collector plate in a porous media. This study performs an extensive exploration of entropy generation. Solar collector plates play a crucial role in energy storage in solar power plants. They help to store and regulate energy at extreme temperatures. This work analyzes the performance of a solar collector plate when the conventional fluid of Ethylene Glycol (EG) is reciprocated by nanoparticles of zirconium dioxide and copper. The ramifications of Magntohydrodynamic (MHD) and Cattaneo–Christov heat and mass flux are also investigated. The expressions of mass and energy are generated by using the Cattaneo–Christov model of heat and mass flux. The Homotopy analysis method (HAM) is utilized to achieve the results of differential equations against various dimensionless parameters. The fluctuating behavior of velocity, concentration and temperature profiles is discussed graphically in this paper. Furthermore, tables are included for the numerical values of skin friction, Sherwood number and Nusselt number for several parameters. As the value of the Darcy parameter raises, the fluid's velocity distribution continuously reduces. The temperature distribution reduces along with the greater values of the thermal relaxation parameter. The concentration profile has shown decreasing impact due to the increasing value of the concentration relaxation parameter. [ABSTRACT FROM AUTHOR]

This key purpose of this study is to investigate soliton solution of the fifth-order Sawada–Kotera and Caudrey–Dodd–Gibbon equations in the sense of time fractional local M -derivatives. This important goal is achieved by employing the unified method. As a result, a number of dark and rational soliton solutions to the nonlinear model are retrieved. Some of the achieved solutions are illustrated graphically in order to fully understand their physical behavior. The results demonstrate that the presented approach is more effective in solving issues in mathematical physics and other fields. [ABSTRACT FROM AUTHOR]

We investigate a (2 + 1)-dimensional nonlinear Schrodinger equation (NLSE), which describes the spin dynamics of (2 + 1)-dimensional inhomogeneous Heisenberg ferromagnetic spin chain (IHFSC) with bilinear and anisotropic interactions in the semiclassical limit. Miscellaneous new solitons solutions are obtained through the generalized Riccati equation mapping method (GREMM). Moreover, the effects of homogeneity on the soliton propagation and interaction are discussed. The derived structure of the obtain solutions offers a rich platform to better understand the nonlinear dynamics in the ferromagnetic materials. [ABSTRACT FROM AUTHOR]

In this study, two integration techniques are employed to reach optical solitons to the (n + 1) -dimensional nonlinear Schrödinger's equation ((n + 1) -NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented. [ABSTRACT FROM AUTHOR]

This study explores the thermodynamic behavior of a reactive hydromagnetic liquid flowing through permeable materials, with convective cooling applied to the walls. This study holds practical significance in optimization of thermal management systems and it is crucial for enhancing the efficiency of controlling thermal runaway. The flow is modeled as a system of partial differential equations which are numerically solved. The modified Adomian Decomposition Method and Pade approximation technique are utilized in solving the equations. The results acquired for velocity and temperature distributions are thereby employed to estimate entropy generation rate with critical values over numerous effects of various boundaries over improvement of thermal runaway utilizing Pade approximation technique to show the significant impact of convective cooling term (Biot number) and other thermophysical parameters on the fluid flow. The outcomes show that fluid velocity continuously increases with rising values of inverse couple stress and fluid temperature increases Biot number. [ABSTRACT FROM AUTHOR]

This paper’s goal is to investigate the oscillatory flow of double-diffusive convection in a Voigt fluid. We re-design the basic equations of the channel flow, which initially appear dimensional, in a dimensionless manner using non-dimensional variables. The oscillation technique transforms the governing equations into coupled ordinary differential equations (CODEs). We have derived the analytical expressions for velocity, temperature, and concentration distribution by solving the CODEs using the direct analytical method. The study focuses on how physical factors, like the thermal Grashof number, the solutal Grashof number, the Prandtl number, the Lewis number, and the Voigt fluid parameter, affect different aspects of flow, such as speed, temperature, concentration, rate of heat transfer, and mass transfer. Notably, the study finds that skin friction increases on both channel plates with increasing injection on the heated plate. The significance of double-diffusive oscillatory flow lies in its ability to improve heat and mass transfer rates, as well as its impact on pattern formation and stability, which influences a wide range of applications from engineering design to environmental studies. [ABSTRACT FROM AUTHOR]

This research examines the flow of incompressible Casson fluid with gyrotactic microorganisms and thermophoretic particle deposition across a sheet, incorporating a nonlinear heat source and the convective boundary conditions. Our motivation stems from the need to optimize heat transfer in renewable energy systems and improve thermal regulation in aerospace engineering, which could inform advancements in heat shield design. The impact of this study extends to renewable energy, aiding heat transfer optimization, and in aerospace engineering, it may inform heat shield design. Medical imaging, chemical engineering and environmental remediation benefit from insights into the fluid behavior and particle transport. Based on heat source and thermophoretic particle deposition, this work investigates the concentration, temperature flow and microorganism distributions. Using suitable similarity variables, all equations for the proposed flow are converted into ODEs. The reduced equations are evaluated using the RKF45 method. The impacts of significant parameters on temperature, concentration, microbiological and flow profiles are determined with the support of graphs. The thermal and concentration distributions are improved with an increase in the thermal radiation, heat generation and magnetic parameter. This study enhances knowledge across disciplines including healthcare diagnostics, chemical engineering and ecological restoration by offering fresh perspectives on the dynamics of fluid movement and the transportation of particles. [ABSTRACT FROM AUTHOR]

This study examines the analytical study of magnetic hydrodynamic stagnation point flow with the impact variable viscosity on a movable surface along with the impact of thermal radiation. The problem is modeled with the help of momentum and energy conservation laws in the form of NLPDEs. The novelty of this study is the combined impact of variable viscosity and thermal radiation with the analytical method. Aluminum oxide nanoparticles and water are used as base fluids in this research work. The authors applied appropriate transformations to convert a collection of dimension forms of NLPDEs to dimensionless forms of NODEs. The transformed NODEs are solved with the help of an approximate analytical method known as the HAM. The effects of different parameters, including electric field, magnetic field, stagnation point flow, thermal radiation PN, and EN on energy and momentum profiles intended, and the results are planned with the help of graphs. [ABSTRACT FROM AUTHOR]