Finite element analysis of couple stress micropolar nanofluid flow by non‐Fourier's law heat flux model past stretching surface

Ibrahim, Wubshet; Gadisa, Gosa

doi:10.1002/htj.21567

Cited by 10 publications

(18 citation statements)

References 23 publications

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“…The obtained result has been confirmed with previously published works. The default values chosen to plot the graphs below are selected based on different kinds of literature and history of the parameters 20,26

\begin{matrix} left \\ P r = 1.5, E c = 0.75, S c = 0.25, γ_{E} = 0.2, γ_{C} = 0.3, β = 2.0, τ = 2.0, N t = N b \\ = 0.5, β_{t} = β_{c} = 0.2, N^{*} = 0.3, K = 0.3, λ = 0.2, \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

“…Hence, an additional equation for the angular velocity field is introduced for the micropolar fluid flow. Under the above assumptions, the governing equations for the boundary layer flow region of micropolar couple stress nanofluids are given by the following system of partial differential equations (PDEs) 20 :

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

\begin{matrix} lefttrue \\ \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = \frac{(μ + k)}{ρ_{f}} \frac{\partial^{2} u}{\partial y^{2}} + \frac{k}{ρ_{f}} \frac{\partial N}{\partial y} - ν false' \frac{\partial^{4} u}{\partial y^{4}} + g {normalΛ}_{1} (T - T_{\infty}) + g {normalΛ}_{2} {(T - T_{\infty})}^{2} \\ + g {normalΛ}_{3} (C - C_{\infty}) + g {normalΛ}_{4} {(C - C_{\infty})}^{2}, \end{matrix}

\frac{\partial N}{\partial t} + u \frac{\partial N}{\partial x} + v \frac{\partial N}{\partial y} = \frac{normalΩ}{ρ j} \frac{\partial^{2} N}{\partial y^{2}} - \frac{k}{ρ j} true(2 N + \frac{\partial u}{\partial y} true),

\begin{matrix} left \\ \frac{\partial T}{\partial t} + u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} +<...> \end{matrix}

…”

Section: Problem Formulationsmentioning

confidence: 99%

“…GFEM (sometimes called weight residual method) is a powerful numerical method used to solve nonlinear coupled differential equations. For the detailed understanding of this method it is best to refer 20,23‐26 …”

Section: Fem Solutionsmentioning

confidence: 99%

“…Very recently, Ibrahim and Gadisa 20 reported the solution of nonlinear convective boundary layer flow of MHD couple stress micropolar nanofluids by non‐Fourier's law of heat flux model past a stretching sheet. From the surveyed works of literature above, the problem of unsteady nonlinear convective boundary layer flow of micropolar couple stress nanofluids over a porous stretching sheet with effects of viscous dissipation and suction/injection by Catteneo‐Christov heat flux model is not yet studied.…”

Section: Introductionmentioning

confidence: 99%

“…From the surveyed works of literature above, the problem of unsteady nonlinear convective boundary layer flow of micropolar couple stress nanofluids over a porous stretching sheet with effects of viscous dissipation and suction/injection by Catteneo‐Christov heat flux model is not yet studied. We reformulated the work of Ibrahim and Gadisa 20 by adding the effects of viscous dissipation, suction/injection, and unsteadiness parameter. The highly nonlinear coupled differential equation obtained from the corresponding governing equations of the boundary layer flow region is solved numerically by the robust method called Galerkin finite element method (GFEM).…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear convective boundary layer flow of micropolar‐couple stress nanofluids past permeable stretching sheet using Cattaneo‐Christov heat and mass flux model

Ibrahim

Gadisa

2020

Heat Trans

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The present work aims to examine the effects of viscous dissipation and unsteadiness parameters on nonlinear convective laminar boundary layer flow of micropolar‐couple stress nanofluid past a permeable stretching sheet with non‐Fourier heat flux model in the presence of suction/injection variable. The unsteadiness in the flow, temperature, and concentration profile is caused by the time‐dependence of the stretching velocity, surface temperature, and surface concentration of the boundary layer flow. Similarity transformation is applied to transform the time‐dependent boundary layer flow equations into the corresponding highly nonlinear coupled ordinary differential equations with appropriate boundary conditions. The robust numerical technique called Galerkin finite element method is used to solve the obtained dimensionless governing equations of the flow. The effects of Eckert number, unsteadiness parameter, suction/injection parameter, mixed convection parameter, material parameter, Schmidt number, and couple stress parameter on linear velocity, angular velocity, temperature, concentration, local skin friction coefficient, local wall couple stress, local Nusselt number, and local Sherwood number is analyzed with the help of graphical and tabular form. Under special conditions, the present result is compared with the existing literature and revealed good agreement. Our result shows that as unsteadiness parameter boost, both heat and mass transfer rate rises. The present study has a significant application in material processing technology.

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