The entropy generation in the Blasius flow boundary layer over permeable wall vertical flat plate and the ratio of entropy generation due to heat transfer and total entropy generation (Bejan number) were investigated in detail. The coupled momentum and energy partial differential equations (PDEs) were transformed into nonlinear ordinary differential equations (ODEs) using similarity transformation

which were then solved numerically using the Runge-Kutta method and the similarity solutions of the dimensionless flow function and dimensionless temperature were obtained. The effects of dimensionless parameters on the entropy generation and Bejan number were investigated. The results are as follows: for suction

the maximum entropy generation appears on the wall and entropy generation decreases monotonically with the increase of similarity variables

the greater suction speed means the greater entropy generation. For injection

the greater injection speed at the wall means the smaller entropy generation. Near the wall

entropy generation increases with the variable viscosity parameter increases. However this effect away from the wall is reversed. Increases in either the injection/suction parameter or the variable viscosity parameter will increase the Bejan number when it's away from the wall and decrease the Bejan number when near the wall. Increases in either the radiation parameter or Reynolds number will decrease entropy generation and Bejan number

while increases in the Biot number will increase entropy generation and Bejan number. The entropy generation due to heat transfer changes with Biot number dramatically when Biot number is within the range of 0 to 2. The total entropy generation is dominated by the entropy generation due to flow when Biot number is small

and dominated by the entropy generation due to heat transfer when Biot number is large. The entropy generation will increase as the slip parameter increases

while the Bejan number decreases. The effect of Grashof number on entropy generation is relatively large

and entropy generation will have more dramatic changes due to changes of similarity variables when Grashof number is larger. Furthermore

entropy generation due to flow is smaller and Bejan number is bigger with a larger slip parameter.