
Nonisothermal flow through a rotating straight duct with wide range of rotational parameter and pressure driven parameter
Mohammad Wahiduzzaman^{a}, Md. Mahmud Alam^{b}, M. Ferdows^{b}, S. Sivasankaran^{c} ^{a} Mathematics Discipline, Khulna University, Khulna9208, Bangladesh
^{b} Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
^{c} Department of Mathematics, University of Malaysia, Malaysia
Abstract:
Numerical study is performed to investigate the Nonisothermal 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 Arclength 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 Nonisothermal flow through a straight duct of rectangular crosssection rotating at a constant angular velocity about the center of the duct crosssection 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 Pressuredriven parameter (centrifugal force) on the flow. We examine the structures in case of rotation of the duct axis and the Pressuredriven 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 Nonsymmetric the secondary flow patterns with 10vortex (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.
Key words:
nonisothermal flow, through straight duct, Pressuredriven parameter, Rotation parameter, spectral method, Chebyshev polynomials, collocation method, Newton–Raphson method.
DOI:
https://doi.org/10.7868/S0044466913100153
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:10, 1571–1589
Bibliographic databases:
UDC:
519.634 Received: 10.07.2012 Revised: 21.12.2013
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Citation:
Mohammad Wahiduzzaman, Md. Mahmud Alam, M. Ferdows, S. Sivasankaran, “Nonisothermal flow through a rotating straight duct with wide range of rotational parameter and pressure driven parameter”, Zh. Vychisl. Mat. Mat. Fiz., 53:10 (2013), 1760; Comput. Math. Math. Phys., 53:10 (2013), 1571–1589
Citation in format AMSBIB
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\paper Nonisothermal flow through a rotating straight duct with wide range of rotational parameter and pressure driven parameter
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