Stoke's First Problem for Casson Fluid between two Side Walls over an Infinite Plate
DOI:
https://doi.org/10.33959/cuijca.v6i1.67Keywords:
Side walls, Stokes first problem, Casson fluid, Exact solutionsAbstract
In this article, the unsteady flow of Casson fluid between two side walls normal to the plate is studied by using Fourier finite and infinite sine transforms technique. The bottom plate subjected to impulsive motion to the fluid at time Exact solutions have been established, which satisfy the governing equation and appropriate boundary and initial conditions. The obtained results are reduce to those solutions consequent to the flow over an infinite plate, when and Newtonian fluid by making Casson parameter Keeping in view the measure velocity value and shear stress in the middle of channel, being not to be affected due to side walls, the required time to attain the steady-state and the distance between the side walls in such conditions is calculated graphically.References
Erdogan, M. E. (2000). A note on an unsteady flow of a viscous fluid due to an oscillating plane wall. International Journal of Non-Linear Mechanics, 35(1), 1-6.
Zeng, Y., & Weinbaum, S. (1995). Stokes problems for moving half-planes. Journal of Fluid Mechanics, 287, 59-74.
Fetecau, C., Vieru, D., & Fetecau, C. (2008). A note on the second problem of Stokes for Newtonian fluids. International Journal of Non-Linear Mechanics, 43(5), 451-457.
Erdoğan, M. E., & İmrak, C. E. (2009). On the comparison of the solutions obtained by using two different transform methods for the second problem of Stokes for Newtonian fluids. International Journal of Non-Linear Mechanics, 44(1), 27-30.
Puri, P., & Kulshrestha, P. K. (1976). Unsteady hydromagnetic boundary layer in a rotating medium. Journal of Applied Mechanics, 43(2), 205-208.
Sulochana, P. (2014). Hall Effects on Unsteady MHD Three Dimensional Flow through a Porous Medium in a Rotating Parallel Plate Channel with Effect of Inclined Magnetic Field. American Journal of Computational Mathematics, 4(05), 396.
Rajagopal, K. R. (1982). A note on unsteady unidirectional flows of a non-Newtonian fluid. International Journal of Non-Linear Mechanics, 17(5), 369-373.
Erdoğan, M. E. (1995). Plane surface suddenly set in motion in a non-Newtonian fluid. Acta Mechanica, 108(1-4), 179-187.
Erdogan, M. E. (2003). On unsteady motions of a second-order fluid over a plane wall. International Journal of Non-Linear Mechanics, 38(7), 1045-1051.
Bandelli, R., Rajagopal, K. R., & Galdi, G. P. (1995). On some unsteady motions of fluids of
second grade.
Fetecău, C., & Zierep, J. (2001). On a class of exact solutions of the equations of motion of a second grade fluid. Acta Mechanica, 150(1-2), 135-138.
Fetecău, C., & Fetecău, C. (2002). The Rayleigh--Stokes problem for heated second grade fluids. International Journal of Non-Linear Mechanics, 37(6), 1011-1015.
Erdogan, M. E. (1998). Effects of the side walls in generalized Couette flow. Applied Mechanics and Engineering, 3(2), 271-286.
Erdoğan, M. E. (2004). Effect of the side walls on the unsteady flow in A duct of rectangular cross-section. Mathematical and Computational Applications, 9(3), 443-448.
Erdoğan, M. E., & İmrak, C. E. (2005). Effects of the side walls on starting flows in ducts. International Journal of Non-Linear Mechanics, 40(1), 103-111.
Erdoğan, M. E., & Imrak, C. E. (2007). The effects of the side walls on the flow of a second grade fluid in ducts with suction and injection. International Journal of Non-Linear Mechanics, 42(5), 765-772.
Casson, N. (1959). A Flow Equation for Pigment-Oil Suspensions of the Printing Ink Type. Rheology of Disperse Systems, London, Pergaman Press.
Dash, R. K., Mehta, K. N., & Jayaraman, G. (1996). Casson Fluid Flow in a Pipe Filled with a Homogeneous Porous Medium. International Journal of Engineering Science, 34(10), 1145-1156.
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.
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.
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.
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.
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.
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.
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.
Mabood, F., Shateyi, S., & Khan, W. A. (2015). Effects of Thermal Radiation on Casson Flow Heat and Mass Transfer around a Circular Cylinder in Porous Medium. The European Physical Journal Plus, 130(9), 1-12.
Mohyud-Din, S. T., & Khan, S. I. (2016). Nonlinear radiation effects on squeezing flow of a Casson fluid between parallel disks. Aerospace Science and Technology, 48, 186-192.
Pramanik, S. (2014). Casson Fluid Flow and Heat Transfer Past an Exponentially Porous Stretching Surface in Presence of Thermal Radiation. Ain Shams Engineering Journal, 5(1), 205-212.
Khan, U., Ahmed, N., Khan, S. I. U., Bano, S., & Mohyud-din, S. T. (2014). Unsteady squeezing flow of Casson fluid between parallel plates. World J. Model. Simul, 10(4), 308-319.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Munsif Ali
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
You are free to:
Share - copy and redistribute the material in any medium or format
Adapt - remix, transform, and build upon the material
The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
Attribution - You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
Non Commercial - You may not use the material for commercial purposes.
No additional restrictions - You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
_.jpg)
