Non-isothermal flow through a rotating straight duct with wide range of rotational parameter and pressure driven parameter

Numerical study is performed to investigate the Non-isothermal flow in a rotating straight duct under various flow conditions. Spectral method is applied as a main tool for the numerical technique, where the Chebyshev polynomial, the Collocation methods, the Arc-length method and the Newton–Raphson method are also used as secondary tools. The characteristics of the flow mentioned above are described here. The incompressible viscous steady Non-isothermal flow through a straight duct of rectangular cross-section rotating at a constant angular velocity about the center of the duct cross-section is investigated numerically to examine the combined effects of Rotation parameter (Coriolis force), Grashof number (parameter which is used in heat, transfer studies involving free, forced or natural convection and is equql to $\frac{L^3g\beta\Delta T}{v^2}$, where $L$ is the characteristic length, $\rho$ the density, $g$ the acceleration due to gravity, $\beta$ the thermal expansion coefficient, $\Delta T$ the temperature difference, $\mu$ the viscosity and $v$ the kinematic viscosity of the fluid. The expansion coefficient $\beta$ is a measure of the rate at which the volume $V$ of the fluid changes with temperature at a given pressure $P$, Prandtl number, aspect ratio and Pressure-driven parameter (centrifugal force) on the flow. We examine the structures in case of rotation of the duct axis and the Pressure-driven parameter with large aspect ratio where other parameters are fixed. The calculations are carried out for $0\leqslant T_r\leqslant 300$, $2\leqslant\gamma\leqslant6$, $G_r=100$, $P_r=7.0$ and $0\leqslant P_r\leqslant 800$ by applying the Spectral method. When $\Omega>0$ and the rotation is in the same direction as the Coriolis force enforces the centrifugal force, multiple solutions of Non-symmetric the secondary flow patterns with 10-vortex (maximum) are obtained in case of $T_r=100$ and 150 with large aspect ratio. The intense of the temperature field is very strong near the heated wall in all cases. Finally, the overall solutions of the problems considered in conclusion.