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The nonlinear differential equations play a prominent role in the mathematical description of many phenomena that occur in our world. A similar set of equations appear in this paper that govern the homogeneous and heterogeneous chemical reactions in the nanofluid flowing between two non-parallel walls. Since the concentration of the homogeneous species is substantially high, quartic autocatalysis is considered for the analysis. It is found to be more effective than the cubic autocatalysis. Further, to avoid the deposition of nanoparticles on the surface, self-propelled microorganisms called gyrotactic microorganisms are allowed to swim in the nanofluid. This movement of microorganisms constitutes a major phenomenon called bioconvection. The set of governing equations thus formed are made dimensionless and the resulting system of equations are solved by Differential Transformation Method (DTM) with the help of Padé approximant that reduces the power series into rational function. This transformation helps in achieving a better convergence rate. The fluid flow analysis is interpreted through graphs and tables where it is observed that the heat source enhances the temperature of the nanofluid. Further, the homogeneous and heterogeneous chemical reaction parameters have significant impacts on the concentration of the reactants. Also, the outcomes indicated that the reaction profiles and motile density profiles increase with the increase in Schmidt number. [ABSTRACT FROM AUTHOR]

In this analysis, we have considered heat transmission in two-dimensional steady laminar nanofluid flow past a wedge. Magnetohydrodynamic (MHD), Brownian motion, viscous dissipation and thermophoresis effects are considered over the porous surface. Similarity transformations have been used to change the governing partial differential equations (PDEs) into nonlinear higher-order ordinary differential equations (ODEs). Governing ODEs with boundary conditions are then converted to the system of first-order initial value problem. After that the modeled system is solved numerically by RK4 technique. Impact of the magnetic number, Eckert number, Prandtl number, Lewis number, Brownian motion, thermophoresis and permeability parameters on the flow domain is analyzed graphically as well as in tabular form. It is noted that magnitude of Nusselt number for the flow regime increases with the increase of nondimensional parameter P r , N b , N t while opposite behavior is observed in case of R. [ABSTRACT FROM AUTHOR]

The study offers a thorough evaluation of the complex fluid dynamics and heat transfer phenomena in Williamson viscoelastic fluid flow, taking into account thermal radiations and variable thermal conductivity. The paper extends its analysis to include heat transfer effects, which are critical in several engineering and industrial applications, and digs into the complexity of non-Newtonian fluid behavior, with a special focus on thermal radiation, heat production, diffusion and viscous dissipation. The study makes use of mathematical models and numerical method RK4 to clarify the nonlinear interactions between convection and diffusion processes in this viscoelastic fluid. The energy and concentration equations are simulated in the presence of the modified Fourier and Fick laws. Moreover, the predicted heat flow is based on the Cattaneo–Christov theory. This research also sheds light on the interaction between rheological properties and thermal characteristics, providing important new knowledge to the broader field of fluid dynamics and heat transfer. [ABSTRACT FROM AUTHOR]

The effectiveness of jet flow in the energy transfer process has made it very useful in industrial applications. These flows also have higher heat transfer coefficients than traditional cooling through convection. The appliances inclusive of the jet make effective use of fluid and enhance the heat transfer rate. The contemporary article investigates the jet flow of power-law nanofluid past a moving wall. The nanofluid is formed by suspending Cu and Al2O3 nanoparticles in water. Furthermore, the jet flow is analyzed in the presence of radiation, which is further assumed to be linear, and the application of Rosseland approximation is considered to be valid. Considering these aspects, the model is designed using partial differential equations (PDE), which are then converted to a system of non-linear ordinary differential equations (ODE) by implementing certain similarity transformations. Thus, the obtained system is solved using numerical methods, and the results are discussed with the help of graphs. The significant conclusions of the analysis were that the increase in the radiation parameter contributed to the increase in the temperature of the nanofluid. The increase in the Prandtl number reported a decrease in the amount of heat absorbed by the nanofluid. [ABSTRACT FROM AUTHOR]

Bioconvection is a fascinating phenomenon observed in various biological systems, where the motion of motile microorganisms generates fluid flow patterns. This article explores the occurrence and characteristics of bioconvection within the context of a jet flow. The study of bioconvection in jet flow involves the interaction between motile microorganisms and the fluid dynamics of the surrounding medium. Microorganisms such as bacteria and algae are known to exhibit directed swimming behavior, which can lead to the formation of dynamic flow structures. Investigating the mechanisms underlying bioconvection in jet flow requires a multidisciplinary approach encompassing fluid dynamics, microbial ecology, and mathematical modeling. Experimental techniques, such as microscopy and particle image velocimetry, along with computational simulations, are employed to analyze the complex interactions between microorganisms and the fluid flow. In this regard, a supportive mathematical model is designed using partial differential equations (PDEs) which are later transformed into ordinary differential equations using similarity transformations. The resulting system of equations is solved using the RKF-45 method and the outcomes are recorded in tables and graphs. The consideration of thermophoresis has shown a significant impact on the heat and mass transfer of the jet flow and both these profiles are observed to increase with thermophoresis. Meanwhile, the Schmidt number decrease their respective mass profiles. Furthermore, the porosity is found to create a drag force which tends to oppose the fluid flow. [ABSTRACT FROM AUTHOR]

In this study, we have analyzed magnetohydrodynamic (MHD) consequences on the heat and mass transmission within unsteady dissipated liquid film flow. Flow is generated due to stretchable surface accompanied with effects of ohmic heating, chemical reaction and heat absorption. Moreover, the flow governing partial differential equations (PDEs) are further modified into equivalent ordinary differential equations (ODEs) by applying regular perturbation method to get its analytical solution after that we have applied sixth-order Runge–Kutta technique to get its numerical solution. These two solutions are validating each other in the simulations. Figures are plotted to study the changes in physical quantities like skin friction coefficient, concentration, velocity, temperature, Sherwood and Nusselt number with the variations of Prandtl numbers Pr, parameters of chemical reaction β , Eckert numbers Ec, magnetic parameter Ha (also known as Hartman number) Schmidt number and coefficient of heat absorption Δ. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis of the flow and heat transfer performance of ternary nanofluid flowing past a stretching sheet under the influence of quadratic convection. The ternary nanofluid is formed by suspending three different nanoparticles, namely, titanium dioxide (TiO2), silver (Ag) and graphene (Gr) in the base fluid water (H2O). Thus, the ternary nanofluid obtained is Gr–Ag–TiO2/H2O where the hybrid nanofluid Ag–TiO2/H2O forms the base fluid for the resulting ternary nanofluid. The addition of TiO2 nanoparticles enhances the photocatalytic nature of the base fluid and makes it useful in various applications concerning the medicinal field. The presence of Gr helps in intensifying the thermal conductivity of water while the suspension of silver nanoparticles ensures chemical stability. Meanwhile, the thermophysical properties of the ternary nanofluid are mathematically defined and the system of equations that describe the flow of a ternary nanofluid past a stretching sheet is framed using differential equations. The outcomes of this study are interpreted through graphs for velocity and temperature profiles of the ternary nanofluid. It was mainly observed that the thermal conductance of ternary nanofluid was higher than the monophase and hybrid nanofluid. Also, the presence of quadratic convection had a prominent impact on the ternary nanofluid flow. The Nusselt number was found to be greater for spherical nanoparticles and it was found to be least for blade-shaped nanoparticles. [ABSTRACT FROM AUTHOR]

The model presented in this paper deals with the investigation of the unsteady laminar flow past a stretchable disk. The nanofluids Al2O3/H2O and Cu/H2O are considered for the analysis where the thermal characteristics and flow behavior of these nanofluids are compared. In addition, the system is subjected to the suction force that has significant impacts on velocity of the nanofluid flow. Further, the nanoparticle solid volume fraction is another important parameter that is discussed which has a prominent role on both profiles of the nanofluid. Furthermore, the investigated mathematical model is framed using PDEs that are transformed to ODEs using suitable transformations. The system of equations obtained in this regard is solved by employing the RKF-45 numerical method where the results are obtained in the form of graphs. Various nanofluids flow parameters arise in the study and the impact of all these parameters has been analyzed and interpreted. Some of the major outcomes are that the higher values of nanoparticle solid volume fraction enhance the temperature while it decreases velocity of the flow. The comparison of flow of the two nanofluids concluded that alumina–water nanofluid has a better velocity while the copper–water nanofluid has a better thermal conductivity. [ABSTRACT FROM AUTHOR]

This investigation aims to inspect the flow and thermal characteristics of hybrid nanoparticles under the effect of thermophoresis and Brownian motion. The hybrid nanofluid is formed by dispersing the silver nanoparticles into the base fluid composed of tungsten oxide and water. The resulting hybrid nanofluid is assumed to flow over a moving wedge. The wedge is a geometry that can be commonly seen in many manufacturing industries, moulding industries, etc., where friction creates more heat and cooling becomes a necessary process. This study currently focuses on such areas of the industries. In this regard, the flow expressions in the form of Partial Differential Equations (PDEs) are obtained by incorporating the modified Buongiorno's model and using boundary layer approximations. The modified Buongiorno model helps us analyze the impact of volume fraction along with the slip mechanisms. Suitable transformations are used to achieve the nondimensional form of governing equations, and further, it transforms the PDE to Ordinary Differential Equation (ODE). The RKF-45 is used to solve the obtained ODE and the boundary conditions. Furthermore, graphic analysis of the solutions for fluid velocity, energy distributions and dimensionless concentration is provided. It was noted that the behavior of the Nusselt and Sherwood numbers was determined by analyzing numerous parameters. The conclusions show that they decrease with greater values of the stratification factors. Additionally, with higher values of the wedge parameter, the magnitude of the velocity field and the thermal boundary layer diminish. [ABSTRACT FROM AUTHOR]

In recent years, a novel technique for producing robust cementitious materials, called nanocomposites, has emerged. These materials are comprised of clay minerals and polymers. As a result, a vertical flat plate has been used to evaluate a clay-based cementitious nanofluid in this research. The impacts of first-order chemical reactions, heat generation/heat absorption, and the Jeffrey fluid model are taken into account for the study of flow. Newtonian heating and the conditions for slippage velocity have also been considered. The mathematical problem for the flow analysis has been established in relations of partially coupled partial differential equations and the model has been generalized using constant proportional Caputo (CPC) fractional derivative. The problem is solved using the Laplace transform technique to provide precise analytical solutions. On the concentration, temperature, and velocity fields, the physics of a number of crucial flow parameters have been examined graphically. The acquired results have been condensed to a very well-known published work to verify the validity of the current work. It is important to note here that the rate of heat transfer in the fluid decreases by 10.17% by adding clay nanoparticles, while the rate of mass transfer decrease by 1.31% when the value of ϕ reaches 0.04. [ABSTRACT FROM AUTHOR]