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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]

AbstractThe two-layer model of the magnetohydrodynamic flow of hybrid nanofluid (HNF) between two disks of the same radii is analyzed in this study. The base fluids of both the hybrid nanofluids are immiscible so that these two fluids form an interfacial layer making the study more unique and innovative. The heat source/sink with viscous dissipation effect on energy equation is discussed. The governing equation is in the form of PDEs that are later reduced to ODEs with the help of the Von Karman transformation. The resulting ODEs are solved using the RK method and the results are interpreted graphically. In addition to temperature and concentration gradient, the radial, tangential and axial velocities for different parameters are studied. The results indicate that the physical ratios such as viscosity and thermal conductivity ratios can improve the fluid motion and temperature even in the presence of magnetic field. Also, the ratio of stretching rate produced by the rotation of disk can effectively control the fluid motion. The two fluid flow between two rotating disk forms an interfacial layer between the fluids results in the increment of heat transfer rate which finds application in the field such as heat ex-changer equipment, Cryogenic systems, electronic appliances, and solar collectors. [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 paper describes the bioconvection phenomenon and its significant influence on the thermal features of the flow of bi-viscous Bingham (BVB) nanofluid past a vertically stretching flat surface. The analysis of the impact of convection parameters is considered along with various other forces. Meanwhile, the flow of BVB nanofluid is put through the slip conditions defined by Thompson and Troian for the velocity at the boundary. The flow of BVB nanofluid is modeled using the partial differential equations (PDEs) under the assumptions of thermophoresis and Brownian motion which occur due to the movement of nanoparticles. Along with these forces, the radiation is also considered so that the obtained results are close to the practical scenarios. Thus, using the proper Lie group similarity transformations, the intended mathematical model is converted into ordinary differential equations (ODEs). The resulting equation system is encoded using the RKF-45 technique, and the outcomes are explained using graphs and tables. The solutions found for the model showed that, for higher ranges of the non-Newtonian fluid parameter, the velocity decreases while the heat transferred by the nanofluid increases. The availability of motile density at the surface grows as the Péclet number rises, whereas the Schmidt numbers decline in their respective profiles. [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]

Due to the higher coefficients of heat and mass transfer, the jet flow has become an effective source for the transfer of heat and mass in various industries. Due to these high coefficients, the heat and mass transfer rates will be high in the appliances equipped with the jet flow. Further, the existence of the magnetic field helps in controlling the velocity and the presence of the gyrotactic microorganisms ensure proper mixing of nanoparticles. A dilute nanoparticle suspension is assumed so that it will not affect the movement of motile cells that leads to bioconvection. Hence, this paper aims to analyze the characteristics of heat transfer as well as mass transfer of the jet flow of Williamson nanofluid past a porous stretching sheet in the existence of microorganisms. The mathematical model obtained as a result of these assumptions is transformed into nonlinear ordinary differential equations for which acceptable solutions are obtained using the numerical method. The results thus obtained are presented graphically and based on the outcomes, it is perceived that the magnetic field has control over the velocity profile thus influencing the thermal profile. The increase in the Williamson parameter also reduces the velocity of the fluid flow. Further, an increase was noticed in the thermal and concentration profiles of the nanofluid for higher values of thermophoresis parameter and the increase in the porosity reduced the speed of the flow of nanofluid. The article deals with the analysis of the flow of Williamson nanofluid in the presence of Arrhenius activation energy. Further, the gyrotactic microorganisms are suspended in the base fluid to ensure stable distribution of nanoparticles and meanwhile, the impact of thermophoresis and Brownian motion are also analyzed. As a result of the increase in the activation energy parameter, the nanoparticles concentration found to decrease. [ABSTRACT FROM AUTHOR]

In this paper, we will define a new metric space called n-gonal graphical b-metric space. We will also prove some fixed point theorems in said metric space and give suitable examples to illustrate our results. These results will help to solve many nonlinear convex models in machine learning and optimization by formulating them in fixed point schemes of optimization. Our paper opens the door for researchers to work in the intersecting area of machine learning and functional analysis in the frame work of n -gonal graphical b -metric space. [ABSTRACT FROM AUTHOR]

Though congruences have their limitations, they have significant importance in the field of number theory and helps in proving many interesting results. Thus, this article has adopted the technique and properties of congruences to identify and prove a set of congruent properties for integer partition. The partition of a positive integer is a way of expressing the number as a sum of positive integers. One such partitions known as regular bipartition triple are discussed in this article. New congruences modulo even integers and modulo prime (p ≥ 5) powers are derived for (2, β)−regular bipartition triples. Also infinite families of congruences modulo 2 for some (2, β)−regular bipartition triples are derived. The theorems stated in this article are proved using the q−series notation and some of the prominent results such as Euler’s pentagonal number theorem and Jacobi’s triple product identities. There are certain lemmas which are derived using these results that help in proving the major results of this article. [ABSTRACT FROM AUTHOR]

The cellular activities of the endothelium layer between lumen and intima are significantly linked to the origin of the disease atherosclerosis. Three stages of atherosclerosis were investigated in this study (40%-mild, 50%-modest, and 60%-acute) concerning the coronary arterial segment. The essence of the hemodynamic factors like flow velocity, pressure, and wall shear stress has been investigated, as well as the interrelationships between them. At all degrees of stenosis, the biophysical relationship between convection-diffusion of low-density lipoproteins (LDL) and convection-diffusion of oxygen in the bloodstream is investigated. The Finite Element Methods (FEM) are used to solve the modeled partial differential equation systems. The method adopted is numerical in nature providing accurate graphical solutions to the framed systems. The physical effects of the deposition of LDL on the arterial wall, like a decrease in the diameter of the lumen, and toughening of the walls, are analyzed through the evaluation of the physical parameters. The study revealed that the deposition of LDL molecules in the post stenotic region leads to the depletion of oxygen in the region leading to the rapid dysfunctioning of the endothelial layer of the lumen-intima boundary. [ABSTRACT FROM AUTHOR]

A new theoretical tri-hybrid nanofluid model for enhancing the heat transfer is presented in this article. This model explains the method to obtain a better heat conductor than the hybrid nanofluid. The tri-hybrid nanofluid is formed by suspending three types of nanoparticles with different physical and chemical bonds into a base fluid. In this study, the nanoparticles TiO2, Al2O3 and SiO2 are suspended into water thus forming the combination TiO2-SiO2-Al2O3-H2O. This combination helps in decomposing harmful substances, environmental purification and other appliances that requires cooling. The properties of tri-hybrid nanofluid such as Density, Viscosity, Thermal Conductivity, Electrical Conductivity and Specific Heat capacitance are defined mathematically in this article. The system of equations that governs the flow and temperature of the fluid are converted to ordinary differential equations and are solved using RKF-45 method. The results are discussed through graphs and it is observed that the tri-hybrid nanofluid has a better thermal conductivity than the hybrid nanofluid. [ABSTRACT FROM AUTHOR]

The bioconvection flow of tiny fluid conveying the nanoparticles has been investigated between two concentric cylinders. The contribution of Lorenz force is also focused to inspect the bioconvection thermal transport of tiny particles. The tiny particles are assumed to flow between two concentric cylinders of different radii. The first cylinder remains at rest while flow is induced due to second cylinder which rotates with uniform velocity. Furthermore, the movement of tiny particles follows the principle of thermophoresis and Brownian motion as a part of thermal and mass gradient. Similarly, the gyro-tactic microorganisms swim in the nanofluid as a response to the density gradient and constitute bio-convection. The problem is modeled by using the certain laws. The numerical outcomes are computed by using RKF -45 method. The graphical simulations are performed for flow parameters with specific range like 1≤Re≤5, 1≤Ha≤5, 0.5≤Nt≤2.5, 1≤Nb≤3, 0.2≤Sc≤1.8, 0.2≤Pe≤1.0 and 0.2≤Ω≤1.0. It is observed that the flow velocity decreases with the increase in the Hartmann number that signifies the magnetic field. This outcome indicates that the flow velocity can be controlled externally through the magnetic field. Also, the increase in the Schmidt numbers increases the nanoparticle concentration and the motile density. [ABSTRACT FROM AUTHOR]

The congruence of certain restricted partition functions known as regular bipartition is discussed in this paper. We particularly investigate the (2,β)-regular bipartitions of n, denoted by B2,β(n), and establish certain congruences for B2,β(n) when β ≥ 3. We derive infinite families of congruences modulo 4 for the (2; 3)-regular bipartition. We also obtain a generalisation of the regular bipartition for modulo p and p². [ABSTRACT FROM AUTHOR]

AgBr acts as a good sensitizer for titanium oxide, hence TiO2-AgBr nanoparticles exhibit high photocatalytic activity which helps decompose methyl orange under visible light irradiation. Methyl orange is a chemical compound that is hard to degrade and has high stability. It is photoreactive and can capture photons from the sun and is highly used as a light harvester in solar cells, hence, it is used in solar applications. In view of this, the present article deals with the analysis of heat transfer in a multilayer flow of two immiscible nanofluids in a vertical channel that finds application in the fields of solar reactors, electronic cooling, and so on. The mathematical model involving the effect of thermal radiation and the presence of heat source is in the form of a system of ordinary differential equations. This system of equations is simplified using the differential transform method-Padé approximant and the resulting equations are solved algebraically. It is observed that the temperature of the coolant does not reach its saturation point faster due to the presence of different base fluids that differ in their thermal conductivity. This helps in maintaining the optimum temperature of the system. [ABSTRACT FROM AUTHOR]

This study deals with the quartic autocatalysis of homogeneous–heterogeneous chemical reaction that occurs in the bioconvective flow of micropolar nanofluid between two horizontally parallel plates. The quartic autocatalysis is found to be more effective than cubic autocatalysis since the concentration of the homogeneous species is substantially high. The upper plate is assumed to be in motion and the lower plate is kept stationary. Such a flow of micropolar fluid finds application in the pharmaceutical industry, microbial enhanced oil recovery, hydrodynamical machines, chemical processing, and so forth. The governing equations for this flow are in the form of the partial differential equation and their corresponding similarity transformation is obtained through Lie group analysis. The governing equations are further transformed to coupled nonlinear differential equations that are linearized through the Successive linearization method and are solved using the Chebyshev Collocation method. The effects of various parameters, such as micropolar coupling parameter, spin gradient parameter, reaction rates, and so forth, are analyzed. It is observed that the fluid flows with a greater velocity away from the channel walls, whereas near the channel walls the velocity decreases with an increase in the coupling parameter. Furthermore, the spin parameter increases the spin gradient viscosity that reduces the microrotation of particles that further decreases the microrotation profile. [ABSTRACT FROM AUTHOR]

The photocatalytic nature of TiO2 finds applications in medicinal field to kill cancer cells, bacteria, and viruses under mild ultraviolet illumination and the antibacterial characteristic of Ag makes the composition Ag-TiO2 applicable for various purposes. It can also be used in other engineering appliances and industries such as humidity sensor, coolants, and in footwear industry. Hence, this study deals with the analysis of the effects of magnetic field, thermal radiation, and quartic autocatalysis of heterogeneous-homogeneous reaction in an electrically conducting Ag-TiO2-H2O hybrid nanofluid. Furthermore, the gyrotactic microorganisms are used as active mixers to prevent agglomeration and sedimentation of TiO2 that occurs due to its hydrophobic nature. The mathematical model takes the form of partial differential equations with viscosity and thermal conductivity being the functions of volume fraction. These equations are converted to ordinary differential equations by using similarity transformation and are solved by RKF-45 method with the aid of shooting method. It is observed that the increase in the size of the needle enhances the overall performance of the hybrid nanofluid. Furthermore, the temperature of the hybrid nanofluid increases with the increase in volume fraction. It is observed that the friction produced by the Lorentz force increases the temperature of the nanofluid. It is further observed that the heterogeneous reaction parameter has more significant effect on the concentration of bulk fluid than the homogeneous reaction parameter. [ABSTRACT FROM AUTHOR]

The genus Viscum (Viscaceae) comprise of several species of hemi-parasitic plants with medicinal properties. Commonly known as mistletoes, these plants grow on other trees with the partial parasitic association. Viscum angulatum B.Heyne ex DC. is one such less explored leafless mistletoe of Asian countries with medicinal claims. In Ayurveda (Bandaka) and Siddha (Pulluri/Pulluruvi), many botanicals from mistletoe families have been attributed with medicinal properties. The objective of the current study is to develop a monograph on quality standards of V. angulatum occurring in high altitude hills of Western Ghats. Aerial parts of V. angulatum were collected and authenticated and preserved in FAA for microscopic studies and some quantity of the plant material was shade-dried and coarsely powdered. Successive extracts were subjected to chromatography and isolation - characterization of the major compounds. Leaf-less quadrangular stem was found to be a diagnostic macroscopic feature of this species. The preliminary phytochemical investigation of extracts showed presence of alkaloids, carbohydrates, coumarins, flavonoids, phytosterols, triterpenoids, saponins and tannins. HPTLC fingerprint of n-hexane and ethyl acetate extracts has been obtained for identification of extracts. The ethyl acetate extract yielded 10-hydroxyoleoside dimethyl ester which can be used as a marker compound for routine quality check of V. angulatum growing on Mussaenda hirsutissima. The set of data obtained in the present investigation can serve as a standard for the identification as well as further studies. These results on standards of this plant are the first report so far. [ABSTRACT FROM AUTHOR]

[Display omitted] The analysis of enhancing the heat transfer of a traditional fluid by adding nanoparticles was effectively studied by many researchers across the globe. In later stages, these nanofluids were made chemically stable by suspending an additional inert nanoparticle thus forming a hybrid nanofluid. The heat transfer characteristics of hybrid nanofluids are discussed in various aspects. Considering these studies, the heat and mass transfer characteristics of ternary nanofluid formed by suspending three different nanoparticles is analysed in this article. The self-propelled microorganisms move within the nanofluid due to the density gradient and it ensures proper mixing of nanoparticles. In order to achieve proper bioconvection caused by microorganisms, the nanoparticle concentration is assumed to be dilute and the fluid with these characteristics is assumed to flow as a jet past a stretching sheet. The mathematical model to analyse such a characteristic flow is framed using the modified Buongiorno's model that describes the impact of volume fraction, thermophoresis and Brownian motion. The mathematical model obtained will be further converted into non-linear differential equations that are solved through the RKF - 45 method. The results obtained through this method are interpreted graphically and the impact of fluid flow parameters on the heat and mass transfer rates are tabulated. It is perceived that the mixed convection parameter enhances the velocity profile. Similarly, the increase in the Brownian motion and thermophoresis enhances the thermal profile. Meanwhile, the increase in the nanoparticle volume fraction helps in enhancing the thermal conductivity and thus the temperature is found to be increasing. [ABSTRACT FROM AUTHOR]