Analyze of fluid flow and heat transfer of nanofluids over a stretching sheet near the extrusion slit

• The boundary layer with slit effects is analyzed.
• The thermal conductivity is a function of local volume fraction of nanoparticles.
• The critical Reynolds number is proposed to distinguish the non-similar region from the self-similar region.
• The Prandtl number significantly affects the critical Reynolds number.
• The heat and mass transfer near the extrusion slit are much higher than the similar region.

The objective of the present study is to analyze the boundary layer flow and heat transfer of nanofluids over a stretching sheet near the extrusion slit in the presence of variable thermal conductivity. The effects of Brownian motion and thermophoresis are taken into account. The governing partial differential equations are reduced to dimensionless form and solved numerically using finite difference scheme and Point Successive Over Relaxation algorithm. The critical Reynolds number is introduced to distinguish the non-similar region from the self-similar region of velocity and temperature profiles. Furthermore, the effects of dimensionless parameters such as Prandlt number, Schmidt number, variable thermal conductivity parameter, Brownian motion and thermophoresis parameters on the velocity and temperature profiles and also on reduced Nusselt number, reduced Sherwood number and critical Reynolds number are investigated. It is found that the critical Reynolds number for the temperature profile is significantly affected by Prandtl number. In addition, the reduced Nusselt and Sherwood numbers found to be much higher in non-similar regions near the extrusion slit than that of self-similar region.