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In this study, magnetohydrodynamic cross fluid model is used to formulate the 2D boundary layer equations of fluid moving on the parabolic surface. The surface is assumed to be in vertical shape due to the convection. The underlying effects of viscous dissipation and chemical reaction are modeled to observe the transportation of heat and mass rate. To understand fluid behavior, the thermophysical properties are considered as variable because they have huge influence in food processing, viscometers, lubricants and various industrial works. The assumed geometry of fluid flows is similar in shape of bullet, submarine, aircraft and car's bonnet, namely paraboloid surface. The modeled equations of cross fluid with mentioned effects are obtained in form of PDEs and then converted these equations in form of ODEs by assuming set of scaling transformations. For the sake of numerical and graphical outcomes, the resulting equations are solved numerically on Matlab software via BVP4c method. Results achieved across velocity indicate that the decay happens by numerous values of Weissenberg number, power law index, viscosity parameter and Hartmann number. The temperature and concentration fields attained increasing influence by thermal conductivity coefficient, Eckert number and thermal diffusivity parameter. [ABSTRACT FROM AUTHOR]

In the present analysis, tangent hyperbolic fluid is assumed to be flowing over a stretching cylinder. The thermophysical characteristics of fluids are assumed to be variable. The thermal and solutal rates are investigated by using viscous dissipation, activation energy, and thermal radiation. The governing equations occur in the form of partial differential equations, and then these equations are transformed into ordinary differential equations by using similarity transformations. Then, by using the BVP4C method, we obtain the numerical solution to the equations. The impacts of the involved parameters, such as Prandtl, Weissenberg, Schmidt, Eckert number, viscosity coefficient, and thermal radiation parameters, are presented through the graphs. The velocity profile decreases due to the power law index, Weissenberg number, and temperature-dependent viscosity. However, it increases due to the Darcy-Forchheimer number and curvature parameter. The temperature distribution rises with the Eckert number, curvature parameter, and radiation parameter. On the other hand, it declined for the Prandtl number and power law index. Similarly, the concentration profile increases for the activation energy, reaction rate, and temperature difference parameter, but it decreases for the curvature parameter and Schmidt number. • Darcy-Forchheimer and temperature dependent viscosity of tangent hyperbolic fluid. • Viscous dissipation, activation enrgy and thermal radiation is assumed. • The MATLAB programme is used to graphically analyze the behavior. • Stretching cylinder is considered. [ABSTRACT FROM AUTHOR]

AbstractIn the present work, the author used a multistep numerical approach, namely the Milne (Predictor and Corrector) method with the Runge-Kutta method, to discuss the synergistic impacts of magnetohydrodynamic (MHD) and stagnation point flow involving a tangent hyperbolic fluid on the surface of a stretched cylinder. The flow field study is constructed with the impact of heat source/sink, chemically reactive species, and the joule heating effect. The phenomenon of concentration and temperature stratification is also taken into account. The Soret and Dufour effects are used to determine the solutal and thermal performance. To create a mathematical model of a physical occurrence, momentum, energy, and concentration laws are employed. The appropriate transformations can be used to convert nonlinear partial differential equations into ordinary differential equations. The Milne (Predictor-Corrector) method along with the Runge-Kutta 4th order scheme is used to determine the numerical findings. The graphical and numerical findings are depicted to show how several parameters influence the respective fields. The finding indicates that the velocity of fluid reduces by making variation in the Hartmann number whereas the temperature region enhances due to Hartmann number. The movement of fluid increases when the stretching ratio parameter is higher but decreases when the Weissenberg number and curvature parameter are higher. The Soret number reduces the concentration region and Dufour number enhances the temperature profile. The temperature distribution rises with higher inputs of the heat source but declines for the heat sink constrain and thermal stratification coefficient. Similarly, the concentration region upsurges for the stretching ratio parameter, while it decreases for the chemical reaction rate and solutal stratification. [ABSTRACT FROM AUTHOR]

This work dealing to solve the numerical results of magnetohydrodynamic flow material (Casson fluid) moving over the slender parabolic surface with temperature dependent viscosity. To make the enhancement in the thermal and solutal fields, we have determined the impact of thermal radiation, viscous dissipation, joule heating, and chemical reaction on the considered flow material. Due to huge applications in coating processes and aerodynamic industries, the suction/Injection is assumed at the surface. With the help of assumed assumptions, the governing equations are obtained in partial differential equation forms, and these equations are translated into ordinary differential equations form by using the Levy‐Lee similarity transformations. The translated forms of ODE's are then numerically solved by using the Adams‐Milne (Predictor–Corrector) technique. The graphical and numerical findings are determined by producing the emerging parameters. The decrement in velocity is noted due to fluid parameter and suction coefficient whereas the enhancement happens due to natural convection. The numerical determination of physical quantities including, Nusselt number, Skin friction and Sherwood number are also examined here and compared the findings with two numerical techniques (Adam‐Milnes and Bvp4c method). [ABSTRACT FROM AUTHOR]

The aim of this work is to present a natural convective and squeezing flow model of two-dimensional couple stress nanofluid which is flowing on the sensory surface with variable fluid viscosity. The fluid flowing on a microcantilever sensory surface and squeezing is happening at free stream. The sensor is also useful to detect the movement of fluid and the variations in thermal and solutal rates. The Cattaneo–Christov model is adopted along with nanoparticle and chemical reaction to explore the transmission of heat and mass rates. The analysis of heat transmission in non-Newtonian couple stress fluid flowing on squeezed sensory surface by using the Cattaneo–Christov heat conduction model has various industrial and scientific applications including the polymer processing, wastewater treatment, chemical reactors, biomedical flows, cooling and heating processes in industries, heat exchangers, microfluidics, oil and gas industries. All the assumptions are applied in the basic governing laws laws and then we get the model of the partial differential equations. The governing model of equations is transmuted into ordinary differential equations form via the transformations and then the numerical results of these ODE’s are examined with a well-defined numerical technique “Shooting Method”. For higher inputs of couple stress, squeezing index and permeability velocity, the fluid’s internal velocity decreases. Because of the Prandtl number and thermal relaxation coefficient, the heat transfer mechanism slows down. Mass transfer increases for greater inputs of the thermal diffusivity coefficient and decreases due to concentration relaxation. Further, the numerical dependency of emerging parameters on the skin friction is illustrated in tabular form. The parametric effects on the model (velocity, temperature and concentration) are introduced using numerical values shown in the table. [ABSTRACT FROM AUTHOR]

The analysis of non-Newtonian fluid flow over an oscillating surface often involves numerical simulations and experimental investigations. Computational fluid dynamics method including finite difference or finite element techniques can be used to crack the governing equations of the fluid flow. In this work, we used the Crank–Nicolson numerical technique to analyze the numerical behavior of unsteady boundary layer flow of Casson fluid with natural convection past an oscillating vertical plate. The temperature-dependent viscosity is assumed for the flow analysis. The impact of chemical reaction and heat generation coefficient is used to examine the mass and heat transferal rates. The investigation of non-Newtonian fluid flow over an oscillating surface is crucial for a wide range of industrial, biomedical, and scientific applications. The governing model of equations occurs in the form of nondimensional PDEs and then we use the dimensionless variables in order to achieve the dimensional PDEs. These equations are numerically solved by using the Crank–Nicolson technique. The Crank–Nicolson scheme is used because it has the ability to provide accurate and stable solutions and make it a valuable numerical technique in various scientific and engineering disciplines. The findings indicate the significance of numerous parameters on the mass, velocity and energy regions. The numerical outcomes of skin friction are observed due to fluid parameter, viscosity parameter, Grashof numbers of heat and solutal rates. [ABSTRACT FROM AUTHOR]

Medullary thyroid carcinoma is a rare tumour that is anatomically located in the thyroid gland but is functionally a neuroendocrine tumour. It is usually a disease of older age group but manifests in a young patient in familial form. It is derived from parafollicular c cells and has a predilection for lymph node metastasis. It is associated with slow growth in thyroid gland with early nodal metastasis. Serum calcitonin is useful as a preoperative marker of disease burden and prognosis. In the preoperative period serum levels of calcitonin can guide regarding the need for compartment wise lymph node dissection and the possibility of distant metastasis. It is used as a tool of surveillance in the postoperative period. The levels of serum CEA and calcitonin and their doubling time is a useful guide in the detection of early recurrence or distant metastasis. Imaging modality useful for diagnosis is USG in a majority of patients. Thus, the initial diagnosis and preoperative assessment of medullary thyroid carcinoma is similar to other forms of thyroid cancer but further management of disease differs significantly form other forms of differentiated thyroid carcinoma or even anaplastic carcinoma. Prognosis however differs according to age, gender, presence or absence of lymph node metastasis at presentation, metastatic disease at presentation and levels of biochemical markers. [ABSTRACT FROM AUTHOR]

In this article, the physical impact on thermal performance of unsteady incompressible hybrid nanofluid C u − G O / (H 2 O) − C 2 H 6 O 2 (50:50 vol%) has been presented by using the implicit finite difference procedure. A rigid circular object is taken for instance at time t = 0 , a free stream flow hits the outer surface of the circular object. The fluid crosses the boundary of the circular object at different positions. A highly non-linear complex partial differential system is achieved which is solved numerically. The infiltration of various parameters for instance: nanoparticle shapes (cylinders, bricks and Platelets) and volume fraction parameters on velocity profile, skin friction, temperature profile and Nusselt number are demonstrated qualitatively through illustrations. Outputs specify that: mono nanofluid and hybrid nanofluid created by extending volume fractions causes diminution in the velocity profile. Furthermore, solid hydrogen bonding of hybrid nanofluid reasons a sharp growth in thermal conductivity and, thus, rise in temperature profile is noticed. Moreover, the heat transfer rate and temperature profile has always been influenced by different shape factor, so the cylindrical shape particles lead this category afterwards, bricks and platelets. It is noticed that rise in volume fraction parameters show reduction in velocity profile, but opposite impact is noticed in temperature distribution. Moreover, the thermal performance of hybrid nanoparticles is better than the mono nanoparticles. • GO- Cu/H2O– C2H6O2 (50:50 vol%) hybrid nanofluid has been presented. • A rigid circular object is taken. • The different shapes of nanoparticles has been considered. • The fluid crosses the boundaries of the circular object at different positions. • A highly non-linear complex partial differential system is achieved which is solved numerically. [ABSTRACT FROM AUTHOR]

The current study deals with the influence of heat and mass transfer characteristics of viscous fluid near a moving wall with transpiration. The wall and free stream velocities are assumed to be decelerating functions. The calculated solution of unsteady Navier–Stokes equation is an exact solution. In the absence of internal energy change, the analytical solutions of energy and concentration equations are calculated for constant wall temperature near rare stagnation point. The influence of transpiration, unsteadiness parameter, Prandtl number, stretching/shrinking wall parameter and Schmidt number on the fluid, heat and mass transfer features have been shown graphically and elaborated in detail. With the particular values of the governing parameters, two branch solutions are calculated for heat and mass transfer phenomena. These closed-form outcomes are exceptional and can be used as a standard modelling for numerical code justification. [ABSTRACT FROM AUTHOR]

A mathematical model is used to discuss a comparative study of AA7072 (nanofluid) and AA7072/AA7075 (hybrid nanofluid) flow through endoscope. For this evaluation, AA7072 (which is the combination of Al (98 %) and Zn (1 %) mixed with metals Si, Fe and Cu) and AA7075 (which is the mixture of Al (90 %) , Zn (6 %) , Mg (3 %) and Cu (1 %) mixed with metals Si, Fe and Mg) are considered as nanoparticles and water as a base fluid. The inner cylinder is endoscope (rigid and fixed) moving with constant velocity (V) , while the external cylinder is sinusoidal (wave moving down to its boundaries) like the shape of artery in the form of concentration and relaxation phenomena. Low Reynolds number and long wavelength estimation is applied for analytic solution. The resulting nonlinear PDEs are transformed into ODEs by perturbation technique. After this, we compare graphically the behavior of nanofluid and hybrid nanofluids for velocity profile, temperature profile, friction forces on inner and outer cylinders, pressure gradient and pressure rise for different values of solid volume fractions and inner cylinder radius. [ABSTRACT FROM AUTHOR]

In this study, we present numerical and theoretical study of enthalpy and solar radiative heat transfer in a generalized Newtonian fluid flow induced by a flat plate. Our theoretical study depends on thermal diffusion coefficient, thermophoretic and viscous dissipation approach for modeling the steady boundary layer flow of heat and mass transfer over a flat surface. Impact of thermal diffusion coefficient with newly introduced enthalpy at heat and mass equations is considered. The boundary layer equations are transformed into system of ordinary differential equations by applying similarity variables and solved numerically by utilizing fifth-order Runge–Kutta integrator scheme with shooting technique. The physical results are explored by utilizing theoretical and numerical approaches. The numerical results acquired for different mechanisms are presented through tables and figures. The physical properties of the appearing parameters on the mean flow, temperature and concentration are presented through graphs and tables The comparative results are calculated for a limited case and good agreement is noted with previously published work. • Carreau fluid flow near a flat surface are investigated. • Viscosity at initial steady state is discussed. • Enthalpy and thermal diffusion coefficient are considered heat and mass equations. • Thermophoretic effect is considered mass equation. • Relationship between kinematic viscosity and intermolecular force is described. [ABSTRACT FROM AUTHOR]

The peristaltic transport of Carreau-Yasuda fluid model over a sinusoidal medium of non-Newtonian nano flow is examined. In this analysis, the channel walls are considered as ciliated with the higher and lower walls. The formulation of the 2D fluid model depends on the nonlinear (PDEs) that are transformed into simple ordinary (ODEs) by applying the dimensionless parameters and long-wavelength approximation. The numerical solution of the 2D system is taken out by applying the MATHEMATICA solver NDSolve function. The impact of various parameters, such as, flow rate parameter F , wave-length number δ , Brownian motion number N b , thermophoresis number N t , and account of eccentricity α on the velocity profile, temperature distribution, and concentration distribution and stream function are addressed with graphs. [ABSTRACT FROM AUTHOR]

The present approach aims to describe the Soret and Dufour effects on the peristaltic flow of heat and mass transfer for two-dimensional tangent hyperbolic fluid model having cilia walls and electro-osmotic phenomenon in an asymmetric channel. To construct the governing equations, this model employs the long wavelength and low Reynolds number approach. The peristaltic phenomenon due to pressure with electro-osmotic flow have been developed. The flow also comprises of heat and mass rate and this phenomenon have been investigated along with viscous dissipation. The impacts of relevant variables on the velocity, temperature and concentration have been examined by using the graphical results in MATHEMATICA. Overall, the objectives of this work involve a comprehensive investigation of the complex interplay between various physical effects and fluid behavior within an asymmetric channel. This research aims to provide insights into the behavior of the system and its potential applications, especially in fields like microfluidics, biotechnology or materials science. [ABSTRACT FROM AUTHOR]

The current work describes the γ − ALOOH/H 2 O nanofluid flow characteristics near a thin film generated due to outer surface of heated rotating cone. The cone is completely immersed in a nanofluid and turned upside down due to rotation, which creates a thin region. Due to rotation, γ − ALOOH/H 2 O nanofluid produces a centrifugal force, while strong surface tension sustains the centrifugal force at the external surface of the fluid film flow. Therefore, the fluid does not diffuse but moves upward along the cone. γ − ALOOH, H 2 O, heated cone and rotating phenomena causes energy generation in the system. The boundary layer theory and fast rotation are implemented to drive the equations of tangential, radial and meridional velocities and temperature profiles for nanoparticles. The two dissimilar branches with a turning point is calculated between film thickness in the centrifugal and Coriolis zones. Modified Rayleigh's criterion is applied to calculate the new outcomes. • Thin nano-film flow is studied over rotating cone. • Boehmite alumina, water, heated cone and rotating phenomena causes energy generation in the system. • Coriolis (Re < 1) and centrifugal (Re«1) zones are calculated by applying small Rossby approximation. • Modified Rayleigh's criteria is applied to get the desired results. [ABSTRACT FROM AUTHOR]

The present analysis reveals the impact of porous medium and mixed convection nano-fluid flow near an exponentially curved surface. For this purpose alumina is treated as nano-particles along with two base fluids such as H 2 O and C 2 H 6 O 2. Under different assumptions the mathematical model of energy and momentum equations are developed by using curvilinear coordinates. The PDEs are transformed into non-linear differential equations by using similarity transformation variables. The table of skin friction and Nusselt number are drawn by fluctuating the values of different parameters for both fluids. Moreover, the numerical solutions are generated in MATLAB by using Bvp4c. Influence of effective and without effective Pr numbers for an incompressible γ A l 2 O 3 − C 2 H 6 O 2 and γ A l 2 O 3 − H 2 O are investigated. We observe that the velocity profile increases for increasing values of curvature, mixed convection and volume fraction of nanoparticles for two different cases effective and with-out effective Prandtl numbers. Moreover, in case of effective P r number, the temperature profile decreases but for with-out effective P r number temperature profile increases. Furthermore, the graphs are drawn to check the behavior various parameters for effective and with-out effective Pr numbers. • Viscous fluid flow near a vertical curved surface are investigated. • Viscosity at initial steady state is constant considered. • Mixed convection and porous medium are considered momentum equations. • Heat generation is considered energy equation. • Alumina particles are considered due to their high conductivity. [ABSTRACT FROM AUTHOR]

This paper examines the steady-state momentum heat and mass transfer flow of a Casson fluid flow in the existence of a pre-exponential factor. The velocity of the fluid over a vertical stretched pin changes linearly with the axial distance when a Casson model is supposed for the viscosity. A similarity transformation eases the Navier–Stokes partial differential equations that are converted into ordinary differential equations and solved numerically for concentration, velocity, and temperature fields. Moreover, viscosity and conductivity are assumed to be dependent on the temperature profile. Results are discussed for two boundary conditions of the pin, while diffusivity is dependent on concentration. A reaction in the form of a pre-exponential factor is taken on the surface of the pin. Parameters such as the mixed convection parameter, viscosity parameter, and viscoelastic parameter are considered for the control of the flow field. In addition, the internal energy change and the Prandtl number are found to examine the temperature field inside the stretched pin, while the Schmidt number, temperature relative parameter, concentration buoyancy parameter, activation energy parameter, and chemical reaction parameter control the concentration field. [ABSTRACT FROM AUTHOR]

This study relates hyperbolic tangent fluid flow on a permeable stretching cylinder with homogeneous–heterogeneous reaction effects. The prevailing continuity, momentum, and concentration equations are transformed into ordinary differential equations using the similarity transformation method. The resulting nonlinear system of equations is numerically tackled with an efficient, unconditionally stable, accurate, and extensively validated finite difference scheme: the Keller box technique. Graphs are sketched for the interpretation of physical parameters. The coefficient of skin friction is included to illustrate the fluid behavior near the surface of the cylinder. Comparison to the preceding literature is provided for better accuracy of numerical results. [ABSTRACT FROM AUTHOR]

The current investigation is communicated to analyze the characteristics of Darcy–Forchheimer second-grade fluid flow enclosed by a deformable sheet in the existence of both variable thermal conductivity and magnetohydrodynamics. The leading nonlinear energy and momentum partial differential equations are converted into nonlinear ordinary differential equations by utilizing suitable analogous approach. Then the acquired nonlinear problem is numerically calculated by utilizing BVP4C (built in) technique in MATLAB. The influence of certain appropriate physical parameters, namely wall thickness, second-grade fluid, Hartmann number, power index, porosity parameter, inertia coefficient, Prandtl number, and thermal conductivity, on temperature and velocity is studied and deliberated in detail. Numerical calculations of Nusselt number and skin friction for distinct estimations of appearing parameters are analysed through graphs and tables. [ABSTRACT FROM AUTHOR]

Transient MHD flow in Carreau–Yasuda nanofluid produced by impulsively started rotating disk is examined in the occurrence of Darcy–Forchheimer and chemical reactive species considering conventional Fourier's and Fick's laws. Appropriate transformations are used to transform the constitutive equations into nonlinear ordinary differential equations and then solve by using improved form of RK-4 Fehlberg scheme (Cash and Karp). The deviation in flow field due to velocity, friction factor, temperature, heat diffusion rate, nanoparticle concentration, and mass transfer rate is analyzed subsequent to various ambient parameters appearing in the problem. The results of the study reveal that Weissenberg number appearing in the equations leads to deceleration of the radial and tangential velocities while the power law index tends to accelerate the radial and tangential velocities. [ABSTRACT FROM AUTHOR]

Current analysis is devoted to explore the computational aspects of variable viscosity on Williamson nanofluid over a non-linear stretching sheet. Viscosity of the fluid is assumed to be depend on temperature and due to thermal stratification, viscosity of the fluid also depends upon thermal diffusion. The basic mathematical problem (system of PDEs) is converted into non-linear ODEs via applying suitable transformations. Computational solutions of the problem is achieved by efficient numerical approach (shooting method). Characteristics of controlling parameters i.e. Lewis number, thermophoresis parameter, Hartmann number, plastic dynamic viscosity parameter, Weissenberg number, Prandtl number, stretching index, Brownian motion parameter, Prandtl number, thermal and solutal stratification parameters are plotted on concentration, velocity and temperature gradients. Furthermore friction factor coefficient, heat and mass diffusion rates are presented through graphs and tables. Conclusions are made on the basis of entire investigation and it is seen that velocity profile reduces for large values of variable viscosity and thermal stratification parameters while thermal stratification parameter shows opposite behavior for temperature profile. Moreover, concentration profile reduces for enhancing values of Lewis number and increases for large values of stretching velocity parameter. [ABSTRACT FROM AUTHOR]

• An incompressible three dimensional viscously dissipated Williamson fluid is analyzed. • Fluid flow is generated by an irregular non-linear stretching surface. • Effects of heat generation and chemical reaction are examined. • Local skin friction, Nusselt number and mass transfer rate are also calculated. This analysis deals with the incompressible, steady, three-dimensional (3D) viscously dissipated Williamson fluid flow near an irregular surface. It has many applications such as synthesis of polymer solutions, plastic manufacturing, food processing, paper production, adhesives, exotic lubricants, suspension solutions etc. The phenomenon is examined in semi-infinite domain and the flow is produced by means of non-linear stretching. An irreversible process is taken by means of fluid particles stress which converts the energy into heat. The most noticeable procedure of this process is the internal friction between the layers of fluid particles which causes heat generation. The governing equations are initially reformed into ODES by applying applicable variables and then numerical solutions are computed via the shooting technique. Newly characteristics of dimensionless variables are illustrated by means of graphs and tables. The detail analysis anticipates that velocity declines by the elevation of Weissenberg number and wall thickness parameters. Further, the temperature enhances with the increase of Eckert number and heat generation parameter and behaved oppositely analogous to development in Prandtl number. [ABSTRACT FROM AUTHOR]

• A theoretical study is carried out to determine electro-osmotic impact on the Williamson fluid model moving peristaltically along a curved channel. • The equations of Poisson and Nernst–Planck are considered to explore the flow behavior. • Using approximations of "long wavelength and small (or zero) Reynolds number". • Resulting in enhanced heat transfer properties of the fluid. The intension of this research is to explore the electro-osmotic flow of chemicalized Williamson fluid moving peristaltically along a curved channel. The equations of Poisson and Nernst–Planck are applied to model electro-osmotic phenomena. The concerning equations are mapped from a fixed framework to moving one by means of co-ordinate transformations. Using approximations of "large wavelength and minimal (or zero) Reynolds number" the governing equations are generalized. The MATLAB Shooting method is used to graphically analyze the behavior. The impact of factors on flow characteristics is depicted graphically. It is observed that due to a small increment in Williamson parameter both temperature and velocity decreases but the pressure increases. Moreover, by improving value of reverse EDL parameter S (the electro-osmotic parameter), the electric potential of Williamson fluid increases. This model is applicable to a variety of biological flows controlled by the electroosmosis process and fluid thermal properties. [ABSTRACT FROM AUTHOR]

The flow of 2-D cross fluid model with mass and heat transmission over a linearly stretched sheet is analyzed in this paper. Furthermore, we have expanded our study by considering the effects of MHD flow, stagnation point, double stratification, heat generation, radiation effect, nanofluid flow, activation energy and mass diffusion. This type of study has not being investigated previously in literature. The flow generating PDEs are altered into ODEs by deploying suitable transformations. The effects of the parameters involved, namely the Weissenberg number, magnetic field coefficient, Brownian motion coefficient, radiation parameter, Damkohler number, thermophoresis coefficient, Schmidt number, activation energy, heat generation parameter and temperature difference coefficient on the velocity, concentration and energy fields are thoroughly scrutinized. The problem is solved through numerical technique (BVP4c) on MATLAB. The outcomes reveal that the velocity curve upsurges for rising Weissenberg number and decreases due to magnetic parameter. The heat field improves for increasing behavior of the Brownian motion, thermophoresis, heat generation, thermal conductivity and radiation coefficient whereas reverse results are obtained due to Prandtl number and stratification parameter. The concentration improves due to thermophoresis parameter and diffusivity coefficient while reverse outcomes are noticed due to Schmidt number, Damkohler number, temperature difference parameter and Brownian motion parameter. [ABSTRACT FROM AUTHOR]

We present the numerical study of the flow on a heated rotating disk for Bingham plastic fluid. Thermo-physical properties and viscous dissipation are assumed with the influence of entropy generation. This kind of study has a significant attentiveness in the fields of applied engineering for their increased mathematical advantages. We analyzed the solutions of fluid flow and entropy phenomenon for the Bingham fluid. The similarity solution was firstly presented by von Kármán for Newtonian fluid, it is found to be beneficial for the Bingham plastic fluid by transforming the boundary layer partial differential equations into ordinary differential equations. Shooting method is used to crack the dimensionless ordinary differential equations. The Bingham model is momentous for unlimited high shear rates for this we suggest these numerical data provide accurate description of the Bingham fluid and entropy minimization near a rotating disk. The outcomes exhibits that the azimuthal velocity profiles upsurges for upward values of Bingham fluid, and the similar behavior for tangential radial velocity is perceived. The temperature curve is noted to be enhanced for higher magnitudes of Eckert number and thermal conduction parameter. The soret number and diffusivity coefficient creates increment in concentration curve. The entropy function in the flow system enhances for up surging the inputs of Bingham fluid coefficient and thermophoresis diffusion. The results are locally similar for various parameters. We have also included the comparison analysis with published works. [ABSTRACT FROM AUTHOR]

A theoretical study is examined by taking the effects of the boundary layer flow over a heated rotating disk for both anisotropic and isotropic surfaces. We used the Carreau fluid model for shear thinning and thickening behaviors and determine the steady flow profiles under the partial slip model. Thermal conductivity and mass diffusivity are adopted to explore the flow phenomena. Numerical solution of the boundary layer equation is then preformed by using a shooting technique. Thermal conductivity and mass diffusivity increase the temperature and concentration profiles. We determine the base flow profiles and give a physical explanation of the problem though figures and tables. This study explores the interesting physical parameters on the base flow, heat and mass transfer profiles. Comparison has been made with the present results of the literature, achieving a good agreement. [ABSTRACT FROM AUTHOR]

This study deals with the investigation of boundary layer nanofluid flow on a slender paraboloid surface. The front tip of bullet, airplane, missiles and rockets are some examples of this surface. The thermal conductivity and viscosity of fluid has importance in many engineering applications such as auto mobile industries, solar power generation and heat exchangers, therefore the fluid property such as viscosity is considered to be temperature dependent. The thermophoretic motion, Brownian motion, heat generation and chemical reaction effects examines the behavior of heat and mass transport. The unsteady governing model includes momentum, heat and concentration equations which occur in the form of coupled PDEs. In order to solve numerically, a set of suitable transformations simplify the basic governing laws and convert these equations in the form of coupled ODEs. To show the graphical behavior, we simplify determine model of equations by using Matlab software via BVP4c method a built in command. At last, the discussion related to graphs for variation in different parameters are included. [ABSTRACT FROM AUTHOR]

The aim of the present analysis is to examine the effects of slip boundary conditions and mixed convection flow of Williamson fluid over a stretching cylinder. The boundary layer partial differential equations are transformed into ordinary differential equations by using group theory transformations. The required ordinary differential equations are solved numerically by using implicit finite difference method known as Keller box method. The influence of dimensionless physical parameters on velocity and temperature profile as well as skin friction coefficient and local Nusselt number are presented graphically. Comparison has been made to the previous literature in order to check the accuracy of the method. [ABSTRACT FROM AUTHOR]

The motivation of this study arises due to huge occurrence of rotating disk in field of real-world processes like rotational air cleaner, turbomachinery, centrifugal pumps, aerospace engineering and chemical engineering. A numerical investigation is undertaken to study the thermo-physical properties of Newtonian fluid flow over a strongly heated rotating disk with temperature dependent viscosity. The solar radiative heat flux is considered in the heat equation. The temperature dependent viscosity and thermo-physical properties are assumed to explore the flow behavior. Numerical solutions of the converted boundary layer equations are then achieved by using fifth order Rung-Kutta Fehlberg integration approach with a shooting method. The attained results are discussed for mean flow profiles and physical interpretations of the problem are given through graphs and tables. It is observed that temperature dependence viscosity for liquids ranges to decrease the base flow profiles, whilst the gaseous viscosity nature has the opposite impact. The mass diffusion coefficient creates enhancement in concentration field. Moreover, correlations are plotted graphically in terms of temperature, concentration, and viscosity. [ABSTRACT FROM AUTHOR]

The aim current work is to examine the comparison analysis of two non-Newtonian fluids (Carreau and Cross) moving in a squeezed channel across two infinite plates. A microcantilever sensor is placed in the channel. The heat transformation analysis is investigated by the heat absorption effect, variable thermal conductivity and thermal radiation. The phenomenon of concentration transfer is studied via chemical reaction and variable mass diffusion. The physical phenomenon of flow model is translated in the form of PDEs by fundamental laws, such as conservation of momentum, energy and mass transfer. It is difficult to calculate the analytical solution of determining PDEs due to nonlinear nature. Therefore the boundary layer approximation utilizes the flow relating differential equations. The dimensionless form of these ODEs is established by using similarity variables. The results are found with the help of well-defined numerical approach 'Shooting method'. The permeable velocity and Weissenberg number makes the reduction in the velocity field. In shear thinning case, velocity declines of both Carreau and Cross fluid. The temperature grows due to thermal radiation and declines due to heat absorption coefficient. The declined impact of chemical reaction is noted on the mass transfer and increment happens for higher values of mass diffusion coefficient. The required results are note down with graphical manner. [ABSTRACT FROM AUTHOR]

This study is based on 2D Carreau fluid flow across a stretchable porous cylinder with thermal radiation, Soret and Dofour effects. The viscosity is supposed to be heat-dependent. The stretching phenomena is taken at the surface. The leading equations of the flow are formed into non-dimensional shape by using suitable correspondence variables. The non-linear ODEs are cracked by using BVP4C procedure with the help of Matlab software. The influence of significant parameters on mass, momentum and heat is explained numerically and graphically. The importance of porous surface is discussed numerically and graphically with the assistance of plots. The porous space has vast range of applications in the various industrial and geological areas. Porous surfaces are extensively applied in petroleum geology, solar collectors, geophysics, filtration, ventilation procedure and material science. The significant aspect of heat radiation is discussed graphically with the assistance of plots. The vital role of Soret and Dufour effects in mass and heat transport on a stretchable cylinder is presented. The reduction in fluid velocity happens for higher inputs of Weissenberg number We while increment in fluids velocity happens due to curvature parameter. The porosity and viscosity parameters express drop in the fluid velocity. The fluid heat is elevated for growing values of the heat radiation and Dufour number while plot shows decrement in Prandtl number. The source of elevation in fluid concentration is witnessed against the Soret number and curvature parameter and opposite behavior is observed with the Schmidt number. The ranges of considers variables taken are We = 0.5, D f = 0.2, n = 0.2, Pr = 1.5, Rd = 0.1, Sr = 0.1, Sc = 1.5.. [ABSTRACT FROM AUTHOR]

In this paper, the two-dimensional, incompressible non-Newtonian Blasius boundary-layer flow over a heated flat plate is considered. The variational viscosity which impact that model is considered. The thermo-physical properties and solar radiation effect are also discussed. Solutions are analyzed for the shear-thinning and thickening flows. The boundary layer governing equations are firstly non-dimensionalzed and then solved with aid of RK-fifth order method along with Newton Raphson method. The physical characteristics of the appearing parameters on the base-flow, temperature and concentration are presented in the form of figures and tables. Comparison has been made with previous literature and found to be in good agreement. [ABSTRACT FROM AUTHOR]

The goal of present work is to explore the two dimensional, unsteady and incompressible squeezed Maxwell fluid flows between infinite parallel plates in a permeable medium. Flows in porous channels/tubes are of particular relevance in a variety of biological and mechanical engineering applications. Sensor surfaces are employed to detect germs and help to diagnose diseases in medical. The computational aspects of thermal radiation and heat generation for thermal boundary layer are investigated. In important engineering activities such as drying, temperature regulation, and moisture distribution, chemical reactions affect heat and mass movement. Mass transfer affected by chemical reaction is analyzed. For porous medium, Darcy law is applied and the governing equations are simplified by boundary layer approach. The similarity transformation is applied to transform the governing equations into ODEs which are solved by BVP4C method. The effects of porosity parameter, permeable velocity and Maxwell number on velocity are studied numerically and graphically. The impacts of heat radiation, Prandtl number and heat generation on temperature field are addressed. The influence of Schmidt number and chemical reaction on concentration field is examined. Velocity of the fluid drop for the improvement in porosity parameter, permeable velocity and Maxwell number. Thermal radiation and heat generation increase the temperature whereas mass diffusivity fall by increasing chemical reaction coefficient and the Schmidt number. Effects of Maxwell parameter, heat generation and chemical reaction on physical quantities are studied. [ABSTRACT FROM AUTHOR]

• Carbon nanotubes are considered. • Flow is assumed in channel. • Heat transfer is considered. The current study aims to examine the peristaltic movement of carbon nanotubes (CNTs) flow in an electro-osmotic curved channel with variable viscosity. No-slip conditions near the channel walls are used. Poisson and Nernst–Planck equations are used to model the electro-osmotic phenomena. Using a curvilinear coordinate system, the equations for nanofluid flow along a curved pipe are formed. Firstly the problem is formulated and then un-dimensionalized. The approximation of long-wavelength along with a lesser Reynolds number has been applied to estimate the equations. The resulting mathematical relations are numerically solved by using the shooting method. To analyze the behavior graphically, we use MATLAB software. Graphical findings show the influence of parameters that affect the flow characteristics. It is noted that the velocity and temperature of the flow decrease by increasing the viscosity parameter. It is also observe that the heat absorption parameter helps to raise the temperature profile for CNTs. [ABSTRACT FROM AUTHOR]

Current discussion is to evaluate the influence of wall properties on thermal and flow performance, through a sinusoidal inclined wavy tube. To fulfill this phenomena we consider a sinusoidal tube having wavy walls, furthermore silicon-dioxide, ferrosoferric-oxide and zinc-oxide are treated as nano-particles and combination of 40% C 2 H 6 O 2 and 60% H 2 O as a base-fluid, but after the literature review we have seen that Iftikhar et al. (2018) presented the consequence of wall properties on copper–water nano-fluid through inclined tube. The out-coming arithmetical results are simplified with the assist of mathematica and perturbation method. Further-more, we graphically evaluate the thermal and flow performance of nanofluids at different rate of solid volume fractions (ϕ) , rigidity parameter (E 1) , Grashof number (G r) , slip parameter (γ) and heat generation parameter. we observed that Solid volume fraction (ϕ) of silicon dioxide, ferrosoferric oxide and zinc oxide causes the reduction of velocity profile. And velocity profile shows the opposite behavior corresponding to (E 1) and (G r). Temperature profile θ (r , t) decreases by developing the amount of (ϕ) for silicon dioxide, ferrosoferric oxide and zinc oxide, and temperature profile moves upward corresponding to heat parameter B. • Wall properties and thermal behavior of nano-fluids flow over an inclined sinusoidal wavy pipe is assumed. • Silicon-dioxide, ferrosoferric -oxide and zinc-oxide are treated as nano-particles and combination of 40% ethylene-glycol and 60% water as a base fluid. • We assume a sinusoidal wavy surface. • The problem is solved by using Mathematica. [ABSTRACT FROM AUTHOR]

When an object moves alongside a curved surface, it shows a curvilinear motion. The perception of curvilinear motion is majorly used in applications which are associated with centripetal and centrifugal forces. In this analysis, we studied the behaviour of nano-fluid and hybrid nano-fluid via curved surface with combined effects of heat generation and porous medium. For nano-fluid the combination of base fluid methanol and nano-particles AA7075 are assumed, while for hybrid nano-fluid base fluid methanol and nano-particles AA7075+AA7072 are used. AA7072 is mixture of zinc and alumina with some metals like copper, silicon and ferrous. Similarly AA7075 is mixture of magnesium, alumina and zinc with metals copper, silicon and ferrous. The partial differential equations are converted into ordinary differential equations by using similarity transformation. With the help of MATLAB software we used Bvp4c method to draw the graphs of the resulting equations and also we discuss the effect of solid volume fraction φ 1 , φ 2 , curvature parameter λ , Heat generation ω and porous medium ε for nano-fluid and hybrid nano-fluid. By enhancing the curvature parameter and volume fraction the temperature and velocity profile also enhances while the velocity profile reduces for porous medium and temperature profile increases for heat generation parameter. Nusselt number and skin friction effects are studied in the form of tables. An entropy generation analysis is also conducted. [ABSTRACT FROM AUTHOR]

The present analysis inspects the numerical investigation of MHD flow of Williamson fluid model over a sheet with variable thickness. Cattaneo–Christov heat flux model, an amended form of Fourier's law, is used to explore the heat transfer phenomena. The governing non-linear problem is presented and transformed into self-similar form by using similarity approach. The developed non-linear problem is solved numerically by using implicit finite difference scheme known as Keller box method. The effects of relevant physical parameters on velocity and temperature profiles are taken into consideration. The important finds are as follows: influence of Hartmann number M on velocity and temperature profile is opposite. Large values of wall thickness parameter α and Weissenberg number λ are suitable for reduction of velocity profile. A comparative investigation between the previously published results and the present results is found to be in good agreement. [ABSTRACT FROM AUTHOR]

The purpose of present analysis is to examine the effects of temperature dependent viscosity and thermal conductivity on MHD stagnation point flow over a stretching cylinder. The momentum and the temperature equations are modeled by using tangent hyperbolic fluid and the effect of viscous dissipation is also considered. The requisite partial differential equations are metamorphosed into ordinary differential equations by using similarity transformations. The succeeding ordinary differential equations are solved by using shooting method. The physical behavior of non-dimensional parameters for momentum and temperature profiles is deliberated through graphs. The numerical values of skin friction coefficient and local Nusselt number are calculated in order to recognize the behavior of fluid near the surface. The comparison with previous literature is completed in order to check the accuracy of the present work. It is found the velocity reduces with increasing power law index, Weissenberg number, Hartmann number and variable viscosity parameter. With the increasing values of curvature parameter, velocity is found to increase. Variable thermal conductivity parameter and Prandtl number shows opposite behavior for temperature profile. [ABSTRACT FROM AUTHOR]

A numerical solution of MHD flow of tangent hyperbolic fluid model over a stretching cylinder is obtained in this paper. The governing boundary layer equation of tangent hyperbolic fluid is converted into an ordinary differential equation using similarity transformations, which is then solved numerically by applying the implicit finite difference Keller box method. The effects of various parameters on velocity profile s are analyzed and discussed in detail. The values of skin friction coefficient are tabulated and plotted in order to understand the flow behavior near the surface of the cylinder. For validity of the model a comparison of the present work with the literature has been made. [ABSTRACT FROM AUTHOR]

This paper addresses the effect of homogeneous-heterogeneous reaction on Williamson fluid model over a stretching cylinder. The boundary layer partial differential equations are converted into ordinary differential equation by using suitable transformations. The non-linear ordinary differential equations are solved by using implicit finite difference Keller box technique. The effects of several pertinent parameters on velocity, temperature and concentration profiles are deliberated graphically. The behavior of skin friction coefficient and Nusselt number are examined through graphs. [ABSTRACT FROM AUTHOR]

The present paper deals with the numerical solution of magnetohydrodynamic (MHD) flow of Williamson fluid model over a stretching cylinder. The governing partial differential equation of Williamson fluid is converted into an ordinary differential equation using similarity transformations along with boundary layer approach, which is then solved numerically by applying the shooting method in conjunction with Runge-Kutta-Fehlberg method. The effect of different parameters on velocity profile is thoroughly examined through graphs and tables. [ABSTRACT FROM AUTHOR]

In present analysis, we investigate the flow behavior of SiO 2 / H 2 O / C 2 H 6 O 2 nanofluid along with magnetic field and heat generation influence on permeable channel having squeezing/dilating walls. The modeled partial differential system including mass balance, momentum and temperature equations are transformed into ordinary differential system by using similarity transformations and achieved the coupled of nonlinear ordinary differential equations. The numerical solution of coupled system of equations is interpreted for velocity and temperature by using Bvp4c method. The graphical behavior of different parameters such as deforming rate L (for velocity we have taken L = ± 0. 1 , ± 0. 7 and ± 1. 2 , wheres for temperature L = − 0. 1 , − 0. 7 and − 0. 9 has been taken), permeating Reynolds number H (for velocity H = 0. 1 , 0. 4 and 0.7 and for temperature H = − 0. 6 , − 0. 7 and − 0. 8 has been taken), Hartman number M (for velocity M = 0. 1 , 1. 3 and 2.5 is taken), heat generation β (for temperature β = 0. 1 , 0. 5 and 0.9 is taken) and solid fraction volume R (for velocity R = 0. 1 , 0. 9 and 1.2 is taken, for temperature R = 0. 7 , 0. 8 and 0.9 is assumed) for temperature and velocity have been plotted using Matlab software. The observation of case I; L > 0 , H > 0 , shows the velocity of both base ( H 2 O and C 2 H 6 O 2 ) fluids increases at middle portion of channel due to increase in L and M. On the other hands the velocity profiles show increasing behavior for H and decreasing behavior for R at the edges of channel. Temperature distribution observation of case I; L > 0 , H > 0 , it is cleared that the temperature of SiO 2 / H 2 O / C 2 H 6 O 2 nanofluid increases due to increase of β. The temperature profile of SiO 2 / H 2 O nanofluid decreases by increase of R, on other hands the temperature profile of SiO 2 / C 2 H 6 O 2 nanofluid decreases on interval (− 1 < h < 0) and increases on interval (0 < h < 1) with increase of R. The observation of case II; L < 0 , H < 0 , deduces that the temperature of SiO 2 / H 2 O / C 2 H 6 O 2 nanofluid increases by increase of H. The graphical results show that temperature profile reveals batter performance for base fluid H 2 O as compared to base fluid C 2 H 6 O 2 . We compared the present results with previous results and found that present results are similar to previous results. • SiO 2 / H 2 O / C 2 H 6 O 2 nanofluid in squeezing/dilating wall are investigated. • Heat generation is considered. • Low Reynolds number and long wavelength approximation is used. • The equations are solved by using perturbation technique. • Relationship between kinematic viscosity and intermolecular forces are described. [ABSTRACT FROM AUTHOR]

This work presents the entropy generation of an incompressible boundary layer flow over a heated flat-plate with temperature dependent viscosity. The viscous dissipation effect is considered in energy equation. Liquid and gas type fluids are discussed for the boundary value problem. Thermo-physical properties are assumed to in momentum, energy and concentration equations. This study has received more interest in applied engineering due to its theoretical and numerical advantages. We investigate the solutions for thermo-physical characteristics of modified viscous model along with entropy generation. The similarity solution was firstly introduced by Blasisus, it is used for the current modified viscous fluid by converting the governing equations into ordinary differential equations. Shooting method is used to solve the ordinary differential equations. The effect of viscosity for gases show an increase behavior for the base flow profile but for liquids opposite nature is noticed. Thermal conductivity and mass diffusivity also increases the temperature and concentration profiles. For large Brinkman number and dimensionless concentration ratio variable the entropy generation increases. The results of the physical parameters on the base flow, temperature, concentration and entropy generation are discussed through figures and are presented in detail. The comparative results are determined for a limited case and good agreement is analyzed with previously published article. [ABSTRACT FROM AUTHOR]

The study of 2D non-Newtonian Sutterby nanofluid flow under the effects of magneto-hydro-dynamics (MHD) over the paraboloid surface is investigated here. The upper part of aircraft, submarine, bullet, and car's bonnet are some samples of the paraboloid surface. The movement of these things depends in boundary layer which is formed within the space on it. The reaction between catalyst at the surface and Sutterby nanofluid yields substantial temperature differences consequently made buoyancy-driven flow in the boundary layer region. First-order activation energy is assumed to model the reaction on the catalyst surface that is sited on the paraboloid surface which starts the free convection. The main prevailing equations are reduced by using appropriate dimensionless variables. The numerical solutions of the dimensionless determining equations are achieved by adopting the Runge-Kutta Fehlberg ("RKF") method. The graphical outcomes of the velocity field depend on the dimensionless quantities such as the Deborah number De ,Hartmann number Ha , temperature and concentration-dependent buoyancy parameters i.e. (G t , G s). The contribution of the thermophoresis coefficient Nt , Prandtl number Pr and Brownian motion parameter Nb is examined for the temperature field. Also the effects of Schmidt number Sc are analyzed for the concentration field. We found that both Deborah number and Hartmann number (De , Ha) provide a decrease in the velocity field. The extreme velocity of the fluid is calculated when the fluid flow is categorized as Newtonian fluid i.e. (De = 0). The numerical outcomes of skin friction, local mass transfer rate and local heat transfer rate are also calculated. A detailed comparison with the numerical method is also given to validate the current results. [ABSTRACT FROM AUTHOR]