Finite-Element Analysis of Transient Heat and Mass Transfer in Microstructural Boundary Layer Flow From a Porous Stretching Sheet

Gupta, Diksha; Kumar, Lalit; Bég, O. Anwar; Singh, B.

doi:10.1615/computthermalscien.2014008401

Cited by 28 publications

(22 citation statements)

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“…FEM uses the opposite approach to FDM, namely numerical integration rather than numerical differentiation. Dropping* notation and applying the Galerkin FEM to Equations to over the element (e)

true(y_{j} \leq y \leq y_{k} true)

, we have

\int_{y_{j}}^{y_{k}} N^{{(e)}^{T}} (\frac{\partial u_{1}^{false(e false)}}{\partial t} + v \frac{\partial u_{1}^{false(e false)}}{\partial y} - p^{false(e false)} - \frac{\partial^{2} u_{1}^{false(e false)}}{\partial y^{2}} + normalH a^{2} u_{1}^{false(e false)} + \frac{u_{1}^{(e)}}{normalD a_{1}} + \frac{normalF s_{1} {Re}_{1}}{normalD a_{1}} u_{1}^{false(e false) 2}) d y = 0

\int_{y_{j}}^{y_{k}} N^{{(e)}^{T}} (\frac{\partial u_{2}^{false(e false)}}{\partial t} + v \frac{\partial u_{2}^{false(e false)}}{\partial y} - p^{false(e false)} - α \frac{\partial^{2} u_{2}^{false(e false)}}{\partial y^{2}} + \frac{u_{2}^{(e)}}{normalD a_{2}} + \frac{normalF s_{2} {Re}_{2}}{normalD}

…”

Section: Galerkin Fem Validationmentioning

confidence: 99%

“…The assembled equations so obtained are solved by any “matrix” numerical technique, for example, Householder’s approach, LU decomposition method, etc. Further details are readily available in the literature . Criteria for the selection of elements are documented by Bég .…”

Section: Galerkin Fem Validationmentioning

confidence: 99%

“…Further details are readily available in the literature. [39][40][41][42][43][44][45] Criteria for the selection of elements are documented by Bég. 45 The nonlinear algebraic system of equations is solved iteratively.…”

Section: Galerkin Fem Validationmentioning

confidence: 99%

See 2 more Smart Citations

Numerical computation of nonlinear oscillatory two‐immiscible magnetohydrodynamic flow in dual porous media system: FTCS and FEM study

Bég

Zaman

Ali

et al. 2019

Heat Trans. Asian Res.

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The transient Hartmann magnetohydrodynamic flow of two immiscible fluids flowing through a horizontal channel containing two porous media with oscillating lateral wall mass flux is studied. A two‐dimensional spatial model is developed for two fluids, one of which is electrically conducting and the other is electrically insulating. Both the fluid regimes are driven by a common pressure gradient. A Darcy‐Forchheimer drag force model is used to simulate the porous media effects on the flow in both the fluid regimes. Special boundary conditions are imposed at the interface. The governing second‐order nonlinear partial differential dimensionless equations are obtained for each region using a set of transformations. The resulting transport equations are controlled by the Hartmann hydromagnetic parameter (Ha), viscosity ratio parameter (α), two Darcy numbers (Da 1 and Da 2), two Forchheimer numbers (Fs 1 and Fs 2), two Reynolds numbers (Re 1 and Re 2), frequency parameter ( εA) associated with the transpiration (lateral wall flux) velocity and a periodic frequency parameter ( ω*t*). Numerical forward time/central space finite‐difference solutions are obtained for a wide range of the governing parameters. Bench marking is performed with a Galerkin finite‐element method (MAGNETO‐FEM), and the results are found to be in excellent agreement. Applications of the model include magnetic cleanup operations in coastal/ocean seabed oil spills and electromagnetic purification of petroleum reservoir fluids.

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“…FEM uses the opposite approach to FDM, namely numerical integration rather than numerical differentiation. Dropping* notation and applying the Galerkin FEM to Equations to over the element (e)

true(y_{j} \leq y \leq y_{k} true)

, we have

\int_{y_{j}}^{y_{k}} N^{{(e)}^{T}} (\frac{\partial u_{1}^{false(e false)}}{\partial t} + v \frac{\partial u_{1}^{false(e false)}}{\partial y} - p^{false(e false)} - \frac{\partial^{2} u_{1}^{false(e false)}}{\partial y^{2}} + normalH a^{2} u_{1}^{false(e false)} + \frac{u_{1}^{(e)}}{normalD a_{1}} + \frac{normalF s_{1} {Re}_{1}}{normalD a_{1}} u_{1}^{false(e false) 2}) d y = 0

\int_{y_{j}}^{y_{k}} N^{{(e)}^{T}} (\frac{\partial u_{2}^{false(e false)}}{\partial t} + v \frac{\partial u_{2}^{false(e false)}}{\partial y} - p^{false(e false)} - α \frac{\partial^{2} u_{2}^{false(e false)}}{\partial y^{2}} + \frac{u_{2}^{(e)}}{normalD a_{2}} + \frac{normalF s_{2} {Re}_{2}}{normalD}

…”

Section: Galerkin Fem Validationmentioning

confidence: 99%

Section: Galerkin Fem Validationmentioning

confidence: 99%

See 1 more Smart Citation

Numerical computation of nonlinear oscillatory two‐immiscible magnetohydrodynamic flow in dual porous media system: FTCS and FEM study

Bég

Zaman

Ali

et al. 2019

Heat Trans. Asian Res.

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“…Additionally, it is very proficient and has been applied to study miscellaneous problems in fluid mechanics and computational fluid dynamics, solid mechanics, mass transfer, heat transfer, and in many other fields. The inclusive features of the finite element method are described by Reddy [39] and Gupta et al Swapna et al [40,41] described that with the finite element technique, a boundary value problem can be solved efficiently and accurately. To resolve the scheme of Equations (9)-(11), firstly we have to consider df dξ =g (13) Equations (9)-(11) are converted into the following form:…”

Section: Interpretation Of Methodsmentioning

confidence: 99%

Finite Element Analysis of Variable Viscosity Impact on MHD Flow and Heat Transfer of Nanofluid Using the Cattaneo–Christov Model

2020

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In this mathematical study, magnetohydrodynamic, time-independent nanofluid flow over a stretching sheet by using the Cattaneo-Christov heat flux model is inspected. The impact of the thermal, solutal boundary and gravitational body forces with the effect of double stratification on the mass flow and heat transfer phenomena is also observed. The temperature-dependent viscosity impact on heat transfer through a moving sheet with capricious heat generation in nanofluids have studied, and the viscosity of the fluid is presumed to deviate as the inverse function of temperature. With the appropriate transformations, the system of partial differential equations is transformed into a system of nonlinear ordinary differential equations. By applying the variational finite element method, the transformed system of equations is solved. The properties of the several parameters for buoyancy, velocity, temperature, stratification, and Brownian motion parameters have examined. The enhancement in the concentration and thermal boundary layer thickness of the nanofluid sheet due to the increment in the viscosity parameter, also increased the temperature and concentration of nanoparticles. Moreover, the fluid temperature declined with the increasing values of thermal relaxation parameter. This displays that the Cattaneo-Christov heat flux model provides a better assessment of temperature distribution. Moreover, confirmation of the code and precision of the numerical method has inveterate with the valuation of the presented results with previous studies.

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“…Many theoretical and computational studies of multiphysical stretching boundary transport phenomena have been communicated in recent years. These include Ali et al (thermal polymer processing), Bég et al (magnetic materials processing with cross‐diffusion), Abel et al (time‐dependent nonisothermal hydromagnetic extrusion flows), Ahmad et al (variable thermal conductivity stretching thermal flow), Gupta et al (unsteady micropolar sheet stretching with wall suction), Yam et al (rheological flow from stretching wedge geometries), Uddin et al (high‐temperature nanofluid boundary layer slip flows from extending/contracting sheets). Further numerical studies include Sajid et al (Newtonian viscous flow from curved stretching sheets), Latiff et al (time‐dependent micropolar nanofluid biological slip flows from shrinking or contracting sheets), Hayat et al viscous thermosolutal transport from oblique extending cylindrical bodies), Bég et al gyrotactic nanobioconvection fully developed flow in stretching/shrinking microchannels, Ali (transpiring heat transfer from a stretched sheet) and Basir et al (external transient axisymmetric nanobioconvection slip boundary layers from a stretching pipe).…”

Section: Introductionmentioning

confidence: 99%

Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non‐Fourier heat flux model

Shamshuddin

Mishra

Bég

et al. 2018

Heat Trans. Asian Res.

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Nonlinear, steady‐state, viscous flow, and heat transfer between two stretchable rotating disks spinning at dissimilar velocities are studied with a non‐Fourier heat flux model. A nondeformable porous medium is intercalated between the disks and the Darcy model is used to simulate matrix impedance. The conservation equations are formulated in a cylindrical coordinate system and via the von Karman transformations are rendered into a system of coupled, nonlinear ordinary differential equations. The emerging boundary value problem is controlled by number of dimensionless parameters, that is, Prandtl number, upper disk stretching, lower disk stretching, permeability, non‐Fourier thermal relaxation, and relative rotation rate parameters. A perturbation solution is developed and the impact of selected parameters on radial and tangential velocity components, temperature, pressure, lower disk radial, and tangential skin friction components and surface heat transfer rate are visualized graphically. Validation of solutions with the homotopy analysis method is included. Extensive interpretation of the results is presented which are relevant to rotating disk bioreactors in chemical engineering.

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Finite-Element Analysis of Transient Heat and Mass Transfer in Microstructural Boundary Layer Flow From a Porous Stretching Sheet

Cited by 28 publications

References 0 publications

Numerical computation of nonlinear oscillatory two‐immiscible magnetohydrodynamic flow in dual porous media system: FTCS and FEM study

Numerical computation of nonlinear oscillatory two‐immiscible magnetohydrodynamic flow in dual porous media system: FTCS and FEM study

Finite Element Analysis of Variable Viscosity Impact on MHD Flow and Heat Transfer of Nanofluid Using the Cattaneo–Christov Model

Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non‐Fourier heat flux model

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