# Three-Dimensional Viscous Dissipative Flow of Nanofluids Over a Riga Plate

Document Type : Full Lenght Research Article

Authors

1 Department of Mathematics Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, Tamil Nadu

2 Department of Mathematics, SRMV College of Arts and Science, Coimbatore-641020, India.

3 Department of Mathematics,Providence College for Women, Coonoor - 643 104, INDIA

4 Mathematics and its Applications in Life Sciences Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam 3Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam,

Abstract

In this study, the physical perspectives on three-dimensional flow of base fluids with nanoparticles are comparatively investigated under the effect of viscous dissipation using Runge-Kutta 4th order numerical procedure. With the help of similarities transformations, the mathematical model which are described as partial differential equations are transmuted into ordinary differential equations. As said, the Runge-Kutta method, assisted by the shooting strategy, is designed to deal numerically with the resulting set of non-linear differential equations. Highlights of the flow-field and thermal field are illustrated quantitatively in plots. Results for local skin friction coefficients and local Nusselt number are reported and analyzed tabularly. The accuracy of present study is verified in comparison to existing literatures and we have identified an astounding understanding. Also, results indicate that, the velocity profile is enhanced by the modified Hartmann number and stretching ratio parameters. The nanofluid, in fact, has elevated skin friction values and is also more suitable for increasing the rate of heat transfer.

Keywords

Main Subjects

#### References

[1] Turkyilmazoglu, M., 2020. Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis. Computer methods and programs in biomedicine, 187, p.105171.
[2] Ahmad, R., Mustafa, M. and Turkyilmazoglu, M., 2017. Buoyancy effects on nanofluid flow past a convectively heated vertical Riga-
plate: A numerical study. International Journal of Heat and Mass Transfer, 111, pp.827-835.
[3] Gholinia, M., Kiaeian Moosavi, S.A.H., Gholinia, S. and Ganji, D.D., 2019. Numerical simulation of nanoparticle shape and thermal ray on a CuO/C2H6O2–H2O hybrid base nanofluid inside a porous enclosure using Darcy's law. Heat Transfer—Asian Research, 48(7), pp.3278-3294.
[4] Turkyilmazoglu, M., 2019. Fully developed slip flow in a concentric annuli via single and dual phase nanofluids models. Computer methods and programs in biomedicine, 179, p.104997.
[5] Gholinia, M., Pourfallah, M. and Chamani, H.R., 2018. Numerical investigation of heat transfers in the water jacket of heavy duty diesel engine by considering boiling phenomenon. Case studies in thermal engineering, 12, pp.497-509.
[6] Ghadikolaei, S.S. and Gholinia, M., 2020. 3D mixed convection MHD flow of GO-MoS2 hybrid nanoparticles in H2O–(CH2OH)2 hybrid base fluid under the effect of H2 bond. International Communications in Heat and Mass Transfer, 110, p.104371.
[7] Dibaei, M. and Kargarsharifabad, H., 2017. New achievements in Fe3O4 nanofluid fully developed forced convection heat transfer under the effect of a magnetic field: An experimental study. Journal of Heat and Mass Transfer Research, 4(1), pp.1-11.
[8] Tajik, M., Dehghan, M. and Zamzamian, A., 2015. Analysis of variance of nanofluid heat transfer data for forced convection in horizontal spirally coiled tubes. Journal of Heat and Mass Transfer Research, 2(2), pp.45-50.
[9] Gholinia, M., Moosavi, S.K., Pourfallah, M., Gholinia, S. and Ganji, D.D., 2019. A numerical treatment of the TiO2/C2H6O2–H2O hybrid base nanofluid inside a porous cavity under the impact of shape factor in MHD flow. International Journal of Ambient Energy, pp.1-8. (Doi: 10.1080/01430750.2019.1614996).
[10] Gailitis, A., 1961. On the possibility to reduce the hydrodynamic drag of a plate in an electrolyte. Appl. Magnetohydrodynamics, Rep. Inst. Phys. Riga, 13, pp.143-146.
[11] Hakeem, A.K., Nayak, M.K. and Makinde, O.D., 2019. Effect of exponentially variable viscosity and permeability on Blasius flow of Carreau nano fluid over an electromagnetic plate through a porous medium. Journal of Applied and Computational Mechanics, 5(2), pp.390-401.
P. Ragupathi / JHMTR 8 (2021) 49- 60 59
[12] Ragupathi, P., Hakeem, A.A., Saranya, S. and Ganga, B., 2019. Non-Darcian three-dimensional flow of Fe3O4/Al2O3 nanoparticles with H2O/NaC6H9O7 base fluids past a Riga plate embedded in a porous medium. The European Physical Journal Special Topics, 228(12), pp.2571-2600.
[13] Ragupathi, P., Hakeem, A.A., Al-Mdallal, Q.M., Ganga, B. and Saranya, S., 2019. Non-uniform heat source/sink effects on the three-dimensional flow of Fe3O4/Al2O3 nanoparticles with different base fluids past a Riga plate. Case Studies in Thermal Engineering, 15, p.100521.
[14] Abdul Hakeem, A.K., Ragupathi, P., Saranya, S. and Ganga, B., 2020. Three dimensional non-linear radiative nanofluid flow over a Riga plate. Journal of Applied and Computational Mechanics, 6(4), pp.1012-1029.
[15] Nasir, N.A.A.M., Ishak, A. and Pop, I., 2019. Stagnation point flow and heat transfer past a permeable stretching/shrinking Riga plate with velocity slip and radiation effects. Journal of Zhejiang University-SCIENCE A, 20(4), pp.290-299.
[16] Shafiq, A., Hammouch, Z. and Turab, A., 2018. Impact of radiation in a stagnation point flow of Walters’ B fluid towards a Riga plate. Thermal Science and Engineering Progress, 6, pp.27-33.
[17] Zaib, A., Haq, R.U., Chamkha, A.J. and Rashidi, M.M., 2019. Impact of partial slip on mixed convective flow towards a Riga plate comprising micropolar TiO2-kerosene/water nanoparticles. International Journal of Numerical Methods for Heat & Fluid Flow, 29(5), pp.1647-1662.
[18] Abbas, T., Bhatti, M.M. and Ayub, M., 2018. Aiding and opposing of mixed convection Casson nanofluid flow with chemical reactions through a porous Riga plate. Proceedings of the institution of mechanical engineers, part E: journal of process mechanical engineering, 232(5), pp.519-527.
[19] Iqbal, Z., Azhar, E., Mehmood, Z. and Maraj, E.N., 2018. Unique outcomes of internal heat generation and thermal deposition on viscous dissipative transport of viscoplastic fluid over a Riga-plate. Communications in Theoretical Physics, 69(1), p.68-76.
[20] Nayak, M.K., Shaw, S., Makinde, O.D. and Chamkha, A.J., 2018. Effects of homogenous–heterogeneous reactions on radiative NaCl-CNP nanofluid flow past a convectively heated vertical Riga plate. Journal of Nanofluids, 7(4), pp.657-667.
[21] Anjum, A., Mir, N.A., Farooq, M., Khan, M.I. and Hayat, T., 2018. Influence of thermal
stratification and slip conditions on stagnation point flow towards variable thicked Riga plate. Results in Physics, 9, pp.1021-1030.
[22] Shaw, S., Nayak, M.K. and Makinde, O.D., 2018. Transient rotational flow of radiative nanofluids over an impermeable Riga plate with variable properties, Defect and Diffusion Forum, 387, pp. 640-652.
[23] Hussain, A., Akbar, S., Sarwar, L., Nadeem, S. and Iqbal, Z., 2019. Effect of time dependent viscosity and radiation efficacy on a non-Newtonian fluid flow. Heliyon, 5(2), p.e01203.
[24] Hakeem, A.A., Saranya, S. and Ganga, B., 2017. Comparative study on Newtonian/non-Newtonian base fluids with magnetic/non-magnetic nanoparticles over a flat plate with uniform heat flux. Journal of Molecular Liquids, 230, pp.445-452.
[25] Rundora, L. and Makinde, O.D., 2018. Unsteady mhd flow of non-newtonian fluid in a channel filled with a saturated porous medium with asymmetric navier slip and convective heating, Applied Mathematics & Information Sciences, 12(3), 483-493, (2018).
[26] Bayareh, M. and Afshar, N., 2020. Forced convective heat transfer of non-Newtonian CMC-based CuO nanofluid in a tube. Journal of Heat and Mass Transfer Research, 7(2), pp.155-163.
[27] Saranya, S., Ragupathi, P., Ganga, B., Sharma, R.P. and Hakeem, A.A., 2018. Non-linear radiation effects on magnetic/non-magnetic nanoparticles with different base fluids over a flat plate. Advanced Powder Technology, 29(9), pp.1977-1990.
[28] Eid, M.R. and Mahny, K.L., 2017. Unsteady MHD heat and mass transfer of a non-Newtonian nanofluid flow of a two-phase model over a permeable stretching wall with heat generation/absorption. Advanced Powder Technology, 28(11), pp.3063-3073.
[29] Durgaprasad, P., Varma, S.V.K., Hoque, M.M. and Raju, C.S.K., 2019. Combined effects of Brownian motion and thermophoresis parameters on three-dimensional (3D) Casson nanofluid flow across the porous layers slendering sheet in a suspension of graphene nanoparticles. Neural Computing and Applications, 31(10), pp.6275-6286.
[30] Raju, C.S., Sandeep, N., Ali, M.E. and Nuhait, A.O., 2019. Heat and mass transfer in 3-D MHD Williamson-Casson fluids flow over a stretching surface with non-uniform heat source/sink. Thermal Science, 23(1), pp.281-293.
60 P. Ragupathi/ JHMTR 8 (2021) 49- 60
[31] Zia, Q.Z., Ullah, I., Waqas, M., Alsaedi, A. and Hayat, T., 2018. Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface. Results in physics, 8, pp.1275-1282.
[32] Prashu and Nandkeolyar, R., 2018. A numerical treatment of unsteady three-dimensional hydromagnetic flow of a Casson fluid with Hall and radiation effects. Results in Physics, 11, pp.966-974.
[33] Muhammad, T., Hayat, T., Shehzad, S.A. and Alsaedi, A., 2018. Viscous dissipation and Joule heating effects in MHD 3D flow with heat and mass fluxes. Results in physics, 8, pp.365-371.
[34] Kumar, K.G., Ramesh, G.K., Gireesha, B.J. and Gorla, R.S.R., 2018. Characteristics of Joule heating and viscous dissipation on three-dimensional flow of Oldroyd B nanofluid with thermal radiation. Alexandria Engineering Journal, 57(3), pp.2139-2149.
[35] Saleem, S., Nadeem, S., Rashidi, M.M. and Raju, C.S.K., 2019. An optimal analysis of radiated nanomaterial flow with viscous dissipation and heat source. Microsystem Technologies, 25(2), pp.683-689.
[36] Nayak, M.K., Shaw, S., Makinde, O.D. and Chamkha, A.J., 2019. Investigation of partial slip and viscous dissipation effects on the radiative tangent hyperbolic nanofluid flow past a vertical permeable Riga plate with internal heating: Bungiorno model. Journal of Nanofluids, 8(1), pp.51-62.
[37] Mahanthesh, B. and Gireesha, B.J., 2018. Scrutinization of thermal radiation, viscous dissipation and Joule heating effects on Marangoni convective two-phase flow of Casson fluid with fluid-particle suspension. Results in physics, 8, pp.869-878.
[38] Upreti, H., Pandey, A.K. and Kumar, M., 2018. MHD flow of Ag-water nanofluid over a flat porous plate with viscous-Ohmic dissipation, suction/injection and heat generation/absorption. Alexandria engineering journal, 57(3), pp.1839-1847.
[39] Hussanan, A., Salleh, M.Z., Khan, I. and Shafie, S., 2018. Analytical solution for suction and injection flow of a viscoplastic Casson fluid past a stretching surface in the presence of viscous dissipation. Neural computing and applications, 29(12), pp.1507-1515.
[40] Ramandevi, B., Reddy, J.R., Sugunamma, V. and Sandeep, N., 2018. Combined influence of viscous dissipation and non-uniform heat source/sink on MHD non-Newtonian fluid flow with Cattaneo-Christov heat flux. Alexandria Engineering Journal, 57(2), pp.1009-1018.
[41] Ghaffarpasand, O., 2018. Characterization of unsteady double-diffusive mixed convection flow with soret and dufour effects in a square enclosure with top moving lid. Journal of Heat and Mass Transfer Research, 5(1), pp.51-68.
[42] Hassanzadeh, R. and Nasrollahzadeh, S., 2020. Heat transfer enhancement in a spiral plate heat exchanger model using continuous rods. Journal of Heat and Mass Transfer Research, 7(1), pp.39-53.
[43] Noghrehabadi, A., Hajidavalloo, E. and Moravej, M., 2016. An experimental investigation of performance of a 3-D solar conical collector at different flow rates. Journal of Heat and Mass Transfer Research, 3(1), pp.57-66.
[44] Wang, C.Y., 1984. The three-dimensional flow due to a stretching flat surface. The physics of fluids, 27(8), pp.1915-1917.
[45] Hayat, T., Shehzad, S.A. and Alsaedi, A., 2013. Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation. Applied Mathematics and Mechanics, 34(7), pp.823-832.
[46] Kumar, K.G., Rudraswamy, N.G. and Gireesha, B.J., 2017. Effects of mass transfer on MHD three dimensional flow of a Prandtl liquid over a flat plate in the presence of chemical reaction. Results in Physics, 7, pp.3465-3471

### History

• Receive Date: 22 August 2020
• Revise Date: 02 December 2020
• Accept Date: 02 December 2020