Unsteady Convective Heat and Mass Transfer Flow in a Thin Liquid Film Over Moving Sheet in a Saturated Permeable Surface

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A note on non-symmetric flow: surface shrinking in mutually orthogonal directions

In this note, we extend the problem treated in (Lok, Math Modelling Anal 24:617–634 (2019)) to the case of permeable surface which is shrinking in mutually orthogonal directions. Both numerical and asymptotic solutions are obtained for two important governing parameters, $$\gamma $$ γ the shrinking rate and S characterizing the fluid transfer through the boundary. In this problem, a restriction on S is required for a solution to exist. This contrasts with the problem in (Lok, Math Modelling Anal 24:617–634 (2019)) where no restriction on S is needed. Numerical solutions show that for a fixed value of S, two critical points $$\gamma _c$$ γ c are observed for $$S > 2$$ S > 2 . Conversely, two critical points $$S_c$$ S c are found for a given value of $$\gamma $$ γ when $$S > 2$$ S > 2 . A discussion on the nonexistence of solution for $$S = 2$$ S = 2 is given and asymptotic solutions for S large and $$(S-2)$$ ( S - 2 ) small are also presented.