Stream Function Solution of the Brinkman Equation in Parabolic Cylindrical Coordinates

Special Topics Rev Porous Media

Deo

2022

Self Cite

The present work deals with the influence of magnetic field on Newtonian fluid sandwiched between two porous cylindrical pipes which are filled with micropolar fluids. Fluid motion is occurring along z * -axis and applied magnetic field is taken in the direction perpendicular to the direction of fluid motion. On applying appropriate boundary conditions, velocity profiles, microrotations, flow rate and shear stresses are obtained for the corresponding fluid regions. The graphs for volumetric flow rate and fluid velocity are plotted and discussed for different values of micropolar parameter, couple stress parameter, porosity, viscosity ratio parameter, Hartmann number, conductivity ratio parameters and Darcy numbers.

Section: Introductionmentioning

confidence: 99%

Effect of Magnetic Field on Newtonian Fluid Sandwiched Between Non-Newtonian Fluids Through Porous Cylindrical Shells

Special Topics Rev Porous Media

Deo

2022

Self Cite

“…The governing equation for fluid flow through the porous medium given by a modification of Darcy's equation [19]. Stream function solution of the Brinkman equation in the cylindrical (circular/parabolic) coordinates is obtained [20,21]. Using cell models, influence of magnetic field on hydrodynamic permeability of biporous membrane relative to the micropolar fluid motion, investigated by Deo et al [22,23].…”

Section: Introductionmentioning

confidence: 99%

Hydromagnetic Flow of Casson Fluid Over a Stretching Plane Through Porous Medium

Deo

2022

Preprint

The current analysis focuses on the MHD effects of a steady Casson fluid flowing overa stretching sheet in the porous medium. To examine the properties of non-Newtonian fluid, a mathematical model for Casson fluid is developed. Similarity transformationis used to convert higher order nonlinear governing partial differential equations (PDEs) into ordinary differential equations (ODEs). Analytical expressions of flow characteristics like velocity and skin friction coefficient are produced by applying the proper boundary conditions. Reports on specific instances of skin friction coefficient and fluid velocity (horizontal/transversal) are supplied. For various values of flow parameters, such as Casson parameter, suction velocity, conductivity, and permeability parameter, fluid flow characteristics, i.e. velocity profiles, and skin friction coefficient are sketched and analysed.

“…In the parabolic, tangent sphere, and cardioid axisymmetric coordinate systems, Protopapas [7] obtained the particular solution of E 2 ψ = 0. Maurya and Lata [8] established the general solution of Darcy equations in three axisymmetric system of coordinates: parabolic, bi-polar cylindrical and parabolic cylindrical coordinates.…”

mentioning

confidence: 99%

“…In the cylindrical polar coordinates, Deo and Maurya [14] presented the generalized stream function solution of the Brinkman equation and deduced the solutions [11,13] as a special case using obtained generalized solution. The general stream function solution of the Brinkman and the Stokes equations in the parabolic cylindrical coordinates, obtained by Maurya and Deo [15].…”

mentioning

confidence: 99%

Brinkman Equation in Tangent Sphere and Cardioid Coordinate Systems: Stream Function Solution

Maurya,

Sharma

2024

Preprint

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In the present investigation, we have identified the stream function solution of the Brinkman equation in both the cardioid coordinates (λ, σ, ζ) and tangent sphere coordinates (τ, η, ζ). Trigonometric functions, special functions such as modified Bessel functions and Bessel functions, are contained in the analytical expressions of the stream function and velocity components. We also discussed about how permeability depends on the estimated stream function solution for the Brinkman equation in the cardioid and tangent sphere coordinate systems, which can be deduced as a particular scenario that corresponds with the solution which is currently available [7]. MSC (2020): 35G05, 35C05, 76S05