Inclined magnetic dipole and nanoscale energy exchange with infinite shear rate viscosity of 3D radiative cross nanofluid

Working nanoliquids are used in bionomical concerns and to enhance the energy in the refrigeration system. The unique thermophysical characteristics of nanoliquids made nanoscience interesting and beneficial for fields of engineering, medical, and industry with real applications, like, food science, employing nanoparticles to deliver drugs, food microbiology, detection of foodborne pathogens, detection of foodborne pathogens, electronic device cooling, controlling fusion, magnetic cell separation, cancer therapeutics, nanocryosurgery, and so forth. The aim of this study is to deliver a broad analysis on nanoscale energy exchange and inclined magnetic dipole impact with the mathematical model of cross nanofluid. Scrutiny of movement of fluid is made by placing the magnetic dipole and buoyancy force. Transport of energy is investigated by thermal radiation, nonuniform heat sink–source while checking of mass transfer facts of activation energy and the chemical process is taken into consideration. Moreover, the nanostructured concepts of thermophoresis and Brownian movement along with zero-mass flux constraint are also utilized for the comprehensiveness of this study. Mathematical relations of cross nanofluid are processed with similarity transformation, shooting methodology, and bvp4c Matlab procedure is rehearsed to get the numerical results of this attempt.     

On heated surface transport of heat bearing thermal radiation and MHD Cross flow with effects of nonuniform heat sink/source and buoyancy opposing/assisting flow

Heat transport subject to nonlinear thermal radiation has multiple applications in physics, industry, engineering field, and space technology, such as aerodynamic rockets, solar power technology, large open water reservoirs, and gas-cooled nuclear reactors. This effort studies the magnetohydrodynamic flow of cross fluid, which is a type of non-Newtonian, along a heated surface. Furthermore, the transportation of heat in the fluid is induced by  thermal radiation. Furthermore, the behavior of opposing/assisting flow and impact of nonuniform heat sink/source is scrutinized. The reserved suitable transformations are carried out to shift the ruling equations into nondimensional class. Through reserved transformations, two nonlinear partial differential equations are altered into corresponding nonlinear ordinary differential equations. Then a scheme of integration referred to as Runge–Kutta–Fehlberg is imposed to get a numerical solution of these. The impact of parameters are mentioned concisely on temperature and velocity profiles in the absence and presence of a magnetic parameter. It is proved that the presence of a magnetic field steps up the velocity and temperature as well.     

Numerical simulation of mixed convective 3D flow of a chemically reactive nanofluid subject to convective Nield's conditions with a nonuniform heat source/sink

The present investigation aims to explore the influence of a mixed convection and nonuniform heat source/sink on unsteady flow of a chemically reactive nanofluid driven by a bidirectionally expandable surface. Convective heat transport phenomenon is used to maintain the temperature of the surface. Moreover, zero mass flux is also accounted at the surface such that the fraction of nanomaterial maintains itself on strong retardation. The governing nonlinear set of partial differential equations is transformed into a set of ordinary differential equations via a suitable combination of variables. The Keller‐Box scheme has been incorporated to make a numerical inspection of the transformed problem. The spectacular impacts of the pertinent constraints on thermal and concentration distributions are elucidated through various plots. Graphical outcomes indicate that the thermal state of nanomaterial and nanoparticles concentration are escalated for elevated amounts of Biot number, porosity parameter and nonuniform heat source/sink constraints. Furthermore, it is also seen that escalating amounts of unsteady parameter, temperature controlling indices, Prandtl number, and expansion ratio parameter reduce the thermal and concentration distributions. Numerical results for the rate of heat transference have been reported in tabular form. The grid independence approach is used to verify the convergence of the numerical solution and the CPU run time is also obtained to check the efficiency of the numerical scheme adopted for finding the solution.     

Activation energy effectiveness in dusty Carreau fluid flow along a stretched cylinder due to nonuniform thermal conductivity property and temperature-dependent heat source/sink

This article studies the boundary layer flow analysis and heat and mass transfer of magnetohydrodynamic (MHD) Carreau fluid around a stretchable circular cylinder, comprehensively studying the suspended dust particles' impact. Here, the viscous fluid is theorized to be incompressible and loaded with spherical dust particles of the same size. Additionally, heat and sink sources are examined in the thermal boundary layer in the existence of both chemical reaction and activation energy influences. A compatible similarity set of transformations are utilized to mutate the system of partial differential equation formed in momentum and temperature equations of the fluid and dust phases as well the concentration equation into a set of ordinary differential equations. Therefore, the mathematical analysis of the problem facilitates and the numerical estimates of the problem are obtained using MATLAB bvp4c function. Computations are iterated for various values of emerging physical parameters from dimensionless boundary layer conservation equations in terms of temperature and non-Newtonian Carreau velocity of fluid and dust phases and concentration distribution. Moreover, the terminology of skin friction and Nusselt and Sherwood numbers have been obtained and studied numerically. Some interesting findings in this study are the heat transfer rate dwindles due to the increase of mass concentration of the dust particle. Also, there is a strengthening of the flow with variance in values of the curvature parameter while a weakening has been observed in the thickness of the thermal boundary layer and this hence improves the heat transfer rate. Therefore, the fluid flow around a stretched cylinder would be better, due to its multiple applications in various progressing industrial technologies such as the cement processing industry, plastic foam processing, watering system channels, and so forth. Also, activation energy plays a significant role in various areas such as the oil storage industry, geothermal, and hydrodynamics.  The dusty fluid flow is very important in the field of fluid dynamics and can be found in many natural phenomena such as blood flow, the flow of mud in rivers, and atmospheric flow during mist. Moreover, MHD applications are numerous including power generation, plasma, and liquid metals, and so forth. A perfect agreement between our results and other studies available in the literature is obtained through carrying out a comparison with treating the problem in special circumstances.     

Effect of nonlinear thermal radiation on silver and copper water nanofluid flow due to a rotating disk with variable thickness in the presence of nonuniform heat source/sink using the homotopy analysis method

An analysis of a steady axisymmetric heat transfer nanofluid flow due to a rotating disk having variable thickness in the presence of nonlinear radiation and nonuniform heat source/sink is presented. Water with Copper (Cu) and Silver (Ag) nanoparticles are utilized in the investigation. The governing equations along with boundary conditions are solved using the homotopy analysis method. A parametric study of the physical parameters is done and results are displayed in the form of graphs. The findings indicate that nonlinear radiation has a significant effect on temperature as well as on wall heat transfer when compared with linear case, which is more useful in few engineering processes.     

Significance of heat source/sink on the radiative flow of Cross nanofluid across an exponentially stretching surface towards a stagnation point with chemical reaction

A numerical review on magnetohydrodynamics radiative motion of Cross nanofluid across an exponentially stretchable surface near stagnation point with varying heat source/sink is addressed. Brownian movement and thermophoretic impacts are assumed. The governing equations for this study are first altered as a system of ordinary differential equations by similarity transformation. With an aid of the Runge–Kutta 4th order mechanism together with the shooting procedure, the impacts of several pertinent parameters including chemical reaction on regular profiles (velocity, temperature, and concentration) are explicated. The consequences of the same parameters on surface drag force, transfer rates of heat, and mass are visualized in tables. From the analysis, it was noticed that the magnetic field parameter enhances the temperature and decreases the velocity of the Cross nanofluid. Also, fluid temperature is an increasing function with thermal radiation and nonuniform heat source/sink. The rate of heat transfer is increased with thermophoresis and diminished with Brownian motion. Sherwood's number is diminished with Brownian motion but it was boosted up with thermophoresis. The present results are compared with published results and those are in agreement.     

OHAM simulation of 3D transverse magnetic field in rotating flow of Maxwell nanofluid over a stretching sheet with chemical reaction and heat source/sink

In this article, we investigate the heat transfer characteristics of a Maxwell nanofluid along a stretching sheet with transverse magnetic field, considering the presence of heat source/sink and chemical reaction. We consider appropriate similarity transformation for transforming the governing nonlinear equations into nondimensional highly nonlinear coupled ordinary differential equations. The optimal homotopy analysis method is utilized for solving the resultant-coupled equations. The impact of all sundry parameters, like, Deborah number, Prandtl number, magnetic parameter, thermophoresis, rotation parameter, chemical reaction, velocity slip, Schmidt number, Brownian motion parameter, heat sources per sink, Biot number, and Eckert number, on the temperature, velocity, and concentration fields is reported, analyzed, and described through graphs and tables. It is noticed that higher values of magnetic parameter and Deborah number reduce the horizontal velocity field. Furthermore, it is observed that the Biot number and heat source/sink parameter enhance the temperature distribution.     

Thermosolutal convective non-Newtonian radiative Casson fluid transport over a vertical plate propagated by Arrhenius kinetics with heat source/sink

In the current study, a mathematical formulation is developed by combining the non-Newtonian (Casson) fluid model to simulate the thermosolutal free convection radiative flow over a vertical surface. The current flow model is formulated with a heat sink/source and radiation driven by Arrhenius kinetics. The basic flow equations are transmuted into a nondimensional form via similarity transformations for which numerical simulations are performed utilizing the Runge-Kutta-Fehlberg method with shooting technique. The results obtained for velocity, energy, and species mass concerning various flow parameters are presented graphically. Computed results for skin friction, Nusselt number, and Sherwood number are tabulated. The results have been verified for limited cases by comparing with various investigations, revealing excellent accuracy. The detailed geometry reveals that an increase in the activation energy enhances the flow velocity and heat transport in the Casson fluid system due to exothermic heat reaction. With the increase of the Frank-Kamenetskii term, there is a substantial rise in temperature distribution and a decrease in concentration profiles due to high Arrhenius exothermic process, which revealed that the presence of Arrhenius kinetics is more effective to improve heat transportation phenomenon. Enhancement of the heat source/sink term completely boosts heat distribution. Rise in Radiation parameter, temperature field increases by reducing heat dissipation to the ambient.     

Inclined magnetized and energy transportation aspect of infinite shear rate viscosity model of Carreau nanofluid with multiple features over wedge geometry

Heat transference in fluid mechanism has a deep influence in real-life applications like hot-mix paving, recovery of energy, concrete heating, heat spacing, refineries, distillation, autoclaves, reactors, air conditioning, and so forth. In this attempt, findings related to energy exchange with features of infinite shear rate viscosity model of Carreau nanofluid by placing inclined magnetic dipole over the wedge are made. The main role in the transportation of heat is exercised by incorporating facts of r adiation, nonuniform heat sink source, Brownian motion, thermophoresis, and chemical reaction. The mathematical system of the infinite shear rate viscosity model of Carreau nanofluid gives a system of partial differential equations and furthermore, these are moved into ordinary differential equations. A numerical procedure is applied via shooting/bvp4c to obtain numerical results. Inclined magnetic dipole gives a lower velocity of Carreau nanofluid. Due to the relaxation time factor velocity of Carreau fluid gets down. A* causes to generate the heat internally, so due to this, temperature increases rapidly. The increasing rate of temperature is found very high for the growing Hartmann number. The rate of mass transport becomes low for gradual increment in the parameter of thermophoresis, wedge angle, and Prandtl. Inclined magnetic dipole gives a lower velocity of Carreau nanofluid. Due to the relaxation time factor, the velocity of the Carreau fluid goes down. The absence and presence of magnetic numbers have no influence on velocity, temperature, and concentration files for Le, R_d, θ_f, γ, We, β, Pr, Nb, Nt, A.     

Squeezing flow of Casson hybrid nanofluid between parallel plates with a heat source or sink and thermophoretic particle deposition

The investigations on the flow of non-Newtonian fluids are becoming one of the major topics in the research field. These liquids have substantial applications in industrial and engineering fields such as drilling rigs, food processing, paint and adhesives, nuclear reactors and cooling systems. On the other hand, hybrid nanofluids play a major role in the heat transfer process. Keeping this in mind, the motion of Casson hybrid nanofluid squeezing flow between two parallel plates with the effect of heat source and thermophoretic particle deposition is examined here. The partial differential equations that govern fluid flow are converted into ordinary differential equations using appropriate similarity variables and those equations are numerically solved using the Runge–Kutta–Fehlberg fourth–fifth-order method by implementing the shooting scheme. The graphs depict the effects of a number of key parameters on fluid profiles in the absence and presence of the Casson parameter. These graphs show that fluid velocity enhances with the augmentation of the local porosity parameter. Thermal dispersal upsurges for enhancement of heat source/sink parameter and the concentration profile escalates for an upsurge of the thermophoretic parameter. Skin friction enhances with enhancement in the local porosity parameter.     

Second order velocity slip and thermal jump of Cu–water nanofluid over a cone in the presence of nonlinear radiation and nonuniform heat source/sink using homotopy analysis method

The purpose of the present paper is to explore the second order slip effects on nanofluid flow over a vertical cone. The effects of nonlinear thermal radiation and nonuniform heat source/sink are also taken into account. Water with copper nanoparticles is used as nanofluid in this investigation. The governing partial differential equations for the flow are converted into ordinary differential equations by using transformations and then are solved using homotopy analysis method. The influence of various important parameters on velocity, temperature, skin‐friction, and Nusselt number are presented through graphs. Results indicate that the velocity and magnitude of skin friction decrease with a rise in first and second order velocity slips. A raise in either first or second order temperature jump causes a fall in temperature. Nonlinear radiation increases the more rapidly when compared to the linear radiation case.     

Influence of thermophoretic deposition and viscous dissipation on magnetohydrodynamic flow with variable viscosity and thermal conductivity

In this study, we numerically explore the impact of varying viscosity and thermal conductivity on a magnetohydrodynamic flow problem over a moving nonisothermal vertical plate with thermophoretic effect and viscous dissipation. The boundary conditions and flow-regulating equations are converted into ordinary differential equations with the aid of similarity substitution. The MATLAB bvp4c solver is used to evaluate the numerical solution of the problem and it is validated by executing the numerical solution with previously published studies. The impacts of several factors, including the magnetic parameter, Eckert number, heat source parameter, thermal conductivity parameter, stratification parameter, Soret, Dufour, Prandtl number, and Schmidt number are calculated and shown graphically. Also, the skin friction coefficient, Nusselt number, and Sherwood number are calculated. Fluid velocity, temperature, and concentration significantly drop as the thermophoretic parameter and thermal stratification parameter increases. As thermal conductivity rises, it is seen that the velocity of the fluid and temperature inside the boundary layer rise as well. Also, the Soret effect drops temperature and concentration profile. The applications of this type of problem are found in the processes of nuclear reactors, corrosion of heat exchangers, lubrication theory, and so forth.     

Influence of homogeneous‐heterogeneous reactions and induced magnetic field on the nonlinear thermal convective radiative Jeffrey liquid flow with heat source/sink

An analysis has been carried out to investigate the effect of homogeneous‐heterogeneous reactions and induced magnetic field on the unsteady two‐dimensional incompressible nonlinear thermal convective velocity slip flow of a Jeffrey fluid in the presence of nonlinear thermal radiation and heat source/sink. We assumed that the flow is generated due to injection at the lower plate and suction at the upper plate. We obtained a numerical solution for the reduced nonlinear governing system of equations via the shooting technique with fourth‐order Runge‐Kutta integration. We plotted the graphs for various nondimensional parameters, like Deborah number, heat source/sink parameter, nonlinear convection parameter, nonlinear radiation parameter, magnetic Reynolds number, Strommer's number, velocity slip parameter, strengths of homogeneous, heterogeneous reaction parameters and skin friction over the nondimensional flow, temperature, concentration profiles and magnetic diffusivity fields. Also, we calculated the numerical values of boundary properties, such as the skin friction and heat transfer rate. We noticed that the temperature of the fluid is enhanced with the radiation parameter, whereas the concentration decreases with increase of the magnetic Reynolds number. The present results have good agreement with published work for the Newtonian case.     

Effect of heat source/sink on MHD flow due to porous rotating disk with variable thickness in the presence of cross diffusion

An analysis of steady magnetohydrodynamic axisymmetric flow of a viscous incompressible electrically conducting fluid due to porous rotating disk with variable thickness in the presence of heat source/sink is presented. Soret and Dufour effects (cross‐diffusion) are also considered. The governing partial differential equations are transformed into a system of nonlinear ordinary differential equations. The homotopy analysis method is used to solve the resulting coupled nonlinear equations under appropriate transformed boundary conditions. A parametric study of the physical parameters is made and results are presented through graphs and tables. The results indicate that the thermal boundary layer is thicker for the flow problems having a heat source when compared with that of the problems without a heat source. It is also found that thickness of the disk is having a high impact on fluid velocity, temperature, and concentration.     

Impact of relative motion of a magnetic field on unsteady magnetohydrodynamic natural convection flow with a constant heat source/sink

This study analyzes time‐dependent magnetohydrodynamics natural convective flow of a viscous incompressible fluid in an annulus with ramped motion of the boundaries. The governing momentum and energy equations are solved analytically, in terms of the modified Bessel function of the first and second kinds. The influence of governing parameters such as the Hartman number, radius ratio, Grashof number, heat absorption parameter, and Prandtl number are discussed with the help of line graphs. It is found that the Hartmann number has a retarding effect on fluid velocity when K = 0.0 and K = 0.5, while the reverse effect is noticed when K = 1.0. The Hartman number also decreases the mass flow rate for all cases of $K$ while it enhances the skin friction at the inner surface of the outer cylinder. It increases the skin friction at the outer surface of the inner cylinder when K = 1.0 and K = 0.0, but decreases the skin friction at the outer surface of the inner cylinder when K = 0.5.     

Study of chemically reactive and thermally radiative Casson nanofluid flow past a stretching sheet with a heat source

Nanoparticle (NP) delivery is an exciting and rapidly developing field that adequately takes care of thermal radiation in blood flow and is likely to have bearing on the therapeutic procedure of hyperthermia, blood flow, and heat transfer in capillaries. The NP parameters such as size, shape, and surface characteristics can be regulated to improve nano-drug delivery efficiency in biological systems. The NPs outperform traditional drug delivery processes in drug carrying capacity and controlled release. The current article investigates the boundary layer flow and heat transfer of thermally radiative Casson nanofluid (NF) over a stretching sheet with chemical reaction and internal heat source. In our study, Cu and Al₂O₃ are taken as NPs in a suitable base fluid. The problem is analyzed by using similarity transformations and is solved with MATLAB's built-in solver bvp4c. The effects of pertinent parameters characterizing the flow model are presented through graphs and tables. The important findings of the investigation are noted as: the use of metallic oxide is more beneficial to attain higher temperature within a few layers close to the bounding surface; the appearance of convexity and concavity in the concentration profile attributed to flow instability, and the constructive and destructive heterogeneous reactions at the bounding surface have distinct roles to modify the NF flow in the boundary layer.     

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.     

Irreversibility analysis of micropolar nanofluid flow in a vertical channel with the impact of inclined magnetic field and heat source or sink

This article examines the inclined magnetic field effect on the flow of micropolar nanofluids in a vertical channel with convective boundary conditions and heat source or sink. Thermodynamics second law is employed to analyze the aspects of entropy generation. The governing differential equations are modified into dimensionless form by using suitable nondimensional variables. These transformed equations are solved by implementing the differential transform technique. The results are analyzed graphically. Skin friction and Nusselt number values are evaluated at the boundary walls of the channel. The major findings of the study are material parameter enhances the microrotation but suppresses both velocity and temperature. Magnetic parameter and angle of the implication of magnetic field decrease the velocity and microrotation. Material parameter and angle of imposed magnetic field minimize the entropy generation.     

Cu‐Al2O3/H2O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

The resent development of research in the field of nano technology introduced hybrid nanofluids which are advanced classes of fluids with augmented thermal properties and it gives better results comparing to regular nanofluid. The aim of the present work is to study the significant effects of variable viscosity and viscous dissipation on a porous stretching sheet in the presence of hybrid nanofluid and radiative heating. In this model, two types of nanoparticles, namely copper (Cu) and alumina oxide (Al₂O₃), are suspended in the base fluid H₂O to form a hybrid nanoliquid. The novelty of this study is to introduce variable viscosity along with natural convection in the momentum equation and viscous dissipation in the energy equation. Mathematical modeling is employed in this study, whereby partial differential equations for the fluid flow are constructed and transformed to a set of ordinary differential equations, and hence resolved computationally by Runge‐Kutta‐Fehlberg method along with shooting scheme. The most important results for relevant parameters concerning the flow heat measure, surface drag, and heat transfer coefficients are thoroughly examined and presented graphically for both Cu‐Al₂O₃/water hybrid nanofluids. There is an increase in hybrid nanofluid velocity profile with mounting values of $\lambda$, and the Cu‐water nanofluid converges to the boundary more quickly than the hybrid nanofluid due to the occurrence of variable viscosity. The results concluded that the Nusselt number of the viscous fluid is lower than that of the nanofluid and hence the hybrid nanofluid (ie, heat transfer rate: normal fluid < nanofluid < hybrid nanofluid). The outcomes of present investigations are in close agreement with the viscous fluid as a particular case.     

Exploration of radiative heat energy on the peristaltic blood flow of a nanofluid in conjunction with a heat source

The peristaltic flow of a conducting nanofluid associated with the Buongiorno model observed within a wavy channel is proposed in this article. In a peristaltic flow, the process of pumping takes place from a lower pressure to a high-pressure region. It is treated as a vehicle through which the liquid passes in a channel due to its dynamic rush and expands in its length. Therefore, an analysis is carried out for the interaction of thermal radiation and heat source on the peristaltic flow of nanofluid past a tapered channel. The crux of this investigation is the interaction of Hall current due to the conjunction of conducting medium. An analytical technique is used to get the solution of the transformed governing equations, and furthermore, the pressure gradient is also evaluated. The flow phenomena characterized by certain parameters are obtained and presented via graphs. An important observation is seen in that the contribution of magnetic field and Hall current may favor the pumping process and the pressure gradient lowering in the conducting medium is one of the important characteristics.