The nanofluid flows in the channel with linearly varying wall temperature

Abstract

In many applications of heat exchanger, due to the heat convection, the wall temperature of the channel usually varies along the streamwise direction. The present paper reports the analysis of nanofluid flows in the channel with linearly varying wall temperature. The non-uniform equilibrium fluid medium model proposed by Buongiorno is applied, where the Brownian diffusion and thermophoresis of nanoparticles are considered. The numerical solutions of laminar flows are determined by the iteration method in conjunction with the Chebyshev collocation method. The results show that: (1) there is a Gaussian distribution of nanoparticle concentration in the wall-normal direction for convective cooling, while its standard deviation depends on the Peclet number and the ratio of Brownian diffusivity to thermophoretic diffusivity; (2) there are obvious stratifications for the viscosity and thermal conductivity in the flow; (3) the velocity decreases significantly with the increase of nanoparticle concentration for convective heating, while there is only a little decrease for the velocity in the cold region for convective cooling.

Keywords

• Nanofluids
• Poiseuille flow
• Heat transfer
• Nanoparticle concentration
• Viscosity stratification