---

Discontinuity, Nonlinearity, and Complexity 11(2) (2022) 363--372 | DOI:10.5890/DNC.2022.06.015

Meenakshi Vadithya$^{1}$, Kishan Naikoti$^{2}$, Madhu Macha$^{3}$

$^{1}$ Jawaharlal Nehru Government Polytechnic College, Hyderabad, Telangana, India

$^{2}$ Department of Mathematics, Osmania University, Hyderabad, Telangana, India

$^{3}$ Department of Mathematics, Chaitanya Bharathi Institute of Technology, Hyderabad, India

Download Full Text PDF

 

Abstract

The present article mainly focuses on effect of thermal radiation on magneto hydrodynamic squeezing flow of Casson fluid between two equidistant plates. Non-linear partial differential equations of motion which are governing the flow are made non-dimensional by imposing similarity transformations. Runge-Kutta-Fehlberg scheme used here to solve these non-linear equations, by converting them into a set of initial value problem with single order. The velocity and temperature profile analysis has been carried out by taking into consideration of different parameters involved in it such as, squeeze number, magnetic number, Eckert number, radiation parameter, Prandtl number and Casson fluid parameter etc., and discussed them graphically in suitable manner such that interesting aspects of the solution can be adopted. And also, numerical results of nusselt number and skin friction co-efficient have been shown in this presentation. Velocity profile increases for increasing magnetic parameter near upper plate but it decreases near lower plate. Further same behavior observed for increasing squeeze number. Temperature profile increases with increasing magnetic parameter, radiation parameter and Casson fluid parameter but decreases with Eckert number.

References

1. [1]	Stephan, J.S. (1884), Versuche \"{u}ber die scheinbare Adh\"{a}sion [Experiments on the apparent adhesion], Math Natur Akad Wiss, 69, 713-721

2. [2]	Reynolds, O. (1886), IV. On the theory of lubrication and its application to Mr. Beauchamp tower's experiments, including an experimental determination of the viscosity of olive oil, Philosophical transactions of the Royal Society of London, 177, 157-234.

3. [3]	Archibald, F.R. (1965), Load capacity and time relations for squeeze films, Trans. Asme, 78, A231-A245.

4. [4]	Grimm, R.J. (1976), Squeezing flows of Newtonian liquid films an analysis including fluid inertia. Applied Scientific Research, 32(2), 149-166.

5. [5]	Wolfe, W.A. (1965), Squeeze film pressures. Applied Scientific Research, Section A, 14(1), 77-90.

6. [6]	Kuzma, D.C. (1968), Fluid inertia effects in squeeze films, Applied Scientific Research, 18(1), 15-20.

7. [7]	Tichy, J.A. and and Winer, W.O. (1970), Inertial considerations in parallel circular squeeze film bearings, Journal of Lubrication Technology, 92(4), 588-592.

8. [8]	Rashidi, M.M., Shahmohamadi, H., and Dinarvand, S. (2008), Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates, Mathematical Problems in Engineering, 2008.

9. [9]	Siddiqui, A.M., Irum, S., and Ansari, A.R. (2008), Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation method. Mathematical Modelling and Analysis, 13(4), 565-576.

10. [10]	Mustafa, M., Hayat, T., and Obaidat, S. (2012), On heat and mass transfer in the unsteady squeezing flow between parallel plates, Meccanica, 47(7), 1581-1589.

11. [11]	Tashtoush, B., Tahat, M., and Probert, D. (2001), Heat transfers and radial flows via a viscous fluid squeezed between two parallel disks. Applied energy, 68(3), 275-288.

12. [12]	Duwairi, H.M., Tashtoush, B., and Damseh, R.A. (2004), On heat transfer effects of a viscous fluid squeezed and extruded between two parallel plates, Heat and mass transfer, 41(2), 112-117.

13. [13]	Merrill, E.W., Benis, A.M., Gilliland, E.R., Sherwood, T.K., and Salzman, E.W. (1965), Pressure-flow relations of human blood in hollow fibers at low flow rates. Journal of Applied Physiology, 20(5), 954-967.

14. [14]	Mohyud-Din, S.T., Usman, M., Wang, W., and Hamid, M. (2018), A study of heat transfer analysis for squeezing flow of a Cas-son fluid via differential transform method. Neural Computing and Applications, 30(10), 3253-3264.

15. [15]	Khan, U., Ahmed, N., Khan, S.I.U., Bano, S., and Mohyud-Din, S.T. (2014), Unsteady squeezing flow of a Casson fluid be-tween parallel plates. World Journal of Modelling and Simulation, 10(4), 308-319.

16. [16]	Saba, F., Ahmed, N., Khan, U., Waheed, A., Rafiq, M., and Mohyud-Din, S.T. (2018), Thermophysical analysis of water based (Cu-Al2O3) hybrid nanofluid in an asymmetric channel with dilating/squeezing walls considering different shapes of nanoparticles, Applied Sciences, 8(9), 1549.

17. [17]	Khan, U., Ahmed, N., and Mohyud-Din, S.T. (2017), Heat transfer effects on carbon nanotubes suspended nanofluid flow in a channel with non-parallel walls under the effect of velocity slip boundary condition: a numerical study, Neural Computing and Applications, 28(1), 37-46.

18. [18]	Ahmed, N., Khan, U., and Mohyud-Din, S.T. (2017), Influence of nonlinear thermal radiation on the viscous flow through a deformable asymmetric porous channel: a numerical study, Journal of Molecular Liquids, 225, 167-173.

19. [19]	Khan, U., Ahmed, N., and Mohyud-Din, S.T. (2017), Soret and Dufour effects on Jeffery-Hamel flow of second-grade fluid between convergent/divergent channel with stretchable walls, Results in physics, 7, 361-372.

20. [20]	Mohyud-Din, S.T., Khan, U., Ahmed, N., and Bin-Mohsin, B. (2017), Heat and mass transfer analysis for MHD flow of nanoflu-id inconvergent/divergent channels with stretchable walls using Buongiorno's model, Neural Computing and Applications, 28(12), 4079-4092.

21. [21]	Khan, U., Ahmed, N., and Mohyud-Din, S.T. (2016), Thermo-diffusion and diffusion-thermo effects on flow of second grade fluid between two inclined plane walls, Journal of Molecular Liquids, 224, 1074-1082.

22. [22]	McDonald, D.A. (1974), Blood flows arteries, Second Edn Arnold London.

23. [23]	Khan, U., Khan, S.I., Ahmed, N., Bano, S., and Mohyud-Din, S.T. (2016), Heat transfer analysis for squeezing flow of a Casson fluid between parallel plates, Ain Shams Engineering Journal, 7(1), 497-504.

24. [24]	Mohyud-Din, S.T. and Khan, S.I. (2016), Nonlinear radiation effects on squeezing flow of a Casson fluid between parallel disks, Aerospace Science and Technology, 48, 186-192.

25. [25]	Ahmed, N., Khan, U., Khan, S.I., Xiao-Jun, Y., Zaidi, Z.A., and Mohyud-Din, S.T. (2013), Magneto hydrodynamic (MHD) squeezing flow of a Casson fluid between parallel disks. International Journal of Physical Sciences, 8(36), 1788-1799.

26. [26]	Ahmed, N., Khan, U., Khan, S.I., Bano, S., and Mohyud-Din, S T. (2017), Effects on magnetic field in squeezing flow of a Cas-son fluid between parallel plates, Journal of King Saud University-Science, 29(1), 119-125.

27. [27]	Khan, H., Qayyum, M., Khan, O., and Ali, M. (2016), Unsteady squeezing flow of Casson fluid with magnetohydrodynamic effect and passing through porous medium, Mathematical Problems in Engineering, 2016.

28. [28]	Ganesh, S., Kirubhashankar, C.K., and Ismail, A.M. (2015), Non-linear squeezing flow of Casson fluid between parallel plates. Int. J. Math. Anal, 9(5), 217-223.

29. [29]	Qayyum, M., Khan, H., and Khan, O. (2017), Slip analysis at fluid-solid interface in MHD squeezing flow of Casson fluid through porous medium. Results in physics, 7, 732-750.

30. [30]	Naduvinamani, N.B. and Shankar, U. (2019), Thermal-diffusion and diffusion-thermo effects on squeezing flow of unsteady magneto-hydrodynamic Casson fluid between two parallel plates with thermal radiation, Sadhana, 44(8), 175.

31. [31]	Khan, S.I., Khan, U., Ahmed, N., and Mohyud-Din, S.T. (2016), Thermal radiation effects on squeezing flow Casson fluid be-tween parallel disks, Communications in Numerical Analysis, 2, 92-107.