Similarity Solution of Entropy Generation for Flow of Nanofluid with Magnetic Field over a Stretching Sheet: A Simple Model from Cooling Systems Rolling

The rolling process is one of the most common processes of making the machinery parts and the workpiece cooling rate is one of the most important parameter in the improved of product properties. In this paper, the flow of nanofluids over a nonlinear stretching sheet with a magnetic field is studied as a simplified model of a rolling process. The stretching velocity of the sheet is assumed to vary as a power function of the distance from the origin. The governing equations are including continuity, momentum and energy balances that by using of similarity solution method are transformed to nonlinear ordinary differential equations and are solved. The similarity solution results of momentum and energy equations are compared with published data, and have achieved appropriate compliance. The results show that increasing the solid volume fraction of the nanoparticles φ, the thermal conductivity of the fluid has increases and Increment of the nonlinear stretching parameter n, decreases heat transfer. Also increment of magnetic parameters M, has reduced the cooling rate. In this paper, Bijan number is introduced as a normative for the qualitative cooling rate in the rolling process. Based on the results increase the solid volume fraction of the nanoparticles φ, the nonlinear stretching parameter n and magnetic parameters M, increased, decreased and decreased the number Bijan respectively. The results of this research can be extended for the increasing of the cooling rate in the rolling process of metals.