 Note that formula_47 is the weighing function when the flow is in positive direction (i.e., from left to right) and formula_48 is the weighing function when the flow is in the negative direction from right to left.So,

If the flow is in positive direction then, Péclet number formula_40 is positive and the term formula_51, so the function formula_48 won’t play any role in the assumption of formula_53 and formula_54.Likewise when the flow is in negative direction, formula_40 is negative and the term formula_56, so the function formula_47 won’t play any role in the assumption of formula_36 and formula_36.