The Viscosity can be imagined as the force that should be applied to a layer of fluid belonging to the plane fixed to the velocity of the layer placed at a fixed distance. For example a fluid flowing in a tube at different speeds: the minimum speed is in the edge of the section (due to friction) and the maximum speed is at the center. The viscosity in this example is that pressure which is exerted on the wall allows a constant speed on the whole section.

Non-newtonian fluids.

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Numerical Methods For Scientific And Engineering Computation

Significance of suction and dual stretching on the dynamics of various hybrid nanofluids: Comparative analysis between type I and type II models

An exertion is executed to explicate thermophysical aspects of viscoelastic fluid flow produced by a nonlinearized stretched surface. Here, viscoelasticity is characterized by Casson fluid model and expressed rheologically in momentum equation. Flow attributes of Casson fluid are thoroughly investigated under transversal magnetized field and along with provision of suction/injection to surface. Flow medium is also considered to be porous. Convective heating is supplied to the surface to depict heat transfer change within the flow domain. Nanosized particles are hanged into the Casson fluid to understand the effectiveness of Brownian motion and thermophoretic forces on the diffusion of particles. Generative chemical reactions are also considered to measure mass transport. Initially, flow narrating differential equations for concerning a problem are attained in differential equations and later on transforming into ordinary differential coupled system via similarity approach. Variations in flow associated distributions against involved parameters are divulged through graphical structures. Wall drag, thermal and mass fluxes are also calculated. Credibility of computing results is tested with the aid of comparison with previously published data in limiting sense.

MHD Casson nanofluid flow over nonlinearly heated porous medium in presence of extending surface effect with suction/injection

Solar radiation effects on MHD stagnation point flow and heat transfer of a nanofluid over a stretching sheet

In this present study, a numerical investigation has been carried out to discuss the steady, two dimensional flow and heat transfer on micropolar nanofluid over a stretching/shrinking sheet with variable suction or injection in the presence of magnetic field and Newtonian heating. Copper (
 $$ {\text{Cu}} $$
 ), alumina (
 $$ {\text{Al}}_{ 2} {\text{O}}_{ 3} $$
 ) and titanium (
 $$ {\text{TiO}}_{ 2} $$
 ) in water-based micropolar nanofluid has been considered for the present investigation. The solutions of the transformed nonlinear equations have been obtained using Runge–Kutta–Gill procedure together with the shooting method. The results are presented graphically and discussed for various resulting parameters. Dual solutions are found to exist in a certain range of the governing parameters. The thickness of thermal boundary layer for Cu nanofluid is more than that of other nanofluids in the cases of shrinking and stretching sheets. Newtonian heating effect significantly increases the thermal boundary layer thickness for both sheets under investigation.

Magnetohydrodynamic micropolar nanofluid past a permeable stretching/shrinking sheet with Newtonian heating

A hydromagnetic transverse flow of an Oldroyd-B-type liquid with a heat flux of the Cattaneo–Christov model with variable thickness has been analyzed. Consider additional impacts of thermal conductivity as well as heat generation. Governing equations were transmitted into a set of nonlinear ordinary differential equations using similarity conversion, and then, numerical solution was evaluated using the procedure Runge–Kutta–Fehlberg. The physical response related to velocity and temperature is investigated computationally. The outcomes also show that the momentum boundary-layer thickness increases the values of magnetic field strength, but the reverse trend is observed for the thermal boundary layer. Impacts of retardation and relaxation time effects are quite the opposite of the temperature field. The obtained computations are useful in transport phenomena which are involving hydromagnetic rheological fluids.

Cattaneo–Christov heat flux theory on transverse MHD Oldroyd-B liquid over nonlinear stretched flow

In this examination, a mathematical model is developed for Darcy free convection with reference to an isothermal vertical cone along with fixed apex half angle, pointing downward in a nanofluid-saturated porous medium. The aim of this methodology is to offer another sort of primary fluid containing nanoparticles and gyrotactic microorganism’s consistence of permeable medium, chemical reaction alongside convective boundary circumstance. The model presents design rules for improvement of imperative fabrication of fertilizer and polymer substance. The present model includes the gyrotactic microorganisms alongside nanoparticles, and cone is dependent on concentration of nanoparticles as well as density of motile microorganisms. Two important impacts Brownian motion as well as thermophoresis are also included in the present model for nanofluids. Reduced system of nonlinear differential equations is derived from governing partial differential of the present flow by using usual transformations along with Oberbeck–Boussinesq approximation. After that, this reduced system is solved numerically with the use of fifth-order Runge–Kutta method in conjunction with the shooting technique. Relevant outcomes are exhibited graphically and talked about quantitatively as for variety in the flow controlling parameters related to the present analysis. Mainly, the observations are bioconvection parameters will in general improve the concentration of the rescaled density of microorganisms and nanoparticles volume fraction and dimensionless motile microorganisms reduce with strong chemical reactions.

Bioconvection in a Convectional Nanofluid Flow Containing Gyrotactic Microorganisms over an Isothermal Vertical Cone Embedded in a Porous Surface with Chemical Reactive Species

The principle aim of the present investigation is to study the boundary layer analysis of nanofluid flow over a bidirectional exponentially stretching sheet in the presence of transverse magnetic field and also in convective condition. The effects of Brownian motion and thermophoretic diffusion of nanoparticle are considered from the mathematical model. Governing partial differential equations are reduced into coupled non-linear ordinary differential equations using suitable similarity transformations, further the system of equations are solved by a new spectral relaxation method. Validation of the results is achieved by comparison with emitting case from previous studies in the literature. Also, it has been shown that the convergence rate of the spectral relaxation method is significantly improved by using the method in conjunction with the successive over relaxation method. The results reveal the existence of interesting Sparrow–Gregg-type Hills for temperature distribution pertinent to some range of parametric values. Moreover the numerical data of drag coefficient, local heat and mass transfer rates are evaluated and analyzed. Effects of local Biot number on temperature and concentration profiles are qualitatively similar. Both the temperature and concentration profiles are enhanced for higher values of local Biot number.

A spectral relaxation method for three-dimensional MHD flow of nanofluid flow over an exponentially stretching sheet due to convective heating: an application to solar energy

Exploiting the impact of Lorentz force and convective heating boundary on second-grade nanofluid flow alongside a Riga pattern is the main objective of the present work. Modelling of the present work is done through Grinberg term and a Lorentz force applied parallel to the wall of a Riga plate. The nanoparticles fraction on the solid surface of Riga pattern maintained a strong retardation because of zero mass flux. Theories of Cattaneo–Christov heat flux and generalized Fick’s relations are employed by following the modern aspects of heat and mass transportations. In the current study, additional features of thermal radiation are also included in the energy equation in terms of linear expressions. In order to make the analysis more worthy, effect of chemical reaction is also included. By applying the suitable variables, constituted problem is converted into dimensionless form. Solution of the problem with desired accuracy is obtained by utilizing popular method called Runge–Kutta–Fehlberg. The graphical representations are used to illustrate the flow controlling parameters involved by their attractive physical consequences. Velocity distribution is observed for the increase with the second-grade parameter. Further, an improved nanoparticles temperature distribution is observed with the increase in radiation parameter and Biot number. Additionally, the distribution of the concentration of nanoparticles increases with increase in values of the thermophoretic parameter. Based on the scientific calculations obtained, it is established that the reported results may play a useful role in production processes and in the improvement of energy and thermal resources.

Kotha Gangadhar

Papers

Magnetohydrodynamic micropolar nanofluid past a permeable stretching/shrinking sheet with Newtonian heating

Cattaneo–Christov heat flux theory on transverse MHD Oldroyd-B liquid over nonlinear stretched flow

Bioconvection in a Convectional Nanofluid Flow Containing Gyrotactic Microorganisms over an Isothermal Vertical Cone Embedded in a Porous Surface with Chemical Reactive Species

A spectral relaxation method for three-dimensional MHD flow of nanofluid flow over an exponentially stretching sheet due to convective heating: an application to solar energy

EMHD Flow of Radiative Second-Grade Nanofluid over a Riga Plate due to Convective Heating: Revised Buongiorno’s Nanofluid Model