Numerical solution for flow of a Eyring–Powell fluid in a pipe with prescribed surface temperature

Nazeer, Mubbashar; Ahmad, Fayyaz; Saeed, Mubashara; Saleem, Adila; Naveed, Sidra; Akram, Zeeshan

doi:10.1007/s40430-019-2005-3

Cited by 36 publications

(15 citation statements)

References 50 publications

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“…Since Equations ( 14)-( 15) are highly nonlinear and coupled differential equations which are solved numerically by using the Runge Kutta method with shooting technique [51][52][53][54]. This method reduces the governing differential equations into the number of first-order differential equations with the missing slopes which are determined via an iterative scheme.…”

Section: Numerical Schemementioning

confidence: 99%

Mathematical modeling and numerical solution of cross‐flow of non‐Newtonian fluid: Effects of viscous dissipation and slip boundary conditions

et al. 2021

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The current investigation deals with the numerical simulation of cross-flow of non-Newtonian fluid. Flow dynamics are studied by considering a uniform channel bounded by porous walls. Transversely acting magnetic fields have also been taken into account on the two-dimensional flow of Tangent-Hyperbolic fluid.Skin friction is addressed by employing the lubrication effects on the porous channel. In addition to this, Fourier's law of conduction is incorporated to highlight the heating effects which attenuates the shear thickening posture of the fluid. Highly nonlinear and coupled differential equations are solved numerically by using the Runge-Kutta method with shooting technique. Thermal and momentum transport is simulated by generating the numerical MATLAB codes. Study reveals that slippery porous walls/channels can effectively be used in chemical and mechanical industries which deal with various kinds of highly viscous flows. Moreover, more energy is contributed by Peclet number and viscous heating parameter and improve the heat transfer rate.Nomenclature: 𝑀, Hartmann number; 𝛽, Slip parameter; 𝑚, Power-law index parameter; 𝑃𝑒, Peclet number; 𝐵𝑟, Viscous-heating parameter/ Brinkman number; 𝐾, Thermal conductivity; 𝑃, pressure-gradient parameter; T, Cauchy stress tensor; 𝜇 0 , Zero shear rate viscosity; 𝜇 ∞ , The infinite shear rate viscosity; 𝑅𝑒, Reynolds number; 𝜎, The electric conductivity; 𝐴 1 , Riviline-Erickson tensor; 𝑆, Extra stress tensor; 𝑇 0 , The temperature of the lower wall; 𝑇 ℎ , The temperature of the heated wall; 𝜌, The density of the fluid; 𝐶 𝑝 , Specific heat; 𝑣 0 , Suction velocity; 𝑇, Dimensionless temperature; Γ, The time constant; 𝐽, The current vector; 𝐵, The uniform external magnetic field; 𝑡, Time

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Section: Numerical Schemementioning

confidence: 99%

Mathematical modeling and numerical solution of cross‐flow of non‐Newtonian fluid: Effects of viscous dissipation and slip boundary conditions

et al. 2021

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“…To find the solution of eqs ( 2) to (10b), the perturbation method [33][34][35] is used here. For this, we assume…”

Section: Perturbation Solutionmentioning

confidence: 99%

Numerical and perturbation solutions of third-grade fluid in a porous channel: Boundary and thermal slip effects

et al. 2020

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The steady flow of a third-grade fluid due to pressure gradient is considered between parallel plane walls which are kept at different temperatures. The space between the plane walls is assumed to be a porous medium of constant permeability. The viscosity of the fluid is taken as constant as well as a function of temperature. It is further assumed that the fluid may slip at the wall surfaces. The consequence of this assumption results in non-linear boundary conditions at the plane walls. The temperature field is also supposed to satisfy thermal slip condition at the walls. The governing equations are modelled under these assumptions and the approximate solution is obtained using the perturbation theory. The skin friction coefficient is a decreasing function of slip parameters in the case of temperature-dependent viscosity models while no variation is noted for the case of constant viscosity via boundary slip parameter. The heat transfer rate increases with the boundary slip parameter and decreases with the thermal slip parameter. The validity of the approximated solution is checked by calculating the numerical solution as well. The absolute error is calculated and listed in tabular form in the case of constant and temperature-dependent viscosity via boundary and thermal slip parameters. The influence of various emerging parameters on flow velocity and temperature profile is discussed through graphs.

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“…The number of investigations performed by the authors by taking the variable properties can be seen in refs. [24][25][26][27] The research efforts related to the movement of non-Newtonian fluids and the solution of highly non-linear equations have progressed significantly during the previous few decades. The non-Newtonian fluid is one of the most common types of fluid, with a nonlinear relationship between the rate of deformation and shear stress.…”

Section: Introductionmentioning

confidence: 99%

Thermal analysis of blood flow of Newtonian, pseudo-plastic, and dilatant fluids through an inclined wavy channel due to metachronal wave of cilia

Al-Zubaidi

Nazeer

Khalid

et al. 2021

Advances in Mechanical Engineering

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This paper is organized to study the heat and mass transfer analyses by considering the motion of cilia for Newtonian, Pseudo-plastic, and Dilatant fluids through a horizontally inclined channel in the presence of metachronal waves and variable liquid properties. A non-Newtonian Rabinowitsch model is used to study the flow of peristalsis through ciliated walls. The slip and convective boundary conditions at the channel walls are taken into account. The mathematical model is developed in the form of complex nonlinear partial differential equations then transformed into simplified form by using the definition of low-Reynolds number with lubrication theory. The analytical solution is obtained by using the perturbation method due to its low computational cost and good accuracy. The graphical outcome is based on the behavior of certain physical parameters on velocity, temperature, and concentration profiles for all three types of fluid. A symbolic software named MATHEMATICA 12.0 is used to find the analytical expression and construct the graphical behavior of all profiles that are taken under discussion. The important results in this study depict that the velocity profile tends to increase in the central region of the channel for Newtonian and Pseudo-plastic fluids and decreases for Dilatant fluid while a reverse behavior is observed near the channel walls. A smaller wavelength causes the wavenumber to accelerate and it tends to decelerate for a larger wavelength. The current study will help to understand the use of the complex rheological behavior of biological fluids in engineering and medical science.

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Numerical solution for flow of a Eyring–Powell fluid in a pipe with prescribed surface temperature

Cited by 36 publications

References 50 publications

Mathematical modeling and numerical solution of cross‐flow of non‐Newtonian fluid: Effects of viscous dissipation and slip boundary conditions

Mathematical modeling and numerical solution of cross‐flow of non‐Newtonian fluid: Effects of viscous dissipation and slip boundary conditions

Numerical and perturbation solutions of third-grade fluid in a porous channel: Boundary and thermal slip effects

Thermal analysis of blood flow of Newtonian, pseudo-plastic, and dilatant fluids through an inclined wavy channel due to metachronal wave of cilia

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