For mass flux as a vector j m, the surface integral of it over a surface S, followed by an integral over the time duration t 1 to t 2, gives the total amount of mass flowing through the surface in that time (t 2 − t 1): m = ∫ ∫ t 1 t 2 ∬ ∬ S j m ⋅ ⋅ n ^ ^ d A d t .