Flow and Heat Transfer of Bingham Plastic Fluid over a Rotating Disk with Variable Thickness

Abstract

This paper studies the steady flow and heat transfer of Bingham plastic fluid over a rotating disk of finite radius with variable thickness radially in boundary layer. The boundary layer flow is caused by the rotating disk when the extra stress is greater than the yield stress of the Bingham fluid. The analyses of the velocity and temperature field related to the variable thickness disk have not been investigated in current literatures. The governing equations are first simplified into ordinary differential equations owing to the generalized von Kármán transformation for seeking solutions easily. Then semi-similarity approximate analytical solutions are obtained by using the homotopy analysis method for different physical parameters. It is found that the Bingham number clearly influences the velocity field distribution, and the skin friction coefficient Cfr is nonlinear growth with respect to the shape parameter m. Additionally, the effects of the involved parameters (i.e. shape parameter m, variable thickness parameter β, Reynolds number Rev, and Prandtl number Pr) on velocity and temperature distribution are investigated and analyzed in detail.

Importance of exponentially falling variability in heat generation on chemically reactive von kármán nanofluid flows subjected to a radial magnetic field and controlled locally by zero mass flux and convective heating conditions: A differential quadrature analysis

“…Further, the dealing of flows near rotating disks is of great interest to the majority of researchers not only for comprehending the occurring flow regimes but also for their diverse uses (e.g., stability control of swirling flows, domestic devices, rotating heat exchangers, visco-rheometers, chemical stirring operations, spinning disk reactors, vehicle engines, and productive aero-hydrodynamic turbines). In this respect, several examinations were accomplished roughly for such flow problems [15][16][17]. In 1921, Von Kármán [18] was the first pioneering scientist who discussed theoretically the dynamical axisymmetric aspect of steady swirling flows driven over a rotating infinite disk for incompressible viscous fluids.…”

Two-phase nanofluid over rotating disk with exponential variable thickness

“…Several recent studies on the modeling of variable thickness rotating disk with index decreasing have been discussed by [27][28][29]. On the other hand, Liu et al (2016) [30] investigated approximate analytical solutions of Bingham fluid over a variable thickness rotating disk with exponential decreasing by HAM. The above-mentioned works are based on the similarity transformation method, and then numerical or analytical solutions are obtained to solve a set of ordinary differential equations.…”

“…Several recent studies on the modeling of variable thickness rotating disk with index decreasing have been discussed by Hayat et al (2017b; 2018, 2018). On the other hand, Liu et al (2016) investigated Bingham fluid over a variable thickness rotating disk with exponential decreasing. They found that the skin friction coefficient grows nonlinearly with respect to the shape parameter.…”

Numerical Investigation of a Two-Phase Nanofluid Model for Boundary Layer Flow Past a Variable Thickness Sheet

“…This method has got extensive successful results by solving many types of nonlinear equations in science and engineering [39,40]. In this paper, HAM is applied to solve the reduced governing equations resulting from the similarity transformation.…”