Creeping flow past a porous approximate sphere – Stress jump boundary condition

Srinivasacharya, D.; Prasad, M. Krishna

doi:10.1002/zamm.201000138

Cited by 7 publications

(3 citation statements)

References 21 publications

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“…These conditions are used extensively in the literature to study different types of fluid mechanical problems (see Naduvinamani et al. [25], Ariel [26], Srinivasacharya and Prasad [27], and references therein). The dimensionless variables to be used in the study are defined as follows:

false(x^{*}, y^{*} false) = \frac{1}{H} false(x, y false), {\overset{q}{true}}^{*} = false(u^{*}, v^{*} false) = \frac{H}{ϕ κ_{m}} false(u, v false) = \frac{H}{ϕ κ_{m}} \vec{q}, t^{*} = \frac{κ_{m}}{H^{2}} t, p^{*} = \frac{K}{ϕ μ κ_{m}} p, T^{*} = \frac{T - T_{0}}{Δ T} .

By substituting Equation () into Equations ()–() and dropping asterisks for simplicity, the governing equations in the dimensionless form can be written as follows:

\nabla \cdot \vec{q} = 0,

\frac{1}{V} [\frac{\partial \overset{q}{true}}{\partial t} + (\vec{q} \cdot \nabla) \overset{q}{true}] = - \nabla p + Λ D \nabla^{2} \vec{q} - \vec{q} + R T \hat{j},

\frac{\partial T}{\partial t} + M false(\overset{q}{true} \cdot \nabla false) T = \nabla^{2} T,

v = 0, <...>

…”

Section: Derivation Of the Bevpmentioning

confidence: 99%

“…The boundary conditions of the Beavers-Joseph's type and stress-jump type are the practical ones and arise due to partial slip or jump at the bounding surfaces. These conditions are used extensively in the literature to study different types of fluid mechanical problems (see Naduvinamani et al [25], Ariel [26], Srinivasacharya and Prasad [27], and references therein). The dimensionless variables to be used in the study are defined as follows:…”

Section: Derivation Of the Bevpmentioning

confidence: 99%

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On the differential transform method of solving boundary eigenvalue problems: An illustration

et al. 2020

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The differential transform method (DTM) is a simple technique based on the Taylor series. Applying the DTM, a given linear boundary eigenvalue problem (BEVP) involving ordinary differential equations is converted into a recurrence relation or a system of recurrence relations for the Taylor coefficients. This ultimately leads to the solution of the problem in the form of an infinite power series with an appropriate region of convergence. The present paper aims to apply the DTM in solving a BEVP arising from the Darcy–Brinkman convection in a rectangular box subject to general boundary conditions whose vertical sidewalls are assumed to be impermeable and adiabatic. The non‐dimensional temperature difference between the plates represented by the Darcy–Rayleigh number, the eigenvalue of the problem, is obtained as a function of the width of the Bénard cell (2πb : b is the horizontal wave number) and other parameters using the DTM. The work includes investigation on the convergence of the series solution. The solution by the DTM is compared with that obtained by the MATLAB bvp4c routine and excellent agreement is found thereby establishing the accuracy of the DTM.

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false(x^{*}, y^{*} false) = \frac{1}{H} false(x, y false), {\overset{q}{true}}^{*} = false(u^{*}, v^{*} false) = \frac{H}{ϕ κ_{m}} false(u, v false) = \frac{H}{ϕ κ_{m}} \vec{q}, t^{*} = \frac{κ_{m}}{H^{2}} t, p^{*} = \frac{K}{ϕ μ κ_{m}} p, T^{*} = \frac{T - T_{0}}{Δ T} .

By substituting Equation () into Equations ()–() and dropping asterisks for simplicity, the governing equations in the dimensionless form can be written as follows:

\nabla \cdot \vec{q} = 0,

\frac{1}{V} [\frac{\partial \overset{q}{true}}{\partial t} + (\vec{q} \cdot \nabla) \overset{q}{true}] = - \nabla p + Λ D \nabla^{2} \vec{q} - \vec{q} + R T \hat{j},

\frac{\partial T}{\partial t} + M false(\overset{q}{true} \cdot \nabla false) T = \nabla^{2} T,

v = 0, <...>

…”

Section: Derivation Of the Bevpmentioning

confidence: 99%

Section: Derivation Of the Bevpmentioning

confidence: 99%

On the differential transform method of solving boundary eigenvalue problems: An illustration

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Gupta and Deo [13] in their study of a creeping flow of non‐Newtonian fluid over a porous sphere obtained velocity in terms of stream function. Srinivasacharya and Krishna Prasad [14] have studied laminar flow over a porous approximate sphere with Brinkman's condition inside the porous region and stress jump condition over fluid—porous interface. The velocity, pressure and drag are computed analytically.…”

Section: Introductionmentioning

confidence: 99%

Stokes flow of Micropolar fluid beyond fluid sphere with slip condition

Kunche

Meduri

2022

Z Angew Math Mech

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The present study is about the impact of the fluid motions of the micropolar fluids internally and externally of the fluid sphere with an interfacial slip condition using the analytic method. This enables to bring out solutions for the flow fields as indicated by the stream functions and the drag of the sphere. The work explores the possibilities of change in the slip and drag conditions and their evaluations are graphically proven. Apart from this, the study also identifies that the micropolar fluid flows beyond the Newtonian fluid sphere and vice versa by analyzing the stream functions and the drag of the sphere.

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Effect of magnetic field on the slow motion of a porous spheroid: Brinkman’s model

Madasu

Bucha

2021

Arch Appl Mech

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Creeping flow past a porous approximate sphere – Stress jump boundary condition

Cited by 7 publications

References 21 publications

On the differential transform method of solving boundary eigenvalue problems: An illustration

On the differential transform method of solving boundary eigenvalue problems: An illustration

Stokes flow of Micropolar fluid beyond fluid sphere with slip condition

Effect of magnetic field on the slow motion of a porous spheroid: Brinkman’s model

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