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