where to measures the diffusion of bees . Our problem concerns the steady - state concentration of bees flying Vin from a hive into a closed and square box of dimensions I X T . Bees cannot pass through the bottom , left or right sides of the box at y = 0 , a = O and a - I , so that the concentration of bees obeys u ( I , y = 0 ) Pu By do ( I = 0 4 ) = QI On ( 1 = T , 3 ) = 0 In other words , a zero flux of bees implies that the derivative of a perpendicular to the box boundaries is zero . The top of the box along y = I is open to a hive between T / 3 and = 27 / 3 , but has bee killing poison elsewhere on the boundary , so that the concentration of bees along y = To is 24 ( 20 31 = TT ) = ( when 5 2 5 2 when IS and 7 3 Use separation of variables to find the steady - state concentration of bees in ( I y ) of b in the closed box . Note that you can write your solution simply if you use the fact that sinh ( my ) - Oat y = 0 . For you In safety , the concentration of bees you should find is shown below . The co There are safest