“…The unknown coefficients, a, b, c, d, e, r, s, t, w, and z can be obtained after solving each transformed function and doing the inverse operation and then applying boundary conditions of the problem (Eq. (19)). For instance, the results obtained by N 1 ¼ N 2 ¼ N 3 ¼ 0:1; Pe h ¼ Pe m ¼ 0:1 and Re = 0.1 when we do the procedure until Fð7Þ, Gð5Þ, Hð5Þ and Uð5Þ are as follows:…”