Time varying rotating disk flow and heat transfer through a porous medium of a non-Newtonian fluid with suction and injection

The time varying flow of an incompressible viscous non-Newtonian fluid above an infinite rotating porous disk in a porous medium is studied with heat transfer. A uniform injection or suction is applied through the surface of the disk. Numerical solutions of the nonlinear partial differential equations which govern the hydrodynamics and energy transfer are obtained. The effect of the porosity of the medium, the characteristics of the non-Newtonian fluid and the suction or injection velocity on the velocity and temperature fields is considered

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

Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation

Background: Non-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature. Methods: The governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time (t), the Grashof number (Gr), the Prandtl number (Pr), and the phase angle (ωt). Skin friction and the Nusselt number are also evaluated. Results: The exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver–Stehfest algorithm. Conclusion: The interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time (t), the Grashof number (Gr), the Prandtl number (Pr), and the phase angle (ωt)

Numerical investigation of Von Karman swirling bioconvective nanofluid transport from a rotating disk in a porous medium with Stefan blowing and anisotropic slip effects

In recent years, significant progress has been made in modern micro- and nanotechnologies related to applications in micro/nano-electronic devices. These technologies are increasingly utilizing sophisticated fluent media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro-organisms. Motivated by bio-nanofluid rotating disk oxygenators in medical engineering, in the current work, a mathematical model is developed for steady convective Von Karman swirling flow from an impermeable power-law radially stretched disk rotating in a Darcy porous medium saturated with nanofluid doped with gyrotactic micro-organisms. Anisotropic slip at the wall and blowing effects due to concentration are incorporated. The nano-bio transport model is formulated using non-linear partial differential equations (NPDEs), which are transformed to a set of similarity ordinary differential equations (SODEs) by appropriate transformations. The transformed boundary value problem is solved by a Chebyshev collocation method. The impact of key parameters on dimensionless velocity components, concentration, temperature and motile microorganism density distributions are computed and visualized graphically. Validation with previous studies is included. It is found that that the effects of suction provide a better enhancement of the heat, mass and microorganisms transfer in comparison to blowing. Moreover, physical quantities decrease with higher slip parameters irrespective of the existence of blowing. Temperature is suppressed with increasing thermal slip whereas nanoparticle concentration is suppressed with increasing wall mass slip. Micro-organism density number increases with the greater microorganism slip. Radial skin friction is boosted with positive values of the power law stretching parameter whereas it is decreased with negative values. The converse response is computed for circumferential skin friction, nanoparticle mass transfer rate and motile micro-organism density number gradient. Results from this study are relevant to novel bioreactors, membrane oxygenators, food processing and bio-chromatography

Finite element analysis of rotating oscillatory magneto-convective radiative micropolar thermo-solutal flow

Micropolar fluids provide an alternative mechanism for simulating micro-scale and molecular fluid mechanics which require less computational effort. In the present paper, a numerical analysis is conducted for the primary and secondary flow characterizing dissipative micropolar convective heat and mass transfer from a rotating vertical plate with oscillatory plate velocity, adjacent to a permeable medium. Owing to high temperature, thermal radiation effects are also studied. The micropolar fluid is also chemically-reacting, both thermal and species (concentration) buoyancy effects and heat source/sink are included. The entire system rotates with uniform angular velocity about an axis normal to the plate. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. The partial differential equations governing the flow problem are rendered dimensionless with appropriate transformation variables. A Galerkin finite element method is employed to solve the emerging multi-physical components of fluid dynamics problem are examined for a variety of parameters including rotation parameter, radiation-conduction parameter, micropolar coupling parameter, Eckert number (dissipation), reaction parameter, magnetic body force parameter and Schmidt number. A comparison with previously published article is made to check the validity and accuracy of the present finite element solutions under some limiting case and excellent agreement is attained. The current simulations may be applicable to various chemical engineering systems, oscillating rheometry, and rotating MHD energy generator near-wall flows

Thermal Radiation and Thermal Diffusion for Soret and Dufour’s Effects on MHD Flow over Rotating Infinite Disk

In general, the thermal radiation and thermal diffusion effects over an electrically conducting, Newtonian fluid in a steady laminar magnetohydrodynamic convective flow over a porous rotating infinite disk with the consideration of heat and mass transfer in the presence of Soret and Dufour’s diffusion effects have been obtained and studied numerically. The governing continuity, momentum, energy and concentration equations are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically. In this chapter, numerical results were presented for velocity (radial, axial and tangential), temperature, concentration and pressure profiles for different parameters of the problem Also, the effects of the pertinent parameters on the radial and tangential skin friction, the rate of heat and mass transfer are obtained and discussed numerically and illustrated graphically

Analytical solution of MHD free convective flow of couple stress fluid in an annulus with Hall and ion-slip effects

This paper presents the Hall and Ion-slip effects on electrically conducting couple stress fluid flow between two circular cylinders in the presence of a temperature dependent heat source. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and then solved using homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, Ion-slip parameter and couple stress fluid parameter on velocity and  temperature are discussed and shown graphically