Chebyshev Approximation for Nanofluid flow of Non-Isothermal Channel Flow under Constant Heat Flux

This paper investigates the Nano-fluid for a non-isothermal channel flow under the effect of a constant pressure gradient acting along the channel axis. Two-dimensional, non-isothermal, steady flow of an incompressible fluid in a channel is taken into consideration. Upper and lower walls of the channel are kept at the same constant heat flux. To consider the effect of conductivity and viscosity, Maxwell and Brinkman’s models are used respectively. The effects of volume fraction, pressure gradient and Reynolds numbers on velocity and temperature profiles are discussed for the Nano-fluid Alumina. Water is used as a base fluid. The comparisons of the flow characteristics, including the distributions of velocity, temperature and volumetric flow rate of aluminum oxide are also given in the paper. Shear stress distribution along the channel axis and pressure gradient for different volume fraction are presented as well.  Discretization is performed using a Pseudospectral technique based on Chebyshev polynomial expansions. The resulting nonlinear, coupled boundary value problem is solved iteratively using Chebyshev pseudospectral method.