Activation energy and binary chemical reaction on unsteady MHD Williamson nanofluid containing motile gyrotactic micro‐organisms

The author presents the influence of Arrhenius activation energy and binary chemical reaction on an unsteady magnetohydrodynamics Williamson nanofluid with motile gyrotactic micro‐organisms. The governing equations are converted to coupled ordinary differential equations with similarity transformations and the fifth‐order Runge‐Kutta Fehlberg method and the shooting algorithm is applied to solve these equations using the appropriate boundary conditions. A detailed investigation considering the effects of different physical parameters on the profiles like velocity, temperature, concentration, and density of motile gyrotactic micro‐organisms was done and plotted graphically. It is found that the thermal boundary layer enhances for the chemical reaction rate and the solutal boundary layer increases for activation energy. Furthermore, the nondimensional Williamson parameter reduces for the velocity profile. The author studied the wall temperature gradient of different fluids and found that temperature gradient decreased for the present study. Comparisons of the present result with published work were done to verify the present code.     

Unsteady bioconvective squeezing flow with higher-order chemical reaction and second-order slip effects

In this investigation, the foremost aim is to study the impact of a higher-order chemical reaction and second-order slip on the bioconvective nanoliquid flow comprising gyrotactic microorganisms between two squeezed parallel plates. The existence of magnetic strength, thermophoretic, and Brownian migration is considered to model the flow. Similarity transformations are implemented to reduce our mathematical model into a set of nonlinear ordinary differential equations along with the requisite boundary conditions. The classical Runge-Kutta-Fehlberg method technique is employed to avail the numerical outcomes of the aforementioned nonlinear foremost equations correlated with the relevant boundary conditions. Parametric flow discussions, like, velocity profile, thermal profile, and heat and mass transport, have been portrayed through indispensable charts and graphs. Physical quantities, like, skin friction, Nusselt number, Sherwood number, and microorganism density number, have been estimated to analyze their numerous applications. The results communicate that temperature diminishes for squeezing factor and first-order velocity slip parameter, but augments for second-order slip parameter. Mass transport accelerates for chemical reaction but reduces for the order of reaction. Microorganism density number amplifies owing to chemical reaction and Peclet number while it decays for chemical reaction. This has advantageous applications in bio-micro-systems, bioreactors, biosensors, biochromatography, magnetic bioseparation devices, biocoating, and ecological fuels.     

Radiative flow of Maxwell nanofluid containing gyrotactic microorganism and energy activation with convective Nield conditions

On the account of industrial and technological applications, the enhancement of energy by inserting nanoparticles is a hot topic in the present century. Therefore, the current analysis presents a theoretical analysis regarding the flow of electrically conducted Maxwell nanofluid over a stretching surface in the presence of the gyrotactic microorganism. In addition, the influence of thermal conductivity and Arrhenius activation energy are considered. By using the apposite transformation, the system of contemporary partial differential expressions is first converted into nonlinear ordinary differential system. The set of these transmuted equations is solved with the help of the shooting method. Reliable results are obtained for the velocity profile, temperature, motile microorganism density and concentration. It is evaluated that by increasing the value of bioconvection Peclet and Lewis numbers, the microorganism distribution exhibited diminishing behavior. These results may be useful in improving the efficiency of heat transfer devices and microbial fuel cells.     

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.     

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.     

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.     

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.     

Thermophoretic particle deposition and heat generation analysis of Newtonian nanofluid flow through magnetized Riga plate

The Riga surface is composed of an electromagnetic actuator that comprises a span-wise associated array of discontinuous electrodes and an everlasting magnet mounted over a planer surface. The electro-magneto-hydrodynamic has an attractive role in thermal reactors, fluidics network flow, liquid chromatography, and micro coolers. Inspired by these applications, a laminar, two-dimensional nanofluid flow with uniform heat sink-source, thermophoretic depositions of the particles, and the Newtonian heating effect are investigated. The equations that describe the fluid motion are reduced into a system of ordinary differential equations with the help of spatial similarity variables. Numeric solutions of ordinary differential equations are executed through the Runge–Kutta–Felhberg 45 order technique via a shooting scheme. The role of various nondimensional factors on physically interesting quantities is elaborated graphically. The velocity profile rises for modified Hartmann number and decreases for porosity parameter. Thermal enhancement is high in the common wall temperature condition comparative to the case of the Newtonian heating conditions. The concentration profile is enhanced with Schmidt number, but the reverse trend is observed for the thermophoretic parameter. The rate of mass transfer is increased with Schmidt number.     

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.     

Heat and mass transfer of magnetohydrodynamic Casson fluid flow over a wedge with thermal radiation and chemical reaction

A numerical computation to analyze the heat and mass transfer mechanism of a magnetohydrodynamic radiative Casson fluid flow over a wedge in the presence of Joule heating, viscous dissipation, and chemical reaction is carried out in this study. The flow-governing partial differential equations are transformed as ordinary differential equations by relevant similarity transformations and subsequently resolved by Runge–Kutta numerical approach with a shooting technique. The characteristics of momentum, thermal, and concentration border layers due to various influencing parameters are graphically outlined and numerically computed by MATLAB software. We present comparative solutions to construe the relative outcomes of Casson fluid versus Newtonian fluid. Computational outcomes of friction factor and Nusselt and Sherwood numbers are tabulated with suitable interpretations. An increase in skin friction values is noted due to an increment in the thermal Grashof number, whereas a decrease is observed due to the chemical reaction parameter. The Casson fluid displays a superior heat transfer mechanism than the Newtonian fluid. Obtained outcomes are in good agreement with the prevailing literature in the limiting case.     

Arrhenius energy effect on the rotating flow of Casson nanofluid with convective conditions and velocity slip effects: Semi-numerical calculations

The present paper focuses on the effects of Arrhenius activation energy on the hydromagnetic rotating flow of Casson nanofluid. Entropy production, viscous dissipation Brownian dispersion, porous medium, velocity slip, magnetic field, convective heat, and mass conditions are taken into consideration. Transformation schemes are used to extract a nonlinear system of the differential equation. The generalized differential transform method (GDTM) is used to compute/obtain the solutions of the present system. Results for the distributions of velocities, nano concentration, and temperature are scrutinized graphically. The accuracy of GDTM is proved via a comparison of numerical and graphical results with the nearest published results by Hayat et al. and found to be excellent. Graphical results are extracted for different values of pertinent parameters versus velocities, nano concentration, and temperature profiles. The results show that more heat is produced due to the process of thermal radiation for which entropy is knowingly improved.     

Entropy minimized MHD microrotations of Cross nanomaterials with cubic autocatalytic chemical reaction

The Cross viscosity model is a generalized non-Newtonian nanofluid model that has widespread engineering and industrial applications like in the synthesis of polymeric solutions, polymeric latex spheres, animal blood, biological fluids, and polyacrylamides. To analyze the micromotion of such nanofluids, a micropolar flow model is introduced. Entropy generation (EG) minimization is important in thermal fluid systems undergoing heat transportation to achieve improved thermohydraulic execution. Homogeneous and heterogeneous reactions involve complex interactions involving the production and consumption of reactant species. Nonlinear thermal radiation plays a vital role in thermal systems undergoing a drastic change in the temperature gradient. The main focus of this study is the investigation of MHD microrotation in Cross nanofluids subject to nonlinear thermal radiation and autocatalytic chemical reactions. The findings from this study show that amplifying the Weissenberg number and power-law index leads to augmentation in axial and transverse fluid velocity components and emaciation in microrotations. Strengthening the magnetic field yields enfeeblement of fluid velocities. In addition, increasing the micropolar parameter leads to the growth of flow velocity, microrotation, and fluid temperature. An increase in Brinkman number contributes to the thicker thermal boundary layer. EG number grows with a rise in Reynolds number.     

Heat transfer analysis in a hydromagnetic Walters' B fluid with elastic deformation and Newtonian heating

In this study, a computational investigation is carried out to examine the interaction of heat generation/absorption with elastic deformation in a viscous hydromagnetic Walters’ B model past a stretching surface under the intensity of Newtonian heating. The model equations which are responsible for the motion of the fluid and heat interactions are reworked to ordinary differential equations by the appropriate similarity variables and solved via the homotopy analysis method. The parameters encountered were discussed through graphs and tables. The result reveals among others that the heat generation and Newtionian heating magnifies the temperature across the layer and makes quiescent fluid experience a thermal effect.     

Entropy generation in Casson nanofluid flow over a surface with nonlinear thermal radiation and binary chemical reaction

We introduce a model that precisely accounts the flow of fluid of Casson nanofluid over a stretched surface with activation energy and analyze entropy generation. The model is an attempt to investigate heat transfer and entropy generation in the laminar boundary layer near a stagnation point. The modified Arrhenius function for activation energy is used. Here, the flow of the fluid is subjected to nonlinear thermal radiation, viscous disipation, binary chemical reaction, and external magnetic field. The coupled nonlinear system is further validated using the spectral lineralization method. The method is found to be accurate and convergent. The results show that the Reynolds number and Casson parameter have a significant effect in entropy generation.     

Influence of radiation and viscous dissipation on MHD heat transfer Casson nanofluid flow along a nonlinear stretching surface with chemical reaction

The present article investigates the influence of Joule heating and chemical reaction on magneto Casson nanofluid phenomena in the occurrence of thermal radiation through a porous inclined stretching sheet. Consideration is extended to heat absorption/generation and viscous dissipation. The governing partial differential equations were transformed into nonlinear ordinary differential equations and numerically solved using the Implicit Finite Difference technique. The article analyses the effect of various physical flow parameters on velocity, heat, and mass transfer distributions. For the various involved parameters, the graphical and numerical outcomes are established. The analysis reveals that the enhancement of the radiation parameter increases the temperature and the chemical reaction parameter decreases the concentration profile. The empirical data presented were compared with previously published findings.     

Buoyancy forces and activation energy on the MHD radiative flow over an exponentially stretching sheet with second‐order slip

The current study explores the effects of second‐order slip and activation energy (AE) on the magnetohydrodynamic and radiative fluid flow caused by a surface with exponential stretching. The binary chemical reaction with mixed convection is considered in this physical model to discover the heat transfer phenomenon. The governing system of equations leads to a set of nonlinear ordinary differential equations by using scaling analysis. The transformed system is calculated computationally by using the most powerful Shooting procedure with the support of MATLAB software. The characteristics of various flow parameters on the governing flow field are exhibited pictorially and deliberated. The results revealed that the coefficient of heat and mass transfer upsurge with growing values of the second‐order slip parameter and skin friction coefficient has a reverse effect on the first‐order slip parameter. The thermal measure of the fluid in the presence of suction and slip conditions is seen to be lesser than that with the nonslip and nonsuction conditions. The heat measure of the fluid augments with the rising buoyancy parameter. The influence of slips coupled with AE is significant in the fluid flow and heat transfer characteristics. The outputs of the current investigation are validated by comparing the Nusselt number with the available results and are found to closely agree as a limiting case.     

Heat and mass transfer flow over a stretching surface with Ohmic heating and chemical reaction

The present study analyzes the effect of chemical reaction on an unsteady magnetohydrodynamic boundary layer viscous fluid over a stretching surface embedded in a porous medium with a uniform transverse magnetic field. A Darcy‐Forchheimer drag force model is employed to simulate the effect of second‐order porous resistance. Dissipative heat energy based on both viscous and Joule dissipation along with a heat source/sink is considered to enhance the energy equation. Similarity analysis is imposed to transform the governing differential equations into a set of nonlinear coupled ordinary differential equations. These sets of equations are solved numerically using the Runge‐Kutta fourth‐order scheme followed by the shooting algorithm. The effects of physical parameters such as magnetic field, Prandtl number, Eckert number, Schmidt number, unsteadiness parameter, and chemical reaction parameters have been discussed on velocity, temperature, and concentration fields. Computation for the coefficient of skin friction, rate of heat and mass transfer is done and presented in a table for validation of the present outcomes.     

Stability analysis on dual solutions of MHD Casson fluid flow with thermal and chemical reaction over a permeable elongating sheet

The endeavor of this study is to explore the nature of dual solutions (steady and unsteady) for the Casson fluid flow with the simultaneous consequences of both thermal and mass transmissions. The flow passes above an absorbent elongating sheet in the existence of a constant magnetic field. The supported leading equations are remodeled into a set of solvable forms with the assist of suitable similarity variables and hence deciphered utilizing the “MATLAB routine bvp4c scheme.” Due to the sudden changes in the surface with time, the temperature and flow behavior over the sheet also change, and hence dual-type flow solutions exist. Stability scrutiny is implemented to examine the less (more) stable and visually achievable solutions. From this study, we have achieved many interesting facts, among them, we can use magnetic and Casson fluid parameters to control the motion of the fluid and to enlarge of thermal transmission of the fluid. This flow model has many important applications in different physical fields, such as engineering sciences, medical sciences, and different industrial processes. One of the most important results, which has been achieved from this investigation, is that the Prandtl number enriches the heat transfer rate of the fluid at the surface during the time-independent case under the suction environment. Also, the chemical reaction parameter helps to enhance the mass accumulation rate of the fluid in both cases.     

MHD rotating flow of a Maxwell fluid with Arrhenius activation energy and non‐Fourier heat flux model

In the present work, the effects of the transfer of heat, as well as the mass phenomenon of a Maxwell fluid in revolving flow over a unidirectional stretching surface are discussed. The result of the magnetic field within the boundary layer is considered. In the energy equation, the heat flux model of non‐Fourier Cattaneo–Christov is employed. The customized Arrhenius function for energy activation is used. By using the transformation strategy, nondimensional expressions are achieved. To predict the highlights of the current effort, the result of the emerging nonlinear differential structure is calculated with the aid of the shooting procedure as well as the Runge–Kutta Fehlberg procedure. The influence of velocity and temperature along with concentration profiles for various physical parameters is analyzed. The involvement of fluid relaxation and thermal retardation phenomena is unequivocally mentioned. The evolution of heat transfer, as well as the rate of mass in the flow of fluids, is illustrated by the use of graphs in addition to tables. Furthermore, the current effort is confirmed by examination with previously published results, which establishes a strategy for the execution of a numerical approach. It is observed that the concentration of a solute in dual combination is relative to both rotation parameters along with activation energy. Besides this, a diminishing pattern in the distribution of temperature is described within the existence of the Cattaneo–Christov flux law by association with the rate of heat transfer because of Fourier's law. The present investigation can be applied in numerous engineering and technical procedures including the development of thin sheets, modeling of plastic sheets, in the lubrication system industry related to polymers, compression, and injection shaping in the area of chemical production and bimolecular reactions. Inspired by those applications, the present work is undertaken.