Natural convection boundary layer flow of nanofluids around different stations of the sphere and into the plume above the sphere

The main intent of the present study is to investigate the natural convection boundary layer flow of nanofluids around different stations of the sphere and eruption of the fluid from the boundary layer in to the plume above the sphere. It is pertinent to point out that in this study heated sphere is treated as point source. The system of transport boundary layer equations is based on the effects of Brownian motion and thermophoresis. The system of dimensioned boundary layer equations is transformed into nondimensional form. Later, the nondimensional form of the mathematical model is solved numerically by using implicit finite difference method. The solution of the problem depends on a controlling parameters Prandtl number P_r, Lewis number , thermophoresis parameter , and Brownian motion parameter . Particularly, it is observed that for Lewis number , Prandtl number P_r, Brownian motion parameter , and thermophoresis parameter the velocity profile is maximum at station and minimum at station . On the other hand temperature distribution is uniform at each station around the sphere and slightly reduced for . It is also observed that nanoparticles concentration is maximum at station and minimum at station We also established the result that with the increase of skin friction is reduced while the heat and mass flux are increased in the plume region‐III.     

Significance of the nonlinear radiative flow of micropolar nanoparticles over porous surface with a gyrotactic microorganism,activation energy,and Nield's condition

Current continuation presents the numerical study regarding stretched flow micropolar nanofluid over moving the sheet in the existence of activation energy and microorganisms. Furthermore, nonlinear aspects of thermal radiation are also utilized in the energy equation which results in the energy equation becomes highly nonlinear. This investigation has been performed by using convective Nield boundary conditions. First, useful dimensionless variables are implemented to reduce the partial differential into ordinary ones. Later on, the approximate solution of the transformed physical problem is computed by using the shooting scheme. A detailed physical interpretation of obtained results is also presented for velocity, temperature, motile microorganisms density, and mass concentration profiles. A detailed graphical explanation for each engineering parameter has been discussed for some specified range like , and The theoretical computations based presented here can be more proficient to attain the maximum efficiency of various thermal extrusion systems and microbial fuel cells.     

Effect of viscous dissipation on finding dual solutions for mixed convection boundary layer flow for nanofluid

The effect of viscous dissipation on mixed convection boundary layer flow for Ag‐water nanofluid under steady‐state condition has been studied numerically for both the buoyancy assisting and opposing flows over a vertical semi‐infinite flat plate. A new co‐ordinate system has been introduced to transform the governing partial differential equations (PDEs) to facilitate the numerical calculations. Then, the local similarity method has been used for approximating the transformed PDEs to ordinary differential equations. Further, the quasi‐linearization method has been introduced to linearize the nonlinear equations and then numerical integration has been carried out using implicit trapezoidal rule along with the principle of superposition. For higher Pr, the coupled differential equations behave like stiff differential equations. To overcome the situation, orthonormalization process has been introduced. The effects of solid volume fraction of nanoparticles , the mixed convection parameter , Prandtl number , and Eckart number have been analyzed on the heat transfer and flow characteristics. It has been observed that the dual solutions are obtained for buoyancy opposing flow only and the range of dual solutions have become wider with the increases in . Further, nanofluids enhance the heat transfer process as compared to conventional heat transfer fluids . Moreover, the addition of viscous dissipation causes less heat transfer in the boundary.     

Barycentric rational interpolation method for numerical investigation of magnetohydrodynamics nanofluid flow and heat transfer in nonparallel plates with thermal radiation

In this study, the problem of heat transfer in the steady two‐dimensional flow of an incompressible viscous magnetohydrodynamics nanofluid from a sink or source between two shrinkable or stretchable plates under the effect of thermal radiation has been studied. The governing differential equations have been solved numerically using a collocation method based on the barycentric rational basis functions. This method employs the derivative operational matrix of the barycentric rational bases and the weights that were introduced by Floater and Hormann. The influence of some embedding parameters, such as the solid volume fraction , the Reynolds number , the Hartmann number , the Prandtl number , the radiation parameter , the stretching‐shrinking parameter, , and the angle of the channel on the temperature distribution and velocity profile has been illustrated by graphs and tables. Numerical results reveal the efficiency and high accuracy of the proposed scheme compared to the previously existing solutions. Furthermore, the implementation of the proposed method is fast and the run time is short.     

Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

In this paper, an attempt has been made to analyze the effects of various parameters, such as Soret and Dufour effects, chemical reaction, magnetic field, porosity on the fluid flow, and heat and mass transfer of an unsteady Casson fluid flow past a flat plate. Convective boundary conditions in heat and mass transfer and slip constant on velocity have been taken into account for analysis. The governing equations of the model have been solved numerically using the MATLAB program bvp4c. The impact of various parameters of the model on the velocity, temperature, and concentration profiles has been analyzed through different graphs. To get an insight into the physical quantities of engineering interest, viz, skin friction, Sherwood number, and Nusselt number, their numerical values have been computed for various parameters. The range of the parameters used in numerical computations are , , , , , , and . It has been noticed from the tabulated values that the skin friction gets enhanced with the increase in the thermal and solutal Grashof number, whereas its reverse effects have been observed with an increase in the Biot number. In limiting case, the present study is also compared with the available results in the literature.     

Tangent hyperbolic nanofluid with mixed convection flow: An application of improved Fourier and Fick's diffusion model

This article presents a tangent hyperbolic fluid with the effect of the combination of forced and natural convection flow of nanoparticle past a bidirectional extending surface. Modified Fick's and Fourier's diffusion theories are incorporated into concentration and energy equations, respectively. Convective boundary conditions and second‐order slip flow are taken in the boundary condition. Nonlinear partial differential equations result after boundary layer approximations of the mathematical formulation of the flow problem. Nonlinear high order ordinary differential equations (ODEs) are formed by applying similarity transformation on the nonlinear partial differential equations. The transformed equations are solved with the bvp4c algorithm from Matlab. The numerical solution of ODEs was obtained and the effect of interesting parameters, dimensionless velocity component along x‐ and y‐axis, temperature, and concentration particle, Re_x, Re_y, , and , were presented through tables and graphs and discussed thoroughly. The results indicated that a decrease in velocity along with the y‐axis results from the increasing behavior of S, M, and n. Decrease in both temperature and concentration results in an increase of but their elongation is a result of increase in Bi. An increase in concentration results in decrease of N and S but a decrease in concentration results in the widening of Sc, Nb, and . Furthermore, enlargement of and results in increase of and modules and elongation of both and results in increase of and (Sc and Nb), respectively. A comparison with previously published literature was performed and a good agreement was found.     

MHD boundary layer of GO–H2O nanoliquid flow upon stretching plate with considering nonlinear thermal ray and Joule heating effect

This essay investigates a steady three‐dimensional laminar boundary layer flow of magnetohydromagnetic radiative of graphene oxide‐water nanofluid over an extensible surface in the attendance of couple stress, thermal ray, and Joule heating impact. Governing equations are solved numerically using the Runge‐Kutta‐Fehlberg 4.5 approach after the transformation of partial differential equations into ordinary differential equations. The main goal of this essay is to check the impacts of variations in the value of numerous parameters on the velocity along x and y‐axis directions () and temperature () profiles, and also on the local skin friction coefficient along x and y‐axis directions in the presence of couple stress (K > 0) and the lack of couple stress (K = 0) and local Nusselt number for the two modes of nonlinear () and linear () thermal ray. The results elucidate that the local Nusselt number for both and modes has a direct connection with radiation parameter (R) and Prandtl number (Pr) and an inverse relation with Eckert number (Ec) and Hartman number (Ha). In addition, the skin friction coefficient has an inverse relation with couple stress (K).     

Computation of entropy generation in dissipative transient natural convective viscoelastic flow

Entropy generation is an important aspect of modern thermal polymer processing optimization. Many polymers exhibit strongly non‐Newtonian effects and dissipation effects in thermal processing. Motivated by these aspects in this study, a numerical analysis of the entropy generation with viscous dissipation effect in an unsteady flow of viscoelastic fluid from a vertical cylinder is presented. The Reiner‐Rivlin physical model of grade 2 (second‐grade fluid) is used, which can envisage normal stress variations in polymeric flow‐fields. Viscosity variation is included. The obtained governing equations are resolved using implicit finite difference method of Crank‐Nicolson type with well imposed initial and boundary conditions. Key control parameters are the second‐grade viscoelastic fluid parameter (), viscosity variation parameter (), and viscous dissipation parameter (). Also, group parameter (), Grashof number (Gr), and Prandtl number (Pr) are examined. Numerical solutions are presented for steady‐state flow variables, temperature, time histories of friction, wall heat transfer rate, entropy, and Bejan curves for distinct values of control parameters. The results specify that entropy generation decreases with augmenting values of , , and Gr. The converse trend is noticed with increasing Pr and . Furthermore, the computations reveal that entropy and Bejan lines only occur close to the hot cylinder wall.     

Numerical simulation of nanoparticle shape and thermal ray on a CuO/C2H6O2–H2O hybrid base nanofluid inside a porous enclosure using Darcy's law

In this study, the physical aspects of magnetohydrodynamic flow and heat transfer of a hybrid base nanofluid in a porous medium under the effect of the shape, thermal radiation, and Lorentz force have been examined using the finite element method. Copper oxide (CuO) of various shapes was dispersed into ethylene glycol 50%‐water 50% (likewise for Fe₃O₄). The Darcy model is chosen because of the porous medium. The effect of changeable, diverse parameters, for example, Hartmann number (Ha), volume fraction (), radiation parameter (), and buoyancy force (Ra), on the streamlines, temperature gradient, and Nusselt number are shown through contours. Outputs show that the Fe₃O₄ nanoparticles have a smaller temperature gradient than that of CuO nanoparticles. The Nusselt number decreases for a larger (Ha) number, but increases for a larger Ra, Rd. The blade shaped nanoparticle has a larger impact on increasing compared with that of other shapes.     

Instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media

We studied linear and nonlinear instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media. We studied the critical Rayleigh number and traced marginal stability curves at different parameters , , , and . We obtained Takens‐Bogdanov and co‐dimension two bifurcation points. The Newell‐Whitehead multiple scheme was employed to derive amplitude equations at Pitchfork and Hopf bifurcation. At the onset of Pitchfork bifurcation we identified Eckhaus and Zigzag instability regions and studied Nusselt number. The system of coupled Landau Ginzburg equations were derived at the onset of Hopf bifurcation and identified secondary instability regions for fixed parameters, steady state mode shifted to standing and traveling waves as increases.     

MHD boundary layer flow of SWCNT‐water and MWCNT‐water nanofluid over a vertical cone with heat generation/absorption

The analysis is carried out to investigate the magneto hydro dynamics (MHD) boundary layer flow, heat and mass transfer characteristics of two carbon nanotubes, namely, single‐wall carbon nanotubes (SWCNTs) and multiwall carbon nanotubes (MWCNTs), with water as the base fluid by taking thermal radiation and chemical reaction into consideration. Suitable similarity conversions are employed to reduce nonlinear partial differential equations into the system of ordinary differential equations, and these equations together with boundary conditions are solved numerically using the finite element method. Velocity, temperature, and concentration distributions as well as skin friction coefficient, Nusselt number, and Sherwood number for diverse values of influencing parameters are examined in detail, and the results are displayed graphically and in tabular form. It is found that the rate of heat transfer is remarkably higher in water‐based MWCNTs than the SWCNTs as the value of the nanoparticle volume fraction parameter rises in the boundary layer regime.     

Conjugate heat transfer from a circular cylinder to a power‐law non‐Newtonian fluid

In this paper, conjugate heat transfer from a circular cylinder with a heat source to a non‐Newtonian power‐law fluid is studied. Numerical calculations are carried out in an unconfined computational domain for Reynolds numbers (), power‐law indices (), and Prandtl numbers () with different heat source values. The pressure coefficient, value, and position of maximum temperature inside the cylinder and the local and average Nusselt number are calculated. Also, the effects of Re, Pr, n, and heat source value on the thermal characteristics in the solid cylinder and the fluid around it are studied and discussed.     

A semianalytical technique for MHD peristalsis of pseudoplastic nanofluid with temperature‐dependent viscosity: Application in drug delivery system

An analysis has been implemented to study the influences of nonconstant viscosity and magnetohydrodynamics on pseudoplastic nanofluid through a porous medium. Ohmic dissipation, chemical reaction, and heat generation are taken into consideration. The current problem is debated under the molds of tiny or zero and approximation. Two models of nonconstant viscosity are deliberated. Model (I)—all parameters are nondimensional and have been measured as constants inside the flow. Model (II)—all these stated nondimensional parameters have been considered to differ with the temperature. Comparison among the solutions achieved by utilizing numerical results and multi‐step differential transform method (Ms‐DTM) is displayed in excellent agreement. Attention is dedicated to , ‐, and parameters. The governing equations for each case have been explained by an easy and highly perfect series established seminumerical Ms‐DTM utilizing Mathematica 11, which uses mathematical software package. Nanofluids are active for drug carrying and drug delivery systems because of the control with the velocity of fluid.     

Studying the effect of radiation on thin‐film sprayed nanofluid flow with heat transfer

In this paper, we discuss thin‐film nanofluid sprayed in non‐Darcian, magnetohydrodynamic, embedding in a porous medium flow and thermal radiation with heat transfer generation on a stretching cylinder. The spray rate is a function of film size. A comparative study is made for the nanoparticles, namely, copper oxide , alumina oxide (), and iron oxide . The governing continuity, momentum, and energy equations of the nanofluid are reduced using similarity transformation and converted into a system of nonlinear ordinary differential equations, which are solved numerically. Numerical solutions are obtained for the velocity and temperature fields as well as for the skin‐friction coefficient and Nusselt number. The pressure distribution and spray rate are also calculated. The results are presented in graphical forms to study the effects of various parameters.     

Laminar natural convection of power‐law fluids over a horizontal heated flat plate

Natural convection of power‐law fluids over a horizontal flat plate with constant heat flux is studied. The stretching transformations relating the similarity forms of the boundary layer velocity, pressure, and temperature profiles are applied to the governing boundary layer equations. The resultant set of coupled ordinary differential equations are solved analytically and numerically using the integral method and the finite difference method, respectively. The results are presented for the details of the velocity and temperature fields for various values of the non‐Newtonian power‐law viscosity index (n) and the generalized Prandtl number (Pr*). At a fixed value of the viscosity index, increasing the Prandtl number increases the skin friction and wall temperature. For Pr* > 1, a lower viscosity index results in larger wall skin friction, temperature scale, and thermal boundary layer thickness, and thus lower Nusselt number. The reverse trend is observed for Pr* < 1. By using an integral solution and the numerical results, a semi‐analytical correlation for the Nusselt number is obtained, valid for and .     

Dynamics of nonuniform viscosity of unsteady CuO–H2O nanofluid flow from a spinning body

This paper studies an unsteady rotating flow over a sphere. The substantial effect of nonuniform viscosity is accounted in the extant study. nanofluid is used in adopted nanofluid model. A comparative study among the upshot of nonuniform viscosity and uniform viscosity on present nanofluid model is established here. Primary equations of adopted model have been standardized through similarity methodology and the subsequent equations have been resolved numerically by expending an RK‐4 shooting exercise. The stimulus of encouraging flow parameters on the flow specific is made accurately through diagrams and charts. We witnessed that the heat transmission rate is intensified for unsteadiness factor of the present flow, which suggests that the rate of cooling improves. The unsteadiness factor supports the flow to upsurge in and the reverse consequence originates in the spinning direction. The heat transmission rate is higher in case of nonuniform viscosity than uniform viscosity.     

Unconditional nonlinear stability for double‐diffusive convection in a porous medium with temperature‐dependent viscosity and density

In this study, fluid flow in a porous medium is analyzed using a Forchheimer model. The problem of double‐diffusive convection is addressed in such a porous medium. We utilize a higher‐order approximation for viscosity‐temperature and density‐temperature, such that the perturbation equations contain more nonlinear terms. For unconditional stability, nonlinear stability has been achieved for all initial data by utilizing the or norms. It also shows that the theory of is not sufficient for such unconditional stability. Both linear instability and nonlinear energy stability thresholds are tested using three‐dimensional (3D) simlations. If the layer is salted above and salted below then stationary convection is dominant. Thus the critical value of the linear instability thresholds occurs at a real eigenvalue , and our results show that the linear theory produces the actual threshold. Moreover, it is known that with the increase of the salt Rayleigh number, R_c, the onset of convection is more likely to be via oscillatory convection as opposed to steady convection. The 3D simulation results show that as the value of R_c increases, the actual threshold moves towards the nonlinear stability threshold, and the behavior of the perturbation of the solutions becomes more oscillatory.     

Analysis of a boundary layer flow over moving an exponentially stretching surface with variable viscosity and Prandtl number

Boundary layer flow phenomenons on a stretching sheet find numerous applications in industrial processes such as manufacture and extraction of rubber and polymer sheets. The current study focuses on two‐dimensional water boundary layer flow on exponential stretching surface with a vertical plate for variable physical properties of fluid such as viscosity and Prandtl number. The Quasilinearization technique has been used on governing equations to transform nonlinear to linear equations and these equations are discretized by finite difference techniques to get numerical solutions. The effect of buoyancy parameters (λ), velocity ratio parameter () and streamwise coordinator (ξ) on velocity profiles (F), temperature profiles (θ), local skin‐friction coefficient (C_fx(Re_Lξexp(ξ)^)1/2) and the local Nusselt number (Nu_x(Re_Lξexp(ξ)^)?1/2) has been analyzed graphically based on numerical outcome. The magnitude of velocity profiles increases and temperature profile decreases approximately by 4% and 16% with increases the buoyancy parameter from λ = 1 to λ = 3 at = 0.5 and ξ = 1.0. The skinfriction and heat transfer coefficient increases approximately by 22% and 27% with an increase in ξ from 0.5 to 1.0 at fixed = 0.5 and λ = 1.0. The variations of velocity profiles and temperature profiles have more impact with as compared to ξ and λ. The benchmark studies were carried out to validate the current results with previously published work and found to be in excellent agreement.     

Heat transfer enhancement using hybrid nanofluids in spiral plate heat exchangers

A possible way to enhance the rate of heat transfer in the spiral plate heat exchanger (SPHE) is by employing hybrid nanofluids as its working medium. Hence, in the present work, effects of hybrid nanofluids on the thermal performance of SPHE has been investigated numerically. First, a countercurrent SPHE is designed and modeled. Later, simulation of SPHE has been carried out by employing conventional fluid , nanofluids , and hybrid nanofluids to investigate the heat transfer rates. Finally, the performance of SPHE using hybrid nanofluid is compared with that of using water and nanofluids. The heat transfer augmentation of approximately 16%‐27% with hybrid nanofluids of overall 4% nanoparticles volume concentration and 10%‐16% with 2% nanoparticles volume concentration is observed when compared with that of pure water. Therefore, it can be inferred that the application of hybrid nanofluids in SPHE seems to be one of the promising solutions for augmentation of its thermal performance.     

Finite element analysis of non‐Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

The present study considers two‐dimensional mathematical modeling of non‐Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second‐grade differential viscoelastic constitutive model is adopted for blood to mimic non‐Newtonian characteristics, and blood is considered to contain a homogenous suspension of nanoparticles. The Vogel model is employed to simulate the variation of blood viscosity as a function of temperature. The governing equations are an extension of the Navier‐Stokes equations with linear Boussinesq's approximation and Buongiorno's nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate nondimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery, and, furthermore, that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nanoparticle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid‐independence study is included. Blood flow, heat, and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity, and magnetic parameters, that is, stenotic diameter (d), viscoelastic parameter (), thermophoresis parameter (), Brownian motion parameter (), and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature, and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration, and skin‐friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nanoparticle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multiphysical nanoscale, and thermomagnetic behavior, and also the simultaneous presence of biorheological behavior (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat, and mass transfer characteristics. The simulations are relevant to the diffusion of nano‐drugs in magnet‐targeted treatment of stenosed arterial disease.