“…We found that in the general scenario where the polytropic exponents γ 1 , γ 2 of the two fluids are arbitrary the admitted Lie symmetries from a algebra of dimension fourth, while when in the special case where the polytropic exponents are equal, that is, γ 1 = γ 2 the admitted Lie symmetries form a sixth dimensional Lie algebra. That result is different from that previously found in the literature where it was found that a sixth dimensional Lie algebra it is admitted only when γ 1 , γ 2 are equal with one, that is, γ 1 = γ 2 = 1 [41].…”