## THERMAL SCIENCE

International Scientific Journal

### NUMERICAL COMPUTATIONS ON FLOW AND HEAT TRANSFER OF CASSON FLUID DUE TO OSCILLATORY MOVING SURFACE

**ABSTRACT**

A numerical study of unsteady hydromagnetic flow of Casson liquid passed through the oscillatory moving surface is presented. The interaction of radiation term is reported in the energy equation. The flow is generated by the rapid move¬ment of elastic surface that stretched back and forth periodically. The number of variables is reduced by introducing dimensionless variables. An implicit technique developed on finite difference algorithm is implemented to the system of PDE. The impact of various parameters like Casson liquid parameter, the oscillation frequency and stretching rate ratio, Hartmann number and effective Prandtl number are shown through various graphs. The observation indicates that the amplitude of the velocity declines by enhancing Casson liquid parameter, oscillation frequency and stretching rate ratio and Hartmann number. The temperature declines by increasing Casson fluid parameter and effective Prandtl number. The results also indicate that the time-series of local Nusselt number increases by enhancing effective Prandtl number.

**KEYWORDS**

PAPER SUBMITTED: 2017-11-30

PAPER REVISED: 2018-02-21

PAPER ACCEPTED: 2018-02-22

PUBLISHED ONLINE: 2018-03-04

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Issue 6**, PAGES [3365 - 3377]

- Shehzad, S. A. , Alsaedi, A. and Hayat, T., Influence of thermophoresis and joule heating on the radiative flow of Jeffrey fluid with mixed convection, Brazilian Journal of Chemical Engineering, 30, 2013, pp. 897-908.
- Han, S., Zheng, L., Li, C. and Zhang, X. Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model, Applied Mathematics Letters, 38, 2014, pp. 87-93.
- Hayat, T., Shafiq, A. and Alsaedi, A., Effect of Joule heating and thermal radiation in flow of third grade fluid over radiative surface, PLOS one, 9, 2014, pp. 3153.
- Hayat, T., Shafiq, A., Mustafa, M. and Alsaedi, A. Boundary layer flow of Walter's B fluid with Newtonian heating, ZeitschriftfürNaturforschung A, 70, 2015, pp. 333-341.
- Mahdy, A and Chamkha, A. J., Diffusion of chemically reactive species of a Maxwell fluid due to an unsteady stretching sheet with slip effect, Thermal Science, 21(6A), 2017, pp. 2357-2367.
- Hussanan, A., Salleh, M. Z., Khan, I. and Tahar, R. M., Unsteady free convection flow of a micropolar fluid with newtonian heating Closed Form Solution,. Thermal Science, 21(6A), 2017, pp. 2313-2326.
- Abbasi, F. M., Mustafa, M., Shehzad, S. A., Alhuthali, M. S. and Hayat, T., Analytical study of Cattaneo-Christov heat flux model for a boundary layer flow of Oldroyd-B fluid, Chinese Physics B, 25, 2016, pp. 014701.
- Krishnamurthy, M. R., Prasannakumara, B. C., Gireesha, B. J. and Gorla, R. S. R., Effect of chemical reaction on MHD boundary layer flow and melting heat transfer of Williamson nanofluid in porous medium, Engineering Science and Technology, an International Journal, 19, 2016, pp. 53-61.
- Bhatti, M. M., Abbas, M. A. and Rashidi, M. M., Combine effects of magnetohydrodynamics (MHD) and partial slip on Peristaltic blood flow of Ree-Eyring fluid with wall properties, Engineering Science and Technology, an International Journal, 19(3), 2016, pp. 1497-1502.
- Walawender, W. P. , Chen, T. Y. and Cala, D. F., An approximate Casson fluid model for tube flow of blood, Biorheology, 12, 1975, pp. 111-124.
- Hayat, T. . Shehzad S. A and Alsaedi, A. Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid, Applied Mathematics and Mechanics (English Edition), 33, 2012, pp. 1301-1312.
- Bhattacharyya, K. Hayat T. and Alsaedi, A. Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer. Chinese Physics B, 22, 2013, pp. 024702.
- Mukhopadhyay, S. Diffusion of chemically reactive species in Casson fluid flow over an unsteady permeable stretching surface, Journal of hydrodynamics, 25, 2013, pp. 591-598.
- Shehzad, S. A. Hayat, T. Qasim M. and Asghar, S. Effects of mass transfer on MHD flow of Casson fluid with chemical reaction and suction, Brazilian Journal of Chemical Engineering, 30, 2013, pp. 187-195.
- Mukhopadhyay, S. and Mandal, I. S. Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux, Chinese Physics B, 23, 2014.
- Mustafa, M. and Khan, J. A. Model for flow of Casson nanofluid past a non-linearly stretching sheet considering magnetic field effects, AIP Advances, 5, 2015, pp. 077148.
- Shehzad, S. A. Hayat , T. and Alsaedi, A. Three-dimensional MHD flow of Casson fluid in porous medium with heat generation, Journal of Applied Fluid Mechanics, 9, 2016, pp. 215-233.
- Rauf, A.. Siddiq, M. K, Abbasi, F. M. Meraj, M. A. ,Ashraf, M. and Shehzad, S. A. , Influence of convective conditions on three dimensional mixed convective hydromagnetic boundary layer flow of Casson nanofluid, Journal of Magnetism and Magnetic Materials, 416, 2016, pp. 200-207.
- Hussain, T., Hussain, S., Hayat, T., Impact of magnetic field in radiative flow of Casson nanofluid with heat and mass fluxes, Thermal Science, (2016) doi: doi.org/10.2298/TSCI150712092H.
- Imtiaz, M. Hayat, T. and Alsaedi, A., Mixed convection flow of Casson nanofluid over a stretching cylinder with convective boundary conditions, Advanced Powder Technology, 27, 2016, pp. 2245-2256.
- Turkyilmazoglu, M., MHD fluid flow and heat transfer due to a shrinking rotating disk, Computers & Fluids, 90, 2014, pp. 51-56.
- Zhang, C. , Zheng, L., Zhang, X. and Chen, G. , MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction, Applied Mathematical Modelling, 39, 2015, pp. 165-181.
- Lin, Y., Zheng, L. , Zhang, X, L., Chen, G., MHD Pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation, International Journal of Heat and Mass Transfer, 84, 2015, pp. 903-911.
- Gireesha, B. J. , Mahanthesh, B. , Manjunatha, P. T. , and Gorla, R. S. R. , Numerical solution of hydromagnetic boundary layer flow and heat transfer past a stretching surface embedded in non-Darcy porous medium with fluid-particle suspension, Journal of Nigerian Mathematical Society, 34, 2015, pp. 267-285.
- Heidary, H., Kermani,M.J. and Dabir, B., Magnetic field effect on convective heat transfer in corrugated flow channel, Thermal Science, 21(5), 2017, pp. 2105-211
- Das, K., Acharya,N., Kundu, P.K., Thin film flow over an unsteady stretching sheet with thermocapillarity in presence of magnetic field, Thermal Science, 21(6A), 2017, pp. 2369-2378.
- Turkyilmazoglu, M.,Mixed convection flow of magnetohydrodynamic micropolar fluid due to a porous heated/cooled deformable plate: exact solutions, International Journal of heat and mass transfer, 105, 2017, pp. 610-622.
- Abbas, Z. , Naveed, M. and Sajid, M. , Hydromagnetic slip flow of nanofluid over a curved stretching surface with heat generation and thermal radiation, Journal of Molecular Liquids, 215, 2016, pp. 756-762.
- Hayat, T. , Ullah, I., Ahmad, B. , and Alsaedi, A. , Radiative flow of Carreau liquid in presence of Newtonian heating and chemical reaction, Results in Physics, 7, 2017, pp. 715-722
- Hayat, T. , Rashid, M. , Imtiaz, M. and Alsaedi, A.., MHD convective flow due to a curved surface with thermal radiation and chemical reaction, Journal of Molecular Liquids, 225, 2017, pp. 482-489.
- Raptis, A., Perdikis, C. and Takhar, H. S., Effect of Thermal Radiation on MHD flow, Appl. Math. 15 Comput. 153 (2004), pp. 645-649..
- Pal, D. , Unsteady convective boundary layer flow and heat transfer over a stretching surface with non-uniform heat source/sink and thermal radiation, International Journal of Computational Methods in Engineering Science and Mechanics, 16, 2015, pp. 170-181.
- Hayat, T. , Muhammad, T., Alsaedi, A. and Alhuthali, M. S., Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation, Journal of Magnetism and Magnetic Materials, 385, 2015, pp. 222-229.
- Sheikhoeslami, M. , Ganji, D. D. , Javed, M. Y. and Ellahi, R. , Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model, Journal of Magnetism and Magnetic Materials, 374, 2015, pp. 36-43.
- . Magyari, E., Pantokratoras, A., Note on the Effect of Thermal Radiation in the Linearized Rosseland Approximation on the Heat Transfer Characteristics of Various Boundary Layer Flows, Int. Comm. Heat Mass Transfer 38 (2011) pp. 554-556.
- Salama, F. A., Effects of radiation on convection heat transfer of cu-water nanofluid past a moving wedge, Thermal Science, 20(2), 2016, pp. 437-447.
- Wang, C. Y. , Nonlinear streaming due to the oscillatory stretching of a sheet in a Viscous, Acta Mechanica, 72, 1988, pp. 261-268.
- Abbas, Z. , Wang, Y. , Hayat, T. And Oberlack, M., Hydromagnetic flow ina viscoelastic fluid due to the oscillatory stretching surface, International Journal of Non-Linear Mechanics, 43,2008, pp. 783-797.
- Abbas, Z. , Wang, Y. , Hayat, T. And Oberlack, M., Slip effects and heat transfer analysis in a viscous fluid over an oscillatory stretching surface, International Journal of Numerical Methods in Fluids, 59, 2009, pp. 443-458.
- Zheng, LC., Jin, X., Zhang, X. X. and Zhang, J. H. ,Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour effects, Acta Mechanica Sinica, 29, 2013, pp. 667-675.
- Ali, N., Khan,S.U., and Abbas, Z., Hydromagnetic flow and heat transfer of a Jeffrey fluid over an oscillatory stretching surface, Z. Naturforsch, 70, 2015, pp. 567-576.
- Khan, S.U., Ali, N., and Abbas, Z., Hydromagnetic flow and heat transfer over a Porous oscillating stretching surface in a Viscoelastic fluid with porous medium, PLOS ONE,10, 2015, pp. 0144299.
- Ali, N., Khan, S.U., Sajid, M., and Zaheer Abbas, Z.,MHD flow and heat transfer of couple Stress fluid over an oscillatory stretching sheet with heat source/sink in porous medium, Alexandria Engineering Journal, 55, 2016, pp. 915-924.
- Turkyilmazoglu, M., The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface, Int. J. Mech. Sci. 77 (2013) 263- 268.
- Hayat, T., Mustafa, M., Pop, I., Heat and mass transfer for Soret and Dufour's effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) pp. 1183-1196.