Numerical modelling of second‐grade fluid flow past a stretching sheet

Basha, Hussain; Reddy, G. Janardhana; Abhishek, Amit; Killead, Annapoorna; Pujari, Vinaya; Kumar, N. Naresh

doi:10.1002/htj.21448

Cited by 23 publications

(11 citation statements)

References 47 publications

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“…Thus, to solve this system of PDE's, we first transformed the system of coupled PDE's to a set of simplified nonlinear ordinary differential equations (ODEs) with the help of the appropriate similarity transformations. Finally, the reduced first order ODEs are solved by using Runge‐Kutta fourth order integration scheme with shooting technique (RK‐SM) 31‐34,42‐51 and the bvp4c matlab function 31‐34,52 . Thus, to achieve the above‐mentioned purpose, the following similarity transformations 9‐14 are suitably used.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Clearly, it is observed that the governing Equations (21) to (23) with conditions Equations (24) to (26) are not amenable to analytical schemes. Hence, in the present paper, an attempt has been made to overcome this difficulty by using RK‐SM 31‐34,42‐51 and bvp4c techniques 31‐34,52 . Thus, before applying the RK‐SM technique, the nonlinear coupled ODE's Equations (21) to (23) are decomposed into a system of first order ODE's and the reduced equations are as follows.…”

Section: Numerical Proceduresmentioning

confidence: 99%

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A generalized perspective of magnetized radiative squeezed flow of viscous fluid between two parallel disks with suction and blowing

Basha

2020

Heat Trans

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In this research article, the electrically conducting magnetized radiative squeezed flow of two-dimensional time-dependent viscous incompressible flow between two parallel disks with heat source/sink and Joule heating effects under the presence of an unsteady homogeneous first order chemical reaction is demonstrated numerically. The considered physical problem is studied under the influence of Lorentz forces to describe the effect of an applied magnetic field. Heat dissipation due to viscosity and Joule heating are considered in the energy equation to demonstrate the behavior of the thermal profile. Also, the thermodynamic behavior of temperature field is described by considering the concept of heat source/sink in the energy equation. The mass transport characteristics of a viscous fluid are described through the time-dependent chemical reaction of first order type with homogenous behavior. Thus, the considered physical problem gives the time-dependent, highly nonlinear coupled partial differential equations, which are reduced to a system of ordinary differential equations by invoking the suitable similarity transformations. The discretized first order ordinary differential equations are solved by using the Runge-Kutta fourth order integration scheme with the

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Section: Mathematical Formulationmentioning

confidence: 99%

Section: Numerical Proceduresmentioning

confidence: 99%

A generalized perspective of magnetized radiative squeezed flow of viscous fluid between two parallel disks with suction and blowing

Basha

2020

Heat Trans

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“…Also, at time

t false' > 0,

the temperature of the cylinder at

r false' = R,

has elevated to

T_{w}^{'}

, whereas at

r^{'} = 0,

it has an adiabatic phase which causes the temperature gradient and the buoyancy force accruing to the motion. As the flow is depending on the coordinate

r^{'}

and time

t^{'}

, the governing momentum and thermal energy equations of the transient free convective flow of a second‐grade fluid in a vertical cylinder using the Boussinesq's approximations are given as 9,35

υ ((), \frac{\partial^{2} u^{'}}{\partial {r^{true'}}^{2}} + \frac{1}{r^{true'}} \frac{\partial u^{'}}{\partial r^{'}}) + \frac{α_{1}}{ρ} ((), \frac{\partial^{3} u^{'}}{\partial t^{'} \partial {r^{true'}}^{2}} + \frac{1}{r^{true'}} \frac{\partial^{2} u^{'}}{\partial t^{'} \partial r^{'}}) - \frac{\partial u^{'}}{\partial t^{'}} + g β (T^{'} - T_{0}^{'}) = 0,

\frac{κ}{ρ C_{p}} ((), \frac{\partial^{2} T^{'}}{\partial {r^{true'}}^{2}} + \frac{1}{r^{true'}} \frac{\partial T^{'}}{\partial r^{'}}) - \frac{\partial T^{'}}{\partial t^{'}} = 0 .

…”

Section: Mathematical Formulationsmentioning

confidence: 99%

“…Reddy et al 33 have examined natural convection and entropy generation on the viscoelastic polymeric fluid flow over a vertical plate. Furthermore, the entropy generation for the transient flow of a second‐grade fluid through a vertical cylinder has been investigated by Reddy et al 34 Basha et al 35 have analyzed chemically reacting second‐grade fluid flow on the stretching sheet. Furthermore, the exact solutions of the transient flow problems in a circular cylinder have been obtained by the researchers 36,37 …”

Section: Introductionmentioning

confidence: 99%

Transient free convection of a second‐grade fluid flowing in a vertical cylinder

Dwivedi

Singh

2020

Heat Trans

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The intention of the present article is to examine the transient effect on the free convection of the second‐grade fluid flowing in a vertical cylinder. We have found the analytical solution of the derived governing partial differential equations in nondimensional form corresponding to the velocity as well as the temperature fields by applying the Laplace transformation method in terms of the Bessel function of the first kind. To obtain the impacts of the appropriate parameters related to the given equations, such as the second‐grade fluid parameter and the Prandtl number, the numerical values of the velocity are discussed and displayed in graphs. Furthermore, the mass flow rate and the skin friction at the inner surface of the cylinder are given in a tabular form. The influence of the second‐grade fluid parameter is to decelerate the velocity as well as the mass flow rate and to enhance the steady‐state time.

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“…However, it is noticed from the available literature that, the Equations to are not easily amenable to any of the direct methods. Therefore, the coupled Equations to with Equations and are simplified by utilizing the standard RK‐SM and bvp4c method . However, the RK‐SM begins by discretising the coupled higher nonlinear ODEs into a system of first order ODEs.…”

Section: Numerical Solution Proceduresmentioning

confidence: 99%

Magnetized impacts of Brownian motion and thermophoresis on unsteady squeezing flow of nanofluid between two parallel plates with chemical reaction and Joule heating

Shankar

Naduvinamani

2019

Heat Trans. Asian Res.

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Present research article investigate the heat and mass transfer characteristics of unsteady magnetohydrodynamic Casson nanofluid flow between two parallel plates under the influence of viscous dissipation and first order homogeneous chemical reaction effects. The impacts of thermophoresis and Brownian motion are accounted in the nanofluid model to disclose the salient features of heat and mass transport phenomena. The present physical problem is examined under the presence of Lorentz forces to investigate the effects of magnetic field. Further, the viscous and Joule dissipation effects are considered to describe the heat transfer process. The non-Newtonian behaviour of Casson nanofluid is distinguished from those of Newtonian fluids by considering the well-established rheological Casson fluid model. The twodimensional partial differential equations governing the unsteady squeezing flow of Casson nanofluid are coupled and highly nonlinear in nature. Thus, similarity transformations are imposed on the conservation laws to obtain the nonlinear ordinary differential equations. Runge-Kutta fourth order integration scheme with shooting method and bvp4c techniques have been used to solve the resulting nonlinear flow equations. Numerical results have been obtained and presented in the form of graphs and tables for various values of physical parameters.It is noticed from present investigation that, the concentration field is a decreasing function of thermophoresis parameter. Also, concentration profile enhances with raising Brownian motion parameter. Further, the present numerical results are compared with the analytical and semianalytical results and found to be in good agreement.Brownian motion, Casson nanofluid, Joule dissipation, magnetic field, squeezing flow, thermophoresis | INTRODUCTIONIn the present days, nanofluids are widely used in most of the industries, technologies, and scientific applications. For an instance, biological solutions, asphalts and glues, melts of polymers and paints, and so forth. Nanofluids are potentially suitable candidates for increasing the heat transfer rate in wide variety of applications. In many of the numerical investigations, nanofluids are treated as common pure fluids. Additionally, nanofluids are considerably used in the squeezing flows for enhancing the heat transfer characteristics. However, the unsteady heat and mass transfer process in squeezing flow of magnetohydrodynamic (MHD) viscous incompressible fluid flow between two parallel plates is one of the most important research area in the present days. Since, squeezing flows have plenty of engineering, scientific, and technological applications in most of the thermodynamic industries. For example, lubrication systems, moving pistons, hydrodynamical machines, hydraulic lifts, dispersion and formation, compression and injection, electric motors, cooling towers, reactor fluidization, polymer processing, processing of chemical equipment's, processing of food, crops damage due to freezing, transmission squeezed film and syringes ...

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Numerical modelling of second‐grade fluid flow past a stretching sheet

Cited by 23 publications

References 47 publications

A generalized perspective of magnetized radiative squeezed flow of viscous fluid between two parallel disks with suction and blowing

A generalized perspective of magnetized radiative squeezed flow of viscous fluid between two parallel disks with suction and blowing

Transient free convection of a second‐grade fluid flowing in a vertical cylinder

Magnetized impacts of Brownian motion and thermophoresis on unsteady squeezing flow of nanofluid between two parallel plates with chemical reaction and Joule heating

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