Heat and Mass Transfer on Non-Newtonian Peristaltic Flow in a Channel in Presence of Magnetic Field: Analytical and Numerical Analysis
- 1 Department of Mathematics, Comilla University, Comilla, Bangladesh
- 2 Department of Mathematics, Comilla University, Comilla, Bangladesh
- 3 Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
Abstract
A study has been arranged to investigate the flow of non-Newtonian fluid in a vertical asymmetrical channel using peristalsis. The porous medium allows the electrically conductive fluid to flow in the channel, while a uniform magnetic field is applied perpendicular to the flow direction. The analysis takes into account the combined influence of heat and mass transfer, including the effects of Soret and Dufour. The flow’s non-Newtonian behavior is characterized using a Casson rheological model. The fluid flow equations are examined within a wave frame of reference that has a wave velocity. The analytic solution is examined using long wavelengths and a small Reynolds number assumption. The stream function, temperature, concentration and heat transfer coefficient expressions are derived. The bvp4c function from MATLAB has been used to numerically solve the transformed equations. The flow characteristics have been analyzed using graphs to demonstrate the impacts of different parameters.
- Bayliss, W.M. and Starling, E.H. (1899) The Movements and Innervation of the Small Intestine. The Journal of Physiology , 24, 99-143. https://doi.org/10.1113/jphysiol.1899.sp000752
- Fetecau, C., Awan, A.U. and Fetecau, C. (2009) Taylor-Couette Flow of an Oldroyd-B Fluid in a Circular Cylinder Subject to a Time-Dependent Rotation. Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie , 52, 117-128.
- Siddiqui, A.M., Hameed, M., Siddiqui, B.M. and Ghori, Q.K. (2010) Use of Adomian Decomposition Method in the Study of Parallel Plate Flow of a Third Grade Fluid. Communications in Nonlinear Science and Numerical Simulation , 15, 2388-2399. https://doi.org/10.1016/j.cnsns.2009.05.073
- Khan, M., Maqbool, K. and Hayat, T. (2006) Influence of Hall Current on the Flows of a Generalized Oldroyd-B Fluid in a Porous Space. Acta Mechanica , 184, 1-13. https://doi.org/10.1007/s00707-006-0326-7
- Siddiqui, A.M., Hameed, M., Siddiqui, B.M. and Babcock, B.S. (2012) Adomian De-Composition Method Applied to Study Nonlinear Equations Arising in Non-Newtonian Flows. Applied Mathematical Sciences , 6, 4889-4909.
- Naz, R., Mahomed, F.M. and Mason, D.P. (2008) Comparison of Different Approaches to Conservation Laws for Some Partial Differential Equations in Fluid Mechanics. Applied Mathematics and Computation , 205, 212-230. https://doi.org/10.1016/j.amc.2008.06.042
- Khalique, C.M. and Mahomed, F.M. (2009) Soil Water Redistribution and Extraction Flow Models: Conservation Laws. Nonlinear Analysis : Real World Applications , 10, 2021-2025. https://doi.org/10.1016/j.nonrwa.2008.03.008
- Mekheimer, K.S., Husseny, S.Z. and Abd El Lateef, A.I. (2011) Effect of Lateral Walls on Peristaltic Flow through an Asymmetric Rectangular Duct. Applied Bionics and Biomechanics , 8, 295-308. https://doi.org/10.1155/2011/424183
- Akram, S., Mekheimer, K.S. and Nadeem, S. (2014) Influence of Lateral Walls on Peristaltic Flow of a Couple Stress Fluid in a Non-Uniform Rectangular Duct. Applied Mathematics & Information Sciences , 8, 1127-1133. https://doi.org/10.12785/amis/080323
- Yin, F. and Fung, Y.C. (1969) Peristaltic Waves in Circular Cylindrical Tubes. Journal of Applied Mechanics , 36, 579-587. https://doi.org/10.1115/1.3564720
- Casson, N. (1959) Rheology of Disperse Systems. Pergamon Press, 84.
- Blair, S.G.W. and Spanner, D.C. (1974) Introduction to Biorheology by GW Scott Blair, Chapter XII on Botanical Aspects by DC Spanner.