Mathematical modeling of free convection for boundary Layer flow over permeable stretching or shrinking sheet in nanofluid

Nanofluids are engineered colloids made of a base fluid and nanopartic1es of size smaller than 100 nm in diameter with low thermal conductivity such as water, oil and ethylene glycol. The presence of nanoparticles in the fluid increases appreciably the effective of thermal conductivity on the fluid and consequently enhances the heat transfer characteristics. In this study, mathematical models are derived for four boundary layer flow and heat transfer problems. Two differential nanofluids equations are used where are the model takes into account the effect of nanopartic1es volume fraction and the model that incorporates the effects of Brownian motion and thermophoresis. Two problems from this study are in linearly stretching/shrinking sheet of nanofluids and another two problems are in exponentially stretching/shrinking sheet of nanofluids is investigated numerically. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved using a shooting method. Numerical results are presented in tables or graphs for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for a range of various parameters such as stretching or shrinking parameter )., nanopartic1e volume fraction 'P, mass suction parameter S, Lewis number Le, Brownian motion parameter Nb and thermophoresis parameter Nt. It is observed that the skin friction coefficient and the local Nusselt number which represents the heat transfer rate at the surface are significantly influenced by these parameters. The results indicate that dual solutions exist in a certain range of the suction parameters for both stretching and shrinking sheet. The study reveals that the steady flow due to an exponentially stretching or shrinking sheet is possible when the mass suction exceeds a certain critical value and it is need more mass suction than the linear case. Mathematically, the flow over an exponentially stretching or shrinking sheet is more effective compare to linear stretching or shrinking sheet due to the velocity of stretching or shrinking sheet grows rapidly while the linear stretching or shrinking sheet velocity moves sequentially. On the other hand, the increase of the nanoparticles volume fraction and the effect of suction cause the skin friction coefficient and the heat transfer rate at the surface to increase. Apart from that, nanofluid can increase the heat transfer rate and accelerates the cooling process. The lowest heat transfer rate is obtained for the Ti02 nanoparticles compared with Cu and Ab03 due to domination of conduction mode of heat transfer. This is because Ti02 has the lowest thermal conductivity compared with others.

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