On the solution of a partial differential equation representing irrotational flow in bispherical polar coordinates

Abstract

The present paper concerns the exact solution of the partial differential equation E2ψ = 0 in bispherical polar coordinates, arising in the study of irrotational fluid motion. It is evident from the solution that the stream function ψ appearing in the equation depends upon Legendre, trigonometric, hyperbolic functions, similar to the solution reported by Khuri and Wazwaz [S.A. Khuri, A.M. Wazwaz, The solution of a partial differential equation arising in fluid flow theory, Appl. Math. Comput. 77 (1996) 295–300] in toroidal coordinates. In addition to this, we have presented a simplified form of solution of E2ψ = 0 in toroidal coordinates, which was previously reported by Khuri and Wazwaz [1].