Novel insights into the computational techniques in unsteady MHD second‐grade fluid dynamics with oscillatory boundary conditions

Ali, Liaqat; Khan, Noor Saeed; Ali, Rohail; Islam, Saeed; Thounthong, Phatiphat

doi:10.1002/htj.21989

Cited by 7 publications

(2 citation statements)

References 64 publications

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“…Finally, unlike the other analytic approximation techniques, the HAM provides a simple way to ensure the convergence of the solution series. So, the analytical technique [39–41] is used to compute the solution of the transformed equations ()– (). Selecting the initial approximations and auxiliary linear operators for velocities, temperature, nanoparticles concentration and gyrotactic microorganisms concentration in the following form

\begin{align} & h_{0}(\zeta ) = 0,\hspace{8.5359pt} {f_{0}}(\zeta ) = \frac{S_1}{\gamma _{4}(1+r_{1})^{i}}\exp (- \zeta ),\hspace{8.5359pt} g_{0}(\zeta ) = \frac{1}{\gamma _{5}(1+r_{1})^{i}}\exp (- \zeta ),\hspace{8.5359pt} \theta _{0}(\zeta ) = \exp (- \zeta ),\nonumber \\ &\phi _{0}(\zeta ) = -\frac{Nt}{Nb}\exp (- \zeta ),\hspace{8.5359pt}\chi _{0}(\zeta ) = \exp (- \zeta ), \end{align}

L_{h} badbreak= h^{'}, L_{f} goodbreak= f^{''} goodbreak- f, L_{g} goodbreak= g^{''} goodbreak- g^{'}, L_{θ} goodbreak= θ^{''} goodbreak- θ,

…”

Section: Non‐dimensional Equations Solution Via Hammentioning

confidence: 99%

Performance of variable characteristics on MHD Jeffery nanofluid over spinning disk with Cattaneo‐Christov heat flux and microswimmers

Khan,

Alshammari,

Noor

et al. 2023

Z Angew Math Mech

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Variable properties like thermal conductivity and variable thickness of the disk are analyzed for the Jeffery nanofluid and gyrotactic microorganisms in rotating system taking into account the Cattaneo‐Christov heat flux, velocity slip and thermal radiation effects. Zero mass flux is assumed at the disk surface for the better and high accuracy of the out‐turn. The governing equations of the problem are transformed into nonlinear ordinary differential equations by introducing the appropriate similarity transformations which are solved analytically by the homotopy analysis method. The effects of all the parameters are given in detail through the graphs.

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\begin{align} & h_{0}(\zeta ) = 0,\hspace{8.5359pt} {f_{0}}(\zeta ) = \frac{S_1}{\gamma _{4}(1+r_{1})^{i}}\exp (- \zeta ),\hspace{8.5359pt} g_{0}(\zeta ) = \frac{1}{\gamma _{5}(1+r_{1})^{i}}\exp (- \zeta ),\hspace{8.5359pt} \theta _{0}(\zeta ) = \exp (- \zeta ),\nonumber \\ &\phi _{0}(\zeta ) = -\frac{Nt}{Nb}\exp (- \zeta ),\hspace{8.5359pt}\chi _{0}(\zeta ) = \exp (- \zeta ), \end{align}

L_{h} badbreak= h^{'}, L_{f} goodbreak= f^{''} goodbreak- f, L_{g} goodbreak= g^{''} goodbreak- g^{'}, L_{θ} goodbreak= θ^{''} goodbreak- θ,

…”

Section: Non‐dimensional Equations Solution Via Hammentioning

confidence: 99%

Performance of variable characteristics on MHD Jeffery nanofluid over spinning disk with Cattaneo‐Christov heat flux and microswimmers

Khan,

Alshammari,

Noor

et al. 2023

Z Angew Math Mech

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“…The present problem is modeled for the curved surface under the effect of magnetic dipole in the presence of gyrotactic microorganisms and cubic autocatalysis chemical reactions in Walter-B fluid which is solved through the analytical method namely homotopy analysis method [69][70][71][72][73][74][75][76][77][78][79][80][81].…”

Section: Introductionmentioning

confidence: 99%

Accessing the thermodynamics of Walter‐B fluid with magnetic dipole effect past a curved stretching surface

et al. 2023

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The effects of magnetic dipole, porosity and heat transfer on the flow of ferromagnetic Walter‐B fluid past a curved stretching sheet is investigated with the gyrotactic microorganisms motion and cubic autocatalysis chemical reactions. The momentum, energy, homogeneous–heterogeneous chemical reactions and gyrotactic microorganisms motion equations, form the problem's governing equations, which are transformed into non‐linear ordinary differential equations via similarity transformations and are solved using an efficient and strong technique namely homotopy analysis method. The effects of the parameters under consideration on dimensionless velocity, temperature, homogeneous–heterogeneous chemical reaction, and motile microorganisms are graphically depicted and discussed in detail. Velocity decreases with the increasing values of curvature parameter while the magnetic dipole effect and Curie temperature parameter increase the heat transfer. The homogeneous chemical reaction and the motile density of microorganisms are enhanced with the rising values of elasticity and ferromagnetic interaction parameters.

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RETRACTED: Analytical simulation of time dependent electromagneto-hydrodynamic flow of Williamson fluid due to oscillatory curved convectively heated Riga surface with variable thermal conductivity and diffusivity

Naveed

Abbas

Imran

2021

Proceedings of the Institution of Mechanical Engineers, Part E:

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The main objective of the present article is to provide an analytical simulation for time dependent boundary layer flow of non-Newtonian Williamson fluid due to stretchable curved oscillatory Riga surface. Also the characteristics of heat and mass transport are studied under the influence of variable thermal conductivity and diffusivity along with convective heat and mass boundary conditions. Additionally, energy equation is also characterized with the impact of heat production. Curvilinear coordinate scheme is followed to attain the boundary layer expressions for the flow model. The governing nonlinear partial differential equations are solved analytically via homotopy analysis method (HAM). Graphs are plotted to examine comprehensively the consequences of various concerned parameters like modified magnetic parameter and radius of curvature, Williamson fluid parameter, relation of the surface's oscillating frequency to its stretching rate constant, Prandtl number, variable conductivity and heat production parameters, Schmidt number and variable diffusivity parameter on concentration, temperature, pressure and velocity profile. Also the outcomes of afore said variables on surface drag force, rate of temperature and mass transmission (Nusselt and Sherwood numbers) are shown in tabular form. The liquid velocity amplitude is enhanced with modified magnetic parameter and shows opposite behavior for Williamson fluid parameter.

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Novel insights into the computational techniques in unsteady MHD second‐grade fluid dynamics with oscillatory boundary conditions

Cited by 7 publications

References 64 publications

Performance of variable characteristics on MHD Jeffery nanofluid over spinning disk with Cattaneo‐Christov heat flux and microswimmers

Performance of variable characteristics on MHD Jeffery nanofluid over spinning disk with Cattaneo‐Christov heat flux and microswimmers

Accessing the thermodynamics of Walter‐B fluid with magnetic dipole effect past a curved stretching surface

RETRACTED: Analytical simulation of time dependent electromagneto-hydrodynamic flow of Williamson fluid due to oscillatory curved convectively heated Riga surface with variable thermal conductivity and diffusivity

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