THERMAL SCIENCE
International Scientific Journal
VARIATION OF PARAMETS METHOD FOR SQUEEZED FLOW OF A CASSON FLUID
ABSTRACT
The implementation of the variation of parameters method (VPM) has been demonstrated for the flow of a Casson fluid through squeezed parallel plates. Governing partial differential equation has been reduced, with the help of similarity transform, to relatively simpler ordinary differential equation. The consequent nonlinear equation is complicated enough to have an exact solution. We have solved that with the help of VPM. The results are displayed with the help of graphs and are decorated with suitable physical explanation.
KEYWORDS
PAPER SUBMITTED: 2019-07-08
PAPER REVISED: 2019-10-13
PAPER ACCEPTED: 2019-10-15
PUBLISHED ONLINE: 2019-11-02
THERMAL SCIENCE YEAR
2019, VOLUME
23, ISSUE
Supplement 6, PAGES [S2185 - S2191]
- Stefan, M.J., Versuch¨ Uber die scheinbare adhesion'', Sitzungsberichte der Akademie der Wissenschaften in Wien. Mathematik-Naturwissen, 69, (1874): 713-721.
- Reynolds, O., 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(1886): 157-234.
- Archibald, F., Load capacity and time relations for squeeze films, Journal of Lubrication Technology, 78 (1956): A231-A245.
- Rashidi, M. M., et al., Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates, Mathematical Problems in Engineering, 2008 (2009).
- Siddiqui, A. M., et al., Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation method, Mathematical Modelling and Analysis, 13(4) (2008): 565-576.
- Ahmed, N., et al., Effects on magnetic field in squeezing flow of a Casson fluid between parallel plates, Journal of King Saud University - Science, 47(7) (2015): 1581-1589.
- Saba, F., et al., A novel coupling of (CNT-Fe 3 O 4 /H 2 O) hybrid nanofluid for improvements in heat transfer for flow in an asymmetric channel with dilating/squeezing walls, International Journal of Heat and Mass Transfer, 136, (2019): 186-195.
- Saba, F., et al., Impact of an effective Prandtl number model and across mass transport phenomenon on the γ AI 2 O 3 nanofluid flow inside a channel, Physica A: Statistical Mechanics and its Applications, 526, (2019) 121083.
- Mrill, E.W., et al., Pressure flow relations of human blood hollow fibers at low flow rates. J. Appl. Physiol. 20, (1965) 954-967.
- McDonald, D.A., Blood Flows in Arteries, second ed. Arnold, London, 1974.
- Mohyud-Din, S.T. et al., Magnetohydrodynamic flow and heat transfer of nanofluids in stretchable convergent/divergent channels, Applied Sciences, (MDPI), 5 (2015), 1639-1664.
- Mohyud-Din, S. T. et al., Thermo-diffusion, Diffusion-thermo and chemical reaction effects on flow of micropolar fluid of asymmetric channel with dilating and contracting permeable walls, Engineering Computations, (Emerald), 34 (2) (2017), 587-602.
- Ramos, J. I. On the variational iteration method and other iterative techniques for nonlinear differential equations, Applied Mathematics and Computation, 199(1), 39-69, 2008.
- Khan, U. et al., Influence of the shape factor on the flow and heat transfer of a water-based nanofluid in a rotating system, European Physical Journal Plus, 132(4), 166, 2017.
- Sikander, W. et al., Optimal solutions for homogeneous and non-homogeneous equations arising in physics, Results in Physics, 7, 216-224, 2017.
- Sikander, W. et al., Coupling of optimal variation of parameters method with Adomian's polynomials for nonlinear equations representing fluid flow in different geometries, Neural Computing and Applications, 1-14, 2017.
