Effect of radiation on laminar natural convection of nanofluid in a vertical channel with single- and two-phase approaches

Abstract

In the present study, heat transfer and laminar flow of a nanofluid in a vertical channel by considering the effect of radiation with single- and two-phase approaches with prescribed surface temperature conditions and prescribed surface heat flux conditions were simulated. The main goal of this study is to investigate the effect of variations of Grashof number (Gr), radiation parameter (Nr) and volume fraction of nanoparticles (ϕ) on flow and heat transfer characteristics. For this goal, flow with Gr\u2009=\u20095, 10, 15 and 20, volume fractions of 0, 0.1 and 0.2 and radiation parameters of Nr\u2009=\u20090, 0.5 and 1 were simulated. The results show that by increasing Grashof number in both cases of constant heat flux and temperature, nanofluid velocity increases and in both cases of constant temperature and heat flux by increasing volume fraction, the velocity and temperature of the nanofluid drops. The presence of moving wall (plate boundary condition) induces secondary flows in the flow field, and the flow movement in the channel will experience drift because of temperature variations and buoyancy forces due to inducement of secondary forces and the effect of penetration of moving plate velocity into the fluid close by it which will affect the entire fluid flow field in the end. For fixed plate case, the velocity of nanofluid at the walls is zero because of fixed position of the plate and presence of no-slip boundary condition on the solid walls. By increasing the applied temperature, the value of kinetic and internal energy of the velocity field rises which results in higher density gradients and higher buoyancy forces. For both constant heat flux and temperature, increasing solid nanoparticles volume fraction results in lowering of the velocity contour elevations. The quantitative level of axial velocity curves for constant heat flux condition compared with constant temperature case for Gr\u2009=\u20095 and Nr\u2009=\u20090.5 is about 2–3 times less. For constant temperature boundary condition, for Gr\u2009=\u20095 and Nr\u2009=\u20090.5 and volume fraction of 0.1%, the maximum velocity happens at regions 30–50% of channel height from the bottom.