Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non-Fourier heat flux model

Nonlinear, steady-state, viscous flow and heat transfer between two stretchable rotating disks spinning at dissimilar velocities is studied with a non-Fourier heat flux model. A non-deformable porous medium is intercalated between the disks and the Darcy model is employed to simulate matrix impedance. The conservation equations are formulated in a cylindrical coordinate system and via the Von Karman transformations are rendered into a system of coupled, nonlinear ordinary differential equations. The emerging boundary value problem is controlled by number of dimensionless dimensionless parameters i.e. Prandtl number, upper disk stretching, lower disk stretching, permeability, non-Fourier thermal relaxation and relative rotation rate parameters. A perturbation solution is developed and the impact of selected parameters on radial and tangential velocity components, temperature, pressure, lower disk radial and tangential skin friction components and surface heat transfer rate are visualized graphically. Validation of solutions with the homotopy analysis method is included. Extensive interpretation of the results is presented which are relevant to to rotating disk bioreactors in chemical engineering

Adomian decomposition method simulation of Von Kármán swirling bioconvection nanofluid flow

The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk. It is known that the deformation of the disk is along the radial direction. In addition to that Stefan blowing is considered. The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit. The primitive mass conservation equation, radial, tangential and axial momentum, heat, nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall (disk surface) and free stream boundary conditions. This highly nonlinear, strongly coupled system of unsteady partial differential equations is normalized with the classical Von Kármán and other transformations to render the boundary value problem into an ordinary differential system. The emerging 11th order system features an extensive range of dimensionless flow parameters i.e. disk stretching rate, Brownian motion, thermophoresis, bioconvection Lewis number, unsteadiness parameter, ordinary Lewis number, Prandtl number, mass convective Biot number, Péclet number and Stefan blowing parameter. Solutions of the system are obtained with developed semi-analytical technique i.e. Adomian decomposition method. Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique

Effect of heating on the stability of the three-dimensional boundary layer flow over a rotating disk

The effect of heating on the stability of the laminar three-dimensional boundary layer flow over a rotating disk was experimentally investigated. Local convective heat transfer coefficients were obtained at different running speeds and heating rates by means of an electrically heated disk apparatus placed in a large water tank. The accuracy of the method was assessed by comparison with predictions of the analytical self-similarity solution for laminar flow, and an excellent agreement was found. By means of local heat transfer measurements, the critical Reynolds number corresponding to the onset of vortices was determined as a function of the wall temperature difference and Prandtl number. A substantial increase of the critical Reynolds number with higher wall temperature difference was observed for the three-dimensional flow. The observed stabilizing effect due to heating of three-dimensional water flows was comparable with the predictions of perturbation analyses conducted for two-dimensional flows

Convective heat transfer from rotating disks subjected to streams of air

This Brief describes systematically results of research studies on a series of convective heat transfer phenomena from rotating disks in air crossflow. Phenomena described in this volume were investigated experimentally using an electrically heated disk placed in the test section of a wind tunnel. The authors describe findings in which transitions between different heat transfer regimes can occur in dependency on the involved Reynolds numbers and the angle of incidence, and that these transitions could be related to phenomenological Landau and Landau-de Gennes models. The concise volume closes a substantial gap in the scientific literature with respect to flow and heat transfer in rotating disk systems and provides a comprehensive presentation of new and recent results not previously published in book form