BRINKMAN EQUATION IN TANGENT SPHERE AND CARDIOID COORDINATE SYSTEMS: STREAM FUNCTION SOLUTION 


By

Deepak Kumar Maurya and Vikas Kumar Sharma 

Department of Mathematics Prof. Rajendra Singh (Rajju Bhaiya) Institute of Physical Sciences for Study and Research, V. B. S. Purvanchal University, Jaunpur, Uttar Pradesh, India- 222001 

Email: deepak893395@gmail.com, vs.vbspu@gmail.com 

(Received: May 03, 2024; In format: May 17, 2024; Revised: June 03, 2024; Accepted: June 16, 2024) 


DOI: https://doi.org/10.58250/jnanabha.2024.54140 



Abstract

In the present investigation, analytical stream function solutions of the Brinkman equation in cardioid coordinates (λ, σ, ζ) and tangent sphere coordinates (τ, η, ζ) are investigated. 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. Authors also discuss 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 [17]. 


2020 Mathematical Sciences Classification: 35G05, 35C05, 76S05. 

Keywords and Phrases: Brinkman equation, Stokes equation, Modified Bessel’s functions, Permeability. 

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