The present study investigates the radiation effects in flow through porous medium over a permeable rotating disk with velocity slip and temperature jump. Fluid properties density

The study of rotating disk flows of electrically conducting fluids has practical applications in many areas, such as rotating machinery, lubrication, computer storage devices, oceanography, viscometry, and crystal growth processes. In 1921, Kármán [

Radiative effects have several applications in physics and engineering field. Radiative heat transfer phenomena are used in nuclear reactors, power generation system, and high temperature plasma on controlling heating factor in industries and in liquid metal fluids. Several researchers investigated the effects of radiation on convective flows. Mansour [

In recent years, the slip flow regime has been widely studied and researchers have been concentrating on the analysis of microscale in microelectromechanical systems (MEMS) associated with the embodiment of velocity slip and temperature jump. Wang [

In most of the research, the fluid properties such as density (

Rashidi et al. [

The main goal of the present study is to investigate radiation effects in the steady flow over a rotating permeable disk in porous medium with velocity slip and temperature jump. To predict the flow behavior accurately variable thermophysical properties are taken into consideration. To the best of the author’s knowledge, radiation effects of flow over rotating disk with velocity and temperature slip with variable thermal properties have not been studied yet. The novelty of present paper is to investigate flow and heat transfer for variable fluid properties with velocity slip and temperature jump, taken into consideration. Also, combined effects for both variable and constant fluid properties for various physical parameters on flow and heat transfer have been obtained and depicted graphically, which gives more insight about fluid flow (Figure

Coordinate system for the rotating disk flow.

Consider a steady slip flow due to permeable rotating disk through porous medium. Assume disk of

Let

Following [

The governing equations of continuity, momentum, and energy for laminar incompressible flow in cylindrical coordinates are [

Subjected to the boundary conditions [

Rosseland approximation has been used for radiation,

^{5} [^{5} and 3.6 × 10^{5} and for values higher than 3.6 × 10^{5}, the flow becomes turbulent. In this study the laminar flow for local Reynolds number that lies in the range 0 < Re < 10000 has been considered.

The values of tangential momentum accommodation number (

The nonlinear coupled ordinary differential equations (

The given boundary value problem is reduced to the following system of initial value problem:

From (

Similarly at

Substitution of

Variation of

| | Kn | Re | Pr | | | | |
---|---|---|---|---|---|---|---|---|

0.2 | 1 | 0.05 | 100 | 1 | 1 | 0.031664472 | 0.775065344 | 0.294793960 |

0.1 | 0.031889982 | 0.796287340 | 0.316358091 | |||||

0 | 0.031640032 | 0.820381366 | 0.337225937 | |||||

0 | 0.096135306 | 0.606295102 | 0.322588407 | |||||

1 | 0.031664472 | 0.775065344 | 0.294793960 | |||||

10 | 0.002466157 | 1.120998830 | 0.286444953 | |||||

0 | 0.205650719 | 1.444447007 | 0.365643631 | |||||

0.02 | 0.084184287 | 1.076778244 | 0.334910515 | |||||

0.05 | 0.031664472 | 0.775065344 | 0.294793960 | |||||

1 | 0.160224176 | 1.332713747 | 0.358173061 | |||||

10 | 0.099394903 | 1.138256045 | 0.341296601 | |||||

100 | 1 | 0.031664472 | 0.775065344 | 0.294793960 | ||||

2 | 0.032372329 | 0.772446756 | 0.576107763 | |||||

3 | 0.032943882 | 0.770489197 | 0.860165056 | |||||

4 | 0.033401361 | 0.768923963 | 1.143141070 | |||||

0 | 0.032501654 | 0.780868622 | 0.521797333 | |||||

1 | 0.031664472 | 0.775065344 | 0.294793960 | |||||

2 | 0.031322694 | 0.773378512 | 0.217716214 | |||||

3 | 0.031155065 | 0.772635266 | 0.181723226 |

In this problem, the physical quantities of interest are local skin friction coefficients and the Nusselt number, which represents the wall shear stress and the rate of heat transfer, respectively. When variable fluid properties are taken into consideration, the fluid near to the disk opposes rotation of the disk, due to presence of tangential shear stress. Therefore, to maintain a steady rotation, it is essential to have torque at the shaft. The skin frictions

Thus (

In this investigation Figures

Effect of variation in the porosity parameter on the (a) radial, (b) tangential, (c) axial, and (d) temperature velocity profiles when

Effect of variation in the suction parameter on the (a) radial, (b) tangential, (c) axial, and (d) temperature velocity profiles when

Effect of variation in the Reynolds number on the (a) radial, (b) tangential, (c) & (d) axial, and (e) temperature velocity profiles when

Effect of variation in the Knudsen number on the (a) radial, (b) tangential, (c) axial, and (d) temperature velocity profiles when

Effect of Prandtl number on temperature distribution when

Figures

Figures

Figure

The effect of Reynolds number Re and Knudsen number Kn on velocity and temperature distribution is plotted in Figures

Figure

Figure

Effect of radiation parameter on temperature distribution when

Figure

Effect of variation in the relative temperature difference parameter on the (a) radial, (b) tangential, (c) axial, and (d) temperature velocity profiles when

Table

Tables

Comparison between the results of present study with the results reported by Kelson and Desseaux [

| Present | Alam et al. [ | Maleque and Sattar [ | Kelson and Desseaux [ | ||||
---|---|---|---|---|---|---|---|---|

| | | | | | | | |

0 | 0.510213845 | 0.615909228 | 0.51022378 | 0.61592380 | 0.51015 | 0.61596 | 0.510233 | 0.615922 |

−2 | 0.242412511 | 2.038595812 | 0.24241310 | 2.03859590 | 0.24251 | 2.03911 | 0.242421 | 2.038527 |

−4 | 0.124738066 | 4.005180582 | 0.12475268 | 4.00526266 | 0.12477 | 4.00537 | 0.124742 | 4.005180 |

−5 | 0.099914142 | 5.002660791 | 0.09991986 | 5.00271176 | 0.09996 | 5.00297 | 0.0999187 | 5.002661 |

Comparison between the results of present study with the results reported by Kelson and Desseaux [

| Present | Alam et al. [ | Maleque and Sattar [ | Kelson and Desseaux [ |
---|---|---|---|---|

| | | | |

0 | 0.326798372 | 0.32637889 | 0.32576 | 0.325856 |

−2 | 1.438764651 | 1.43876482 | 1.44212 | 1.437782 |

−4 | 2.842381877 | 2.84369011 | 2.84470 | 2.842381 |

−5 | 3.551223146 | 3.55222471 | 3.55411 | 3.551223 |

In this study, we have investigated radiation effect on velocity profile for all components and temperature profile through rotating disk in porous medium for variable fluid properties and in particular case for constant fluid properties also. By similarity transformation governing equations transformed into nonlinear ordinary differential equations which are solved numerically by using Runge-Kutta method with shooting technique. Based on the resulting solutions the following conclusions can be drawn:

The radial, tangential, and axial velocity profiles decrease while the temperature increases with the increasing values of porosity parameter.

The increasing value of Reynolds and Knudsen number decreases the fluid velocity components and temperature and suction parameter also shows the same effect.

For the effect of the radiation parameter on the temperature distribution, it is seen that the temperature distribution decreases with the increasing values of radiation parameter and also it has been observed that the radial and tangential skin friction values decrease with increase in the radiation parameter.

The authors declare that they have no competing interests.