## THERMAL SCIENCE

International Scientific Journal

### NUMERICAL COMPUTING PARADIGMS FOR THE DYNAMICS OF SQUEEZING RHEOLOGY OF THIRD GRADE FLUID

**ABSTRACT**

In the current study, investigation for the time-dependent flow of third grade fluid between two disks is presented by exploiting the competency of numerical solvers based on Adams and implicit backward difference methods. The applicable mathematical equations are derived and simplified using boundary-layer approach. Transformations are invoked for conversion of PDE to ODE. Numerical treatment is done with Adams and backward difference scheme. The graphical and numerical illustrations are incorporated to present the effect of physical quantities in fluidic system involving squeezing disks. The level of accuracy is achieved with the help of absolute error graph between Adams and Backward difference scheme for each variants of the system model. Validation of the performance on the basis of convergence analysis also presented.

**KEYWORDS**

PAPER SUBMITTED: 2019-05-08

PAPER REVISED: 2020-03-27

PAPER ACCEPTED: 2020-04-01

PUBLISHED ONLINE: 2020-05-02

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**6**, PAGES [4173 - 4182]

- Fetecau, C., Fetecau, C., Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder, International Journal of Engineering Science., 44(2006), 11-12, pp.788-796.
- Jamil, M., Rauf, A., Fetecau, C. and Khan, N.A., 2011. Helical flows of second grade fluid due to constantly accelerated shear stresses. Communications in Nonlinear Science and Numerical Simulation, 16(4), pp.1959-1969.
- Hayat, T., Nawaz, M., Asghar, S. and Mesloub, S., 2011. Thermal-diffusion and diffusion-thermo effects on axisymmetric flow of a second grade fluid. International Journal of Heat and Mass Transfer, 54(13-14), pp.3031-3041.
- Tan,W., Masuoka, T., Stokes' first problem for a second grade fluid in a porous half-space with heated boundary. International Journal of Non-Linear Mechanics, 40 (2005), 4, pp.515-522.
- Khan, A.A., Bukhari, S.R., Marin, M. and Ellahi, R., 2019. Effects of chemical reaction on thirdgrade MHD fluid flow under the influence of heat and mass transfer with variable reactive index. Heat Transfer Research, 50(11).
- Ahmad, A., Asghar, S., Flow of a second grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field. Applied Mathematics Letters, 24 (2011), 11, pp.1905-1909.
- Okoya, S.S., 2019. Computational study of thermal influence in axial annular flow of a reactive third grade fluid with non-linear viscosity. Alexandria Engineering Journal, 58(1), pp.401-411.
- Shafiq, A., Khan, I., Rasool, G., Seikh, A.H. and Sherif, E.S.M., 2019. Significance of double stratification in stagnation point flow of third-grade fluid towards a radiative stretching cylinder. Mathematics, 7(11), p.1103.
- Hayat, T., Awais, M., Simultaneous effects of heat and mass transfer on time-dependent flow over a stretching surface. International Journal for Numerical Methods in Fluids, 67 (2011), 11, pp.1341-1357.
- Hayat, T., Safdar, A., Awais, M. and Hendi, A.A., 2011. Unsteady Three-Dimensional Flow in a Second-Grade Fluid over a Stretching Surface. Zeitschrift für Naturforschung A, 66(10-11), pp.635-642.
- Fetecau, C., Fetecau, C. and Rana, M., 2011. General solutions for the unsteady flow of second-grade fluids over an infinite plate that applies arbitrary shear to the fluid. Zeitschrift für Naturforschung A, 66(12), pp.753-759.
- Sajid, M., Mughees, M., Ali, N. and Shahzad, H., 2019. A theoretical analysis of blade coating for third-grade fluid. Journal of Plastic Film & Sheeting, 35(3), pp.218-238.
- Khan, Z., Shah, R.A., Altaf, M., Islam, S. and Khan, A., 2018. Effect of thermal radiation and MHD on non-Newtonian third grade fluid in wire coating analysis with temperature dependent viscosity. Alexandria engineering journal, 57(3), pp.2101-2112.
- Bilal, S., Majeed, A.H., Mahmood, R., Khan, I., Seikh, A.H. and Sherif, E.S.M., 2020. Heat and Mass Transfer in Hydromagnetic Second-Grade Fluid Past a Porous Inclined Cylinder under the Effects of Thermal Dissipation, Diffusion and Radiative Heat Flux. Energies, 13(1), p.278.
- Hayat, T., et al., Impact of temperature dependent heat source and nonlinear radiative flow of third grade fluid with chemical aspects. Thermal Science, (2018), doi.org/10.2298/TSCI180409245H
- Sahoo, B., Do, Y., Effects of slip on sheet-driven flow and heat transfer of a third grade fluid past a stretching sheet. International Communications in Heat and Mass Transfer, 37 (2010) 8, pp.1064-1071.
- Abbasbandy, S., Hayat, T., On series solution for unsteady boundary layer equations in a special third grade fluid. Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 8, pp.3140-3146.
- Awais, M., Awan, E.S., Rehman, S.U. and Raja, M.A.Z., Hydro magnetic Falkner-Skan Fluid reheolgy with heat transfer properties. Thermal Science, (2020), Vol 24 No .1A, pp. 339-346.
- Siddiqa, S., Naqvi, S.B., Begum, N., Awan, S.E. and Hossain, M.A., 2018. Thermal radiation therapy of biomagnetic fluid flow in the presence of localized magnetic field. International Journal of Thermal Sciences, 132, pp.457-465.
- Awan, S.E., Awais, M., Rehman, S.U., Niazi, S.A. and Zahoor Raja, M.A., 2018. Dynamical analysis for nanofluid slip rheology with thermal radiation, heat generation/absorption and convective wall properties. AIP Advances, 8(7), p.075122.
- Hayat, T., Yousaf, A., Mustafa, M. and Obaidat, S., 2012. MHD squeezing flow of second-grade fluid between two parallel disks. International journal for numerical methods in fluids, 69(2), pp.399-410.
- Awais, M., Awan, S.E., Muqaddass, N., Rehman, S.U. and Raja, M.A.Z., Numerical and analytical approach for Sakiadis rheology of generalized polymeric material with magnetic field and heat source/sink. Thermal Science, (2020) Vol 24, pp. 1183-1194.
- Awan, S.E., Khan, Z.A., Awais, M., Rehman, S.U. and Raja, M.A.Z., 2018. Numerical treatment for hydro-magnetic unsteady channel flow of nanofluid with heat transfer. Results in Physics, 9, pp.1543-1554.
- Awais, M., Hayat, T., Muqaddass, N., Ali, A. and Awan, S.E., 2018. Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material. Results in physics, 8, pp.1038-1045.
- Awais, M., Awan, S.E., Iqbal, K., Khan, Z.A. and Raja, M.A.Z., 2018. Hydromagnetic mixed convective flow over a wall with variable thickness and Cattaneo-Christov heat flux model: OHAM analysis. Results in physics, 8, pp.621-627.
- Awais, M., Malik, M.Y. and Awan, S.E., 2017. Generalized magnetic effects in a Sakiadis flow of polymeric nano-liquids: Analytic and numerical solutions. Journal of Molecular Liquids, 241, pp.570-576.
- Raja, M.A.Z., Mehmood, A., ur Rehman, A., Khan, A. and Zameer, A., 2018. Bio-inspired computational heuristics for Sisko fluid flow and heat transfer models. Applied Soft Computing, 71, pp.622-648.
- Khan, J.A., Raja, M.A.Z., Syam, M.I., Tanoli, S.A.K. and Awan, S.E., 2015. Design and application of nature inspired computing approach for nonlinear stiff oscillatory problems. Neural Computing and Applications, 26(7), pp.1763-1780.
- Mehmood, A., Afsar, K., Zameer, A., Awan, S.E. and Raja, M.A.Z., 2019. Integrated intelligent computing paradigm for the dynamics of micropolar fluid flow with heat transfer in a permeable walled channel. Applied Soft Computing, 79, pp.139-162.