Unsteady Flow of Casson Fluid between Two Side Walls over an Infinite Plate

Authors

DOI:

https://doi.org/10.33959/cuijca.v6i1.64

Keywords:

Casson fluid, Exact solution, Side walls, Oscillating shear stress

Abstract

In the present study, the velocity field corresponding to the unsteady flow of Casson fluid between two parallel side walls perpendicular to an infinite plate that exerts an oscillating shear stress to the fluid is determined with the help of Fourier sine and cosine transforms. Exact solutions are obtained and given in simple form as a combination of transient and steady-state solutions, which satisfy the governing equation and all imposed initial and boundary conditions. These solutions are reduced to the similar solutions corresponding to the motion over an infinite plate, when and Newtonian fluid by making Casson parameter Furthermore, effect of side walls on the motion of fluid, the time which is required to attain the steady state and the distance between the side walls for which their presence can be ignored are graphically determined.

References

Chaoyang, W. and Chuanjing, T. (1989). Boundary layer flow and heat transfer of non- Newtonian fluid in porous media international jurnal heat and fluid flow 10(5), 160-165.

Qasim, M. (2013). Heat and mass transfer in a Jeffrey fluid over a stretching sheet with heat source/sink. Alexandria Engineering Journal, 52(4), 571-575.

Hayat, T., & Abbas, Z. (2008). Heat transfer analysis on the MHD flow of a second grade fluid in a channel with porous medium. Chaos, Solitons & Fractals, 38(2), 556-567.

Abbas, Z., Sajid, M., & Hayat, T. (2006). MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel. Theoretical and Computational Fluid Dynamics, 20(4), 229-238.

Hassan, M. A., Pathak, M., & Khan, M. K. (2013). Natural convection of viscoplastic fluids in a square enclosure. Journal of Heat Transfer, 135(12), 122501.

Marner, W. (1972). Transient free convection in a Bingham plastic on a vertical flat plate, 25(5), 219-226.

Zakaria, M. N., Abid, H., Khan, I., & Sharidan, S. (2013). The effects of radiation on free convection flow with ramped wall temperature in Brinkman type fluid. Jurnal Teknologi, 62(3), 33-39.

Prasad, V. R., Vasu, B., Anwar, B. O., & Parshad, R. (2011). Unsteady free convection heat and mass transfer in a Walters-B viscoelastic flow past a semi-infinite vertical plate: a numerical study. Thermal Science, 15(suppl. 2), 291-305.

Khan, I., Fakhar, K., & Anwar, M. I. (2012). Hydromagnetic rotating flows of an Oldroyd-B fluid in a porous medium. Special Topics & Reviews in Porous Media: An International Journal, 3(1).

Casson, N. (1959). A Flow Equation for Pigment-Oil Suspensions of the Printing Ink Type. Rheology of Disperse Systems, London, Pergaman Press.

Kataria, H. R., & Patel, H. R. (2016). Soret and heat generation effects on MHD Casson fluid flow past an oscillating vertical plate embedded through porous medium. Alexandria Engineering Journal, 55(3), 2125-2137.

Subba Rao, A., Ramachandra Prasad, V., Bhaskar Reddy, N., & Anwar Bég, O. (2015). Heat Transfer in a Casson Rheological Fluid from a Semi‐infinite Vertical Plate with Partial Slip. Heat Transfer—Asian Research, 44(3), 272-291.

Mustafa, M., Hayat, T., Pop, I., & Aziz, A. (2011). Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate. Heat Transfer—Asian Research, 40(6), 563-576.

Hussanan, A., Salleh, M. Z., Tahar, R. M., & Khan, I. (2014). Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating. PloS one, 9(10), e108763.

Raju, C. S. K., Sandeep, N., & Saleem, S. (2016). Effects of induced magnetic field and homogeneous–heterogeneous reactions on stagnation flow of a Casson fluid. Engineering Science and Technology, an International Journal, 19(2), 875-887.

Bhattacharyya, K. (2013). Boundary Layer Stagnation-Point Flow of Casson Fluid and Heat Transfer towards a Shrinking/Stretching Sheet. Frontiers in Heat and Mass Transfer (FHMT), 4(2).

Bhattacharyya, K., Hayat, T., & Alsaedi, A. (2014). Exact solution for boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 94(6), 522-528.

Khalid, A., Khan, I., Khan, A., & Shafie, S. (2015). Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium. Engineering Science and Technology, an International Journal, 18(3), 309-317.

Makanda, G., Shaw, S., & Sibanda, P. (2015). Effects of Radiation on MHD Free Convection of a Casson Fluid from a Horizontal Circular Cylinder with Partial Slip in Non-Darcy Porous Medium with Viscous Dissipation. Boundary Value Problems, 2015(1), 1-14.

Makanda, G., Shaw, S., & Sibanda, P. (2015). Diffusion of chemically reactive species in Casson fluid flow over an unsteady stretching surface in porous medium in the presence of a magnetic field. Mathematical Problems in Engineering, 2015.

Vieru, D., Fetecau, C., & Fetecau, C. (2008). Flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate. Applied Mathematics and Computation, 200(1), 459-464.

Fetecau, C., Fetecau, C., Kamran, M., and Vieru, D. (2009). Int. J. Non-Newton. Fluid Mech. 156, 189.

Erdoğan, M. E., & İmrak, C. E. (2009). Some effects of side walls on unsteady flow of a viscous fluid over a plane wall. Mathematical Problems in Engineering, 2009.

Fetecau, C., Rana, M., & Fetecau, C. (2013). Radiative and porous effects on free convection flow near a vertical plate that applies shear stress to the fluid. Zeitschrift für Naturforschung A, 68(1-2), 130-138.

Yao, Y., & Liu, Y. (2010). Some unsteady flows of a second grade fluid over a plane wall. Nonlinear Analysis: Real World Applications, 11(5), 4442-4450.

Vieru, D., Fetecau, C., & Sohail, A. (2011). Flow due to a plate that applies an accelerated shear to a second grade fluid between two parallel walls perpendicular to the plate. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 62(1), 161-172.

Fetecau, C., Fetecau, C., & 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), 753-759.

Vieru, D., Fetecau, C., & Rana, M. (2012, May). Starting solutions for the flow of second grade fluids in a rectangular channel due to an oscillating shear stress. In E. T. Baskoro, & D. Suprijanto (Eds.), AIP Conference Proceedings (Vol. 1450, No. 1, pp. 45-54). AIP.

Shahid, N., Rana, M., & Imran, M. A. (2011). Flow of an Oldroyd-B fluid over an infinite plate subject to a time-dependent shear stress. Journal of Prime Research in Mathematics, 7, 52-62.

Sohail, A., Vieru, D., & Imran, M. A. (2013). Influence of side walls on the oscillating motion of a Maxwell fluid over an infinite plate. Mechanics, 19(3), 269-276.

Nadeem, S., Haq, R. U., & Lee, C. (2012). MHD flow of a Casson fluid over an exponentially shrinking sheet. Scientia Iranica, 19(6), 1550-1553.

Sneddon, I. N., & Transforms, F. (1951). McGraw Hill Book Co. Inc., New York.

Sneddon I. N. (1955). Functional Analysis, Encyclopedia of Physics, Springer, Berlin.

Fetecau, C., Vieru, D., & Fetecau, C. (2011). Effect of Side Walls on the Motion of a Viscous Fluid Induced by an Infinite Plate that Applies an Oscillating Shear Stress to the Fluid. Open Physics, 9(3), 816-824.

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Published

2023-12-12

How to Cite

Ali, M. (2023). Unsteady Flow of Casson Fluid between Two Side Walls over an Infinite Plate. City University International Journal of Computational Analysis, 6(1), 30–40. https://doi.org/10.33959/cuijca.v6i1.64

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