Investigation of variable thermo-physical properties of viscoelastic rheology: A Galerkin finite element approach

Qureshi, Imran Haider; Nawaz, M.; Rana, Shafia; Nazir, Umar; Chamkha, Ali J.

doi:10.1063/1.5032171

Cited by 31 publications

(18 citation statements)

References 21 publications

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“…Heat and mass transport phenomena are demonstrated by exhausting the generalized descriptions of Fourier's and Fick's law through the Cattaneo‐Christov theory . Furthermore, temperature‐dependent thermal conductivity and mass diffusion are engaged along with thermal radiation . Under the principle of the boundary layer, the governing laws present the considered physical occurrence depicted in Figure and are articulated as

\frac{\partial u_{1}}{\partial x} goodbreakinfix+ \frac{\partial u_{2}}{\partial y} goodbreakinfix+ \frac{\partial u_{3}}{\partial z} goodbreakinfix= 0,

u_{1} \frac{\partial u_{1}}{\partial x} goodbreakinfix+ u_{2} \frac{\partial u_{1}}{\partial y} goodbreakinfix+ u_{3} \frac{\partial u_{1}}{\partial z} goodbreakinfix+ δ_{1} ε_{1 a} goodbreakinfix= ν_{α} \frac{\partial^{2} u_{1}}{\partial z^{2}} goodbreakinfix+ ν_{α} δ_{2} ε_{2 a} goodbreakinfix+ ε_{2 b} goodbreakinfix- \frac{σ B_{\circ}^{2}}{ρ} (u_{1} + δ_{1} u_{3} \frac{\partial u_{1}}{\partial z}),

\begin{matrix} true \\ left {italicϵ}_{1 a} = {(u_{1})}^{2} \frac{\partial^{2} u_{2}}{\partial x^{2}} + {(u_{2})}^{2} \frac{\partial^{2} u_{2}}{\partial y^{2}} + {(u_{3})}^{2} \frac{\partial^{2} u_{2}}{\partial z^{2}} + 2 u_{1} u_{2} \partial^{2} u_{1} <...> \end{matrix}

…”

Section: Flow Field Analysis and Mathematical Depictionmentioning

confidence: 99%

“…Heat and mass transport phenomena are demonstrated by exhausting the generalized descriptions of Fourier's and Fick's law through the Cattaneo-Christov theory. 21,23 Furthermore, temperature-dependent thermal conductivity and mass diffusion 26,31 are engaged along with thermal radiation. 14,19,[28][29][30] Under the principle of the boundary layer, the governing laws present the considered physical occurrence depicted in Figure 1 and are articulated as 11 12 13 11 1 2 2 2 2 2 2 2 3 2 2 2 1 1 2 1 12 3 1 1 2 2 2 3 2 1 3 13 2 3 3 3 1 2…”

Section: Flow Field Analysis and Mathematical Depictionmentioning

confidence: 99%

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Thermal performance of an MHD radiative Oldroyd‐B nanofluid by utilizing generalized models for heat and mass fluxes in the presence of bioconvective gyrotactic microorganisms and variable thermal conductivity

Sohail

Naz

Bilal

2019

Heat Trans. Asian Res.

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The current paper analyzes the thermal and concentration attributes with the temperature‐dependent mass diffusion coefficient and thermal conductivity for the flow of an Oldroyd‐B nanoliquid over a stretchable configuration using the Buongiorno model under the application of boundary layers. The mechanisms of heat and mass transport are modeled by using the revised definitions of heat and mass fluxes. Mathematical expressions for the conservation laws are transformed into ordinary differential expressions by making the appropriate changes. The resulting complexly structured expressions are handled via an optimal homotopy procedure. The impact of influential variables on the desired solutions is plotted, tabulated, and discussed in detail. Comparative analysis of the thermal wall flux coefficient, concentration flux coefficient, density magnitude of the motile microorganisms, and reduced dimensionless stresses with already published research as a limiting case of this exploration is presented for the validity of the proposed scheme, and an excellent agreement is observed, which confirms the reliability of the homotopic solution.

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\frac{\partial u_{1}}{\partial x} goodbreakinfix+ \frac{\partial u_{2}}{\partial y} goodbreakinfix+ \frac{\partial u_{3}}{\partial z} goodbreakinfix= 0,

u_{1} \frac{\partial u_{1}}{\partial x} goodbreakinfix+ u_{2} \frac{\partial u_{1}}{\partial y} goodbreakinfix+ u_{3} \frac{\partial u_{1}}{\partial z} goodbreakinfix+ δ_{1} ε_{1 a} goodbreakinfix= ν_{α} \frac{\partial^{2} u_{1}}{\partial z^{2}} goodbreakinfix+ ν_{α} δ_{2} ε_{2 a} goodbreakinfix+ ε_{2 b} goodbreakinfix- \frac{σ B_{\circ}^{2}}{ρ} (u_{1} + δ_{1} u_{3} \frac{\partial u_{1}}{\partial z}),

\begin{matrix} true \\ left {italicϵ}_{1 a} = {(u_{1})}^{2} \frac{\partial^{2} u_{2}}{\partial x^{2}} + {(u_{2})}^{2} \frac{\partial^{2} u_{2}}{\partial y^{2}} + {(u_{3})}^{2} \frac{\partial^{2} u_{2}}{\partial z^{2}} + 2 u_{1} u_{2} \partial^{2} u_{1} <...> \end{matrix}

…”

Section: Flow Field Analysis and Mathematical Depictionmentioning

confidence: 99%

Section: Flow Field Analysis and Mathematical Depictionmentioning

confidence: 99%

Thermal performance of an MHD radiative Oldroyd‐B nanofluid by utilizing generalized models for heat and mass fluxes in the presence of bioconvective gyrotactic microorganisms and variable thermal conductivity

Sohail

Naz

Bilal

2019

Heat Trans. Asian Res.

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“…Following studies 12,[27][28][29] weighted residual approximations (WRA) for the system dened in eqn (9)-(12) are given below…”

Section: Galerkin Finite Element Formulationmentioning

confidence: 99%

Computational fluid dynamic simulations for dispersion of nanoparticles in a magnetohydrodynamic liquid: a Galerkin finite element method

2018

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“…Several studies 8,26,[28][29][30][31][32] have investigated the fluid flow over stretching or shrinking sheets under the slip boundary conditions. Such types of flow configurations are observed in various engineering and industrial processes, namely, the boundary layer along material handling conveyors, crystal growth, paper production, metallurgical processes, etc.…”

Section: Introductionmentioning

confidence: 99%

Effects of variable thermophysical properties on mixed convection slip flow over a wedge

Roy

Saha

et al. 2019

Heat Trans. Asian Res.

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This paper reveals the characteristics of mixed convection slip flow of an electrically conducting fluid over a wedge subject to temperature dependent viscosity and thermal conductivity variations. The system of dimensionless nonsimilar governing equations has been solved by an implicit finite difference method. We also use stream‐function formulation to reduce the governing equations into a convenient form, which are valid for small and large time regimes. These are solved employing the perturbation method for small time and the asymptotic method for large time. Numerical solutions yield a good agreement with the series solutions. Because of the increase in the mixed convection parameter, the peak of the velocity profile increases whereas the maximum temperature decreases. In contrast, the local skin‐friction coefficient and local Nusselt number are found to increase with the mixed convection parameter. For higher values of the velocity slip and temperature jump conditions, the local skin‐friction coefficient and the local Nusselt number are found to increase. The viscosity parameter enhances the local skin friction and the local Nusselt number. But the converse characteristic is observed for the thermal conductivity parameter. The results could be used in microelectromechanical systems, fabrication, melting of polymers, polishing of artificial heart valves, etc.

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Investigation of variable thermo-physical properties of viscoelastic rheology: A Galerkin finite element approach

Cited by 31 publications

References 21 publications

Thermal performance of an MHD radiative Oldroyd‐B nanofluid by utilizing generalized models for heat and mass fluxes in the presence of bioconvective gyrotactic microorganisms and variable thermal conductivity

Thermal performance of an MHD radiative Oldroyd‐B nanofluid by utilizing generalized models for heat and mass fluxes in the presence of bioconvective gyrotactic microorganisms and variable thermal conductivity

Computational fluid dynamic simulations for dispersion of nanoparticles in a magnetohydrodynamic liquid: a Galerkin finite element method

Effects of variable thermophysical properties on mixed convection slip flow over a wedge

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