Study of a nonuniform heat source over a Riga plate using nth-order chemical reaction on Oldroyd-B nanofluid flow for two-dimensional motion

A variety of fluid models are proposed, due to the uncertain flow diversity and rheological features of non-Newtonian fluids, out of which, viscoelastic Oldroyd-B nanofluid is considered here with a nonuniform heat source over a Riga plate using an nth-order chemical reaction. The ever increasing demand for chemical reactions in hydrometallurgical, chemical, and biomedical industries necessitates studying the behavior of heat and mass transfer in the presence of chemical reaction; a few of its applications are manufacturing of glassware or ceramics, food processing, polymer production, particulate water inflows, dehydration and drying operations in the chemical industry, and numerous applications in agricultural fields and many branches of engineering and sciences. To solve the set of nonlinear DEs, which are found after applying a suitable transformation on the governing nonlinear PDEs, a robust numerical technique, such as the fourth-order Runge–Kutta method, is employed in the current motion problem. Also, the influences of all substantial thermophysical parameters are discussed graphically and analytically. Furthermore, the major outcomes of the results are: attenuation in the relaxation time leads to a rise in the fluid momentum significantly near the wall and the solutal profile retards with an enhanced Brownian motion that results in the retardation in the bounding surface thickness of the profile.     

Thermal and solutal Marangoni stagnation point Casson fluid flow over a stretching sheet in the presence of radiation,Soret and Dofour effect with chemical reaction

The Marangoni flow is involved with microgravity and earth gravity, which causes undesirable effects in crystal growth experiments. Crystal growth experiments were designed in such a manner so as to appraise MIR (space station), which is one of the best platforms for protein crystallization and radiation experiments. In this article, a model is proposed with a stagnation point and a Casson fluid flow at the interface of the plate in the presence of Marangoni convection influenced by a magnetic field and chemical reaction. Furthermore, it is considered that both temperature and concentration surface tension vary linearly with the interface. It is important to choose similarity transformations for implementing nonlinear differential equations into linear ordinary differential equations. We solved the system of differential equations using fourth order Range‐Kutta method with suitable shooting techniques, and the results are displayed through graphs. A comparison is made with the earlier existing literature, and it shows a very good agreement. The results and a detailed discussion of velocity, temperature, and concentration have been shown graphically. The favorable and unfavorable buoyancy force to Marangoni flow, the features of temperature and concentration field, have been investigated.     

Numerical investigation of MHD convective free stream nanofluid flow influenced by radiation and chemical reaction over stretching cylinder

Chemically reacting magnetohydrodynamic radiative flow of convective free stream nanofluid through a stretching cylinder using Buongiorno's model is discussed. The behavior of Brownian motion and thermophoresis is also appropriate. By adopting the similarity transformation, the partial differential equation is diminished into a first-order ordinary differential equation (ODE). Since transformed equations are highly nonlinear these ODEs are solved by using mathematical simulation. The shooting procedure has been adopted to resolve converted equations along the attendant Runge–Kutta–Fehlberg technique. The reason behind the present work is to research the effects of different parameters of fluid, namely, magnetic parameter, free stream velocity, Brownian motion, thermophoresis, chemical reaction, heat radiation, Lewis number on nanoparticle concentration, temperature, and velocity distribution. The impact of significantly participating parameters on velocity, concentration, and temperature distribution is distinguished with appropriate physical significance. The convergence of solutions for temperature, velocity, and concentration profiles is studied carefully. The measured challenges of nanofluids are scale-up capacity, increase in nanofluid viscosity, nanoparticle dispersion, and nanofluid cost. It is observed that nanoparticle temperature rises for more value of Brownian motion parameter while it declines for higher Lewis number. The current study in the cylindrical region is related to novel free stream flow in the presence of chemical reactions along with convective conditions which find applications in electronic systems like microprocessors and in a wide variety of industries and in the field of biotechnology. The current research helps control the transport phenomena, helping production companies to find the quality of the desired product.     

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

The effect of viscous dissipation and thermal radiation on mixed convective heat transfer of an MHD Williamson nanofluid past a stretching cylinder in the existence of chemical reaction is analyzed in this study. When energy equation is formulated, the variable thermal conductivity is deliberated. By proposing applicable similarity transformations, nonlinear ordinary differential equations (ODEs) are attained from partial differential equations. These nondimensional ODEs are computed through Runge-Kutta method integrated with shooting method using MATLAB software. The results found numerically are in agreement with that of the published works of similar nature in a limiting case. The results of the local Nusselt number, skin friction coefficient, and Sherwood numbers are organized in tables. The influence of protuberant parameters on temperature, velocity, and concentration is presented by graphs. From the results, it is seen that for higher values of variable thermal conductivity parameter, the local Sherwood number and skin friction coefficient upsurge, whereas the local Nusselt number diminishes.     

Lubrication aspects in an axisymmetric magneto nanofluid flow with radiated chemical reaction

This paper addresses the effects of axisymmetric magnetohydrodynamic stagnation point flow of nanofluid through the lubrication of power‐law fluid by taking the general slip at the interfacial condition. The impacts of radiated chemical reaction, thermophoresis, and Brownian motions are further accounted. The fluid is impinging orthogonally on the surface via power‐law slim coating liquid lubrication. The partial differential system is governed for both the lubricant and the base fluid. Using dimensional analysis, the arisen partial differential system is modified to ordinary differential systems subject to nonlinear boundary conditions. An implicit numerical technique namely the Keller‐Box method is executed to formulate the solution of developed nonlinear expressions. The influence of different involved constraints on quantities of interest are sketched and discussed. The effects of the skin friction coefficient, heat transfer, and concentration rate at the surface are given and analyzed. The condition from full slip to the no‐slip can be achieved from the present solution. The obtained solutions are matched through the existing data and observed good agreement.     

Entropy generation in MHD Williamson nanofluid over a convectively heated stretching plate with chemical reaction

This investigation focuses on the influence of thermal radiation on the magnetohydrodynamic flow of a Williamson nanofluid over a stretching sheet with chemical reaction. The phenomena at the stretching wall assume convective heat and mass exchange. The novelty of the present study is the thermodynamic analysis in the nonlinear convective flow of a Williamson nanofluid. The resulting set of the differential equations are solved by the homotopy analysis method. We explored the impacts of the emerging parameters on flow, heat, and mass characteristics, including the rate of entropy generation and the Bejan number through graphs, and extensive discussions are provided. The expressions for skin friction, Nusselt and the Sherwood numbers are also analyzed and explored through tables. It is concluded that the rate of mass transfer may be maximized with the variation of the Williamson and chemical reaction parameters. Moreover, the entropy generation rate and the Bejan number are augmented via increasing the Williamson parameter.     

Effects of the viscous dissipation and chemical reaction on Casson nanofluid flow over the permeable stretching/shrinking sheet

A steady two‐dimensional Casson nanofluid flow over the permeable stretching/shrinking sheet along the viscous dissipation and the chemical reaction is studied in this article. The convective boundary condition is incorporated in energy equation. Similarity variables are applied to convert the governing partial differential equations into ordinary differential equations. The numerical solutions of the equations are obtained by using the shooting method with Maple implementation. The numerical findings indicate occurrence of the dual solutions for a certain range of stretching/shrinking and suction parameters. Therefore, a stability analysis is done to find the solution that is stable and physically realizable. The effects of the pertinent physical parameters on velocity, temperature, and concentration profiles are investigated graphically. Numerical results of various parameters involved for skin friction coefficient, the local Nusselt as well as Sherwood numbers are determined and also discussed in detail. The Casson and suction parameters decrease the velocity in the first solution, whereas they increase it in the second solution. The rate of heat transfer increases in both solutions with an increment in Eckert number, Biot number, thermophoresis, and Brownian motion parameters. Thermophoresis and Brownian motion parameters show opposite behavior in the nanoparticle's concentration. The nanoparticle concentration decreases in both solutions with increment in Schmidt number, Brownian motion, and chemical reaction parameters.     

Energy analysis of non-Newtonian nanofluid flow over parabola of revolution on the horizontal surface with catalytic chemical reaction

Nanofluids are special functional fluids, which are designed to reduce the loss of energy and maximize the transport of heat. The thermophoresis and Brownian motion of the particle are important factors in the transport of heat in these fluids. The rise in heat transport shows encouraging effects in control of dissipation of energy and reduces entropy generation. In the current study, two-dimensional non-Newtonian Casson nanofluid flow on an upper horizontal surface of a parabola is investigated. The impact of catalytic surface chemical reactions has been account also due to its industrial importance. For this flow problem, the governing equations are modeled using the law of conservation of mass, momentum, heat, and concentration equation. The fitting transformations are taken to change governing couple partial differential equations and domain into local similar ordinary differential equation and domain of [0,∞). Using the "RK4" approach with Newton's shooting schemes via MATLAB tools, the numerical solution of dimensionless governing equations is sorted. It is observed that the Casson fluid parameter caused a drop in temperature profile, and the chemical reaction parameter is the source of the rise in the temperature field.     

Quadratic mixed convective nanofluid flow past a moving yawed cylinder in the presence of thermal radiation and diffusive liquids

The fluid flow around a yawed cylinder helps to understand the practical implications for undersea applications, such as managing transference, separating the boundary layer above submerged blocks, and suppressing recirculating bubbles. As many authors such as Roy, Chiu and Lienhard, Roy and Saikrishnan, and Revathi et al. have analyzed a boundary layer flow over a yawed cylinder, and their work sticks to only forced convection, we are interested to work on mixed convection flow. Therefore, the work of these researchers has stimulated us to work on the present article. As a result, we have examined the work on triple diffusion quadratic mixed convective nanofluid flow over a moving yawed cylinder. The impact of yaw angle, which exists due to the inclination of a vertically moving cylinder away from the origin, is mathematically investigated in the present paper by converting the governing equations into a compatible form using appropriate nonsimilar transformations and the quasilinearization technique. Nanofluids have crucial usages in science and technology, marine engineering, and applications in industries such as plastic, polymer industries, cancer home therapy, and building sciences. Many processes in new engineering areas occur at high temperatures, and knowledge of radiation heat transfer becomes very important for designing the pertinent equipment. Nuclear power plants, gas turbines, and the various propulsion devices for aircraft, missiles, satellites, and space vehicles are examples of such engineering areas. The finite difference approximation is employed to solve the resulting equations. Enhancing the magnitude of thermal radiation enhances the temperature of the liquid and the energy transport strength. However, liquid hydrogen and liquid oxygen species concentration patterns are reduced in nanofluid compared to traditional liquids. At the same time, the outcomes behave conversely in the case of their wall gradients. Furthermore, the temperature of the liquid enhances the enhancing values of Brownian motion and thermophoresis characteristics. Moreover, nanoparticle mass transport augments with enhancing yaw angle and Lewis number values. Both species' concentration profiles decrease for increasing values of yaw angle. The velocity profiles increase for increasing values of velocity ratio parameter in the spanwise and chordwise directions.     

Entropy optimization analysis of Marangoni convective flow over a rotating disk moving vertically with an inclined magnetic field and nonuniform heat source

The present study investigates the Marangoni convective fluid flow over a rotating disk with an inclined magnetic field and in the presence of a nonuniform heat source when the disk moves upward/downward with nonconstant velocity with the incorporation of the second law of thermodynamics. The Keller-box method is applied to the reduced system of equations to draw graphical illustrations. The study of these illustrations to examine the effects of involved pertinent parameters, like, magnetic field, Marangoni number, angle of inclination, vertical disk movement parameter, heat source, and disk rotation, on velocity and temperature profiles, reveals some interesting findings. From the analysis, it can be concluded that the skin friction coefficient increases with more angle of inclination and the Marangoni number with the reverse trend in case of vertical disk movement. Also, the Marangoni number and vertical disk motion diminish the Nusselt number with a positive effect in the case of more angle of inclination. The rate of entropy generation is enhanced with the temperature ratio parameter while it diminishes with the inclined magnetic field of any strength. The current study in its reduced form is in excellent agreement with earlier published work to ensure the validity of the used numerical scheme.     

Numerical computation on Marangoni convective flow of two‐phase MHD dusty nanofluids under Brownian motion and thermophoresis effects

The current theoretical study describes the Marangoni thermal convective flow of magnetohydrodynamic dusty nanofluids along a wavy vertical surface. The two‐phase mathematical model is developed under the influence of thermal radiation and exponentially varying space‐dependent heat source. Pure and hybrid nanoparticles together with dust particle suspension in the base fluid are taken into consideration to characterize the behavior of the flow. Brownian motion and thermophoresis mechanisms are considered, since it enhances the convection features of dusty nanofluid. Appropriate transformations are adopted to modify the flow governing equations and boundary conditions to dimensionless form. The forward finite difference scheme is implemented to illustrate the resultant coupled partial differential equations. The Newton quasi‐linearization technique is utilized to reduce the nonlinear system into a linear form, which is solved thereafter by Thomas algorithm. The responses of velocity, temperature, concentration, friction factor, and heat and mass transfer rate profiles with various governing parameters are discussed and portrayed graphically. The study evidences that the radiation and space‐dependent heat generating parameters strengthen the temperature distribution. Also, the heat transfer rate appreciably rises with the increment in Marangoni convection. The solution methodology and accuracy of the model is validated by generating the earlier outcomes for nonradiating nanofluid flow without heat source/sink.     

Radiation and slip effects on MHD Maxwell nanofluid flow over an inclined surface with chemical reaction

The numerical solutions of the upper-convected Maxwell (UCM) nanofluid flow under the magnetic field effects over an inclined stretching sheet has been worked out. This model has the tendency to elaborate on the characteristics of “relaxation time” for the fluid flow. Special consideration has been given to the impact of nonlinear velocity slip, thermal radiation and heat generation. To study the heat transfer, the modified Fourier and Fick's laws are incorporated in the modeling process. The mass transfer phenomenon is investigated under the effects of chemical reaction, Brownian motion and thermophoresis. With the aid of the similarity transformations, the governing equations in the ordinary differential form are determined and then solved through the MATLAB's package “bvp4c” numerically. This study also brings into the spotlight such crucial physical parameters, which are inevitable for describing the flow and heat transfer behavior. This has been done through graphs and tables with as much precision and exactitude as is possible. The ascending values of the magnetic parameter, the Maxwell parameter and the angle of the inclined stretching sheet cause decay in the dimensionless velocity while an assisting behavior of the thermal and concentration buoyancy parameters is noticed.     

Cattaneo–Christov heat flux model for heat transfer of Marangoni boundary layer flow in a copper–water nanofluid

The Cattaneo–Christov heat flux is first utilized to explore the heat transfer characteristics of Marangoni boundary layer flow in a copper–water nanofluid. The Marangoni boundary layer flow is driven by exponential temperature. Five different types of nanoparticle shapes including sphere, hexahedron, tetrahedron, column and lamina are considered for the copper–water nanofluid. The nonlinear system of partial differential equations is reduced by similarity transformations and then solved numerically by the shooting method. It is found that sphere nanoparticle has better heat transfer enhancement than other nanoparticle shapes and both the temperature and the thickness of the thermal boundary layer are lower for the Cattaneo–Christov heat flux model than the classical Fourier's law of heat conduction.     

Influence of relaxation-retardation viscous dissipation on chemically reactive flow of Oldroyd-B nanofluid with hyperbolic boundary conditions

The present analysis is meant to explore the computational solution of the problem dealing with the impact of relaxation-retardation viscous dissipation and chemical reaction on the flow of Oldroyd-B nanofluid over a Riga plate. Hyperbolic time-varying boundary conditions are taken into consideration. The basic modeled problem being transformed into nonlinear differential equations are solved numerically by efficient fourth-order Runge-Kutta method along with shooting technique. Characteristics of controlling parameters on velocity, temperature, and concentration along with skin friction, Nusselt number, and Sherwood number profiles are presented with the help of well-featured graphs. The relaxation and retardation parameters affect well flow profiles. In addition, an accelerated flow pattern is accomplished due to the augmentation of the modified Hartmann number. Furthermore, the presence of relaxation-retardation viscous dissipation improves the temperature field.     

Influence of Hall current effect on hybrid nanofluid flow over a slender stretching sheet with zero nanoparticle flux

The present article explores steady, incompressible, and electrically conducting viscous hybrid-nanofluid flow through an impermeable slender stretching sheet. We have opted for water (H₂O) as base fluid and two nanoparticles namely Al₂O₃ and graphene for the hybrid-nanofluid. The consequence of nonuniform magnetic field and Hall current is accounted for in the flow distribution. Zero mass-flux boundary conditions have been included here. The leading partial differential equations of the acknowledged model revise to similarity variables. Next, the subsequent equations are numerically solved by a shooting scheme based on Runge–Kutta fourth-order procedure. The consequences of boosting flow factors on transport systems are achieved accurately through the requisite figures and charts. Concentration outlines are dual in nature when the wall-thickness factor intensifies. The rate of heat and mass transmit augments with wall-thickness factor.     

Numerical analysis on the heat and mass transfer MHD flow characteristics of nanofluid on an inclined spinning disk with heat absorption and chemical reaction

This work examines the heat transfer properties of magnetohydrodynamic nanofluid flow. Through a similarity conversion, the leading structure of partial differential equations is changed to that of ordinary differential equations. A rigorous mathematical bvp4c methodology is used to generate numerical results. The purpose of this study is to characterize the different temperature, concentration, and velocity limitations on a nanofluid with a magnetic effect that is spinning. The findings for rotating nanofluid flow and heat transfer characteristics of nanoparticles are shown using graphs and tables. The influence of physical factors such as heat transfer rates and skin friction coefficients is studied. When the magnetic parameter M is raised, the velocity of the nanoliquid decreases. A rise in thermal radiation (Rd) causes the temperature graphs to grow substantially, although the concentration profiles exhibit the opposite tendency. The effect of the convective heat transfer factor Bi on temperature is shown to increase as Bi increases, but the concentration distribution decreases as Biot increases.     

Free convection flow of a magneto-micropolarnanofluid over an orthogonal plate in a saturated porous medium

This study presents a similar solution for a free convective flow of a micropolar nanofluid through an orthogonal plate in a saturated porous medium under the impact of magnetic field. The internal heating generation and without internal heating generation in the problem are explained. A set of nonlinear differential equations was converted into ordinary differential equations by appropriate conversions. This system of equations was numerically solved using bvp4c function in Matlab. Numerical results for the angular velocity, velocity, temperature, Nusselt number, and skin friction are discussed. Calculations were done by parametrizing volume fraction parameter, micropolar, magnetic field, Darcy number, and the Prandtl number. Finally, this study intends to develop an intuitive understanding of similar models by emphasizing the physical arguments, which may be applicable for coating materials in chemical engineering, for instance, robust paints, production of aerosol deposition, and water-soluble solution thermal treatment.     

MHD nonlinear radiative flow of Carreau nanofluid with variable chemical reaction: An approach to control global warming

Solar energy is a significant source of clean and renewable energy, which can be harnessed to control global warming/pollution levels. Carreau nanofluid models have been used in the cooling of solar devices so as to upgrade the efficiency of solar energy systems. The energy equation is modeled by adopting nonlinear thermal radiation because it has a major role on the solar energy absorption capacity of nanofluid. Diffusion of species involving chemical reactions in boundary layer flow finds overwhelming applications in pollution studies, polymer production, in the design of chemical processing equipments, and so forth. In view of this, the present article is developed to evaluate the impact of nonlinear thermal radiation, chemical reaction, and applied magnetic field to the flow of Carreau nanoliquid induced by exponentially extendable surface. The outcomes of the preset study include that more magnetized the conducting fluid contributes more controlled motion of both shear thinning and shear thickening fluids. Axial and transverse surface viscous drag forces, rate of heat, and mass transportation augment with raising Weissenberg parameter while temperature and concentration fields attain a descending trend due to it. In addition, augmented temperature ratio parameter upgraded the thermal field.