The combined effects of thermal radiation

temperature dependent viscosity

slip and no-slip boundary conditions over a permeable vertical flat plate on the dimensionless velocity and temperature fields of Blasius laminar boundary layer flow were deeply investigated. By taking similarity variables

the coupled partial differential equations describing the velocity and temperature fields were transformed into nonlinear ordinary differential equations

and then solved numerically using the Runge-Kutta method. The effects of dimensionless parameters on the velocity and temperature fields were investigated with a focus on the analysis of velocity and temperature profiles

with the dimensionless parameters varying under the slip boundary condition. The results indicate that the existence of suction will make the boundary layer thinner

and the boundary layer will be thicker in the case of injection. In contrast with no-slip boundary conditions

the boundary layers of velocity and temperature are all thinner at wall slip boundary conditions. Increasing either the variable viscosity parameter a or the injection and suction parameter will increase the local skin friction coefficient and the local Nusselt number Nu while reducing the velocity and temperature boundary layers thickness. Furthermore

the temperature boundary layer thickness will decrease as the Biot number Bi

Brinkmann number Br decrease or as the Prandtl number Pr and thermal radiation parameter R increase.