Peristaltic flow of a heated Jeffrey fluid inside an elliptic duct: streamline analysis

doi:10.1007/s10483-021-2714-6

Abstract

Abstract: The peristaltic flow of a heated Jeffrey fluid inside a duct with an elliptic cross-section is studied. A thorough heat transfer mechanism is interpreted by analyzing the viscous effects in the energy equation. The governing mathematical equations give dimensionless partial differential equations after simplification. The final simplified form of the mathematical equations is evaluated with respect to the relevant boundary conditions, and the exact solution is attained. The results are further illustrated by graphs, and the distinct aspects of peristaltic flow phenomena are discussed.

Key words: peristalsis, elliptic duct, Jeffrey fluid, streamline

2010 MSC Number:

S. NADEEM, S. AKHTAR, A. SALEEM. Peristaltic flow of a heated Jeffrey fluid inside an elliptic duct: streamline analysis. Applied Mathematics and Mechanics (English Edition), 2021, 42(4): 583-592.

TrendMD

References

[1] JAFFRIN, M. Y. and SHAPIRO, A. H. Peristaltic pumping. Annual Review of Fluid Mechanics, 3, 13-37(1971)
[2] BARTON, C. and RAYNOR, S. Peristaltic flow in tubes. The Bulletin of Mathematical Biophysics, 30, 663-680(1968)
[3] BÖHME, G. and FRIEDRICH, R. Peristaltic flow of viscoelastic liquids. Journal of Fluid Mechanics, 128, 109-122(1983)
[4] SIDDIQUI, A. M. and SCHWARZ, W. H. Peristaltic flow of a second-order fluid in tubes. Journal of Non-Newtonian Fluid Mechanics, 53, 257-284(1994)
[5] NADEEM, S. and AKRAM, S. Peristaltic flow of a Jeffrey fluid in a rectangular duct. Nonlinear Analysis:Real World Applications, 11, 4238-4247(2010)
[6] AKBAR, N. S. Peristaltic flow of a nanofluid in a diverging tube for Jeffrey fluid. Journal of Computational and Theoretical Nanoscience, 11, 1335-1341(2014)
[7] RASHID, M., ANSAR, K., and NADEEM, S. Effects of induced magnetic field for peristaltic flow of Williamson fluid in a curved channel. Physica A:Statistical Mechanics and Its Applications, 553, 123979(2020)
[8] SALEEM, A., AKHTAR, S., ALHARBI, F. M., NADEEM, S., GHALAMBAZ, M., and ISSAKHOV, A. Physical aspects of peristaltic flow of hybrid nano fluid inside a curved tube having ciliated wall. Results in Physics, 19, 103431(2020)
[9] AKRAM, S. and SALEEM, N. Analysis of heating effects and different wave forms on peristaltic flow of Carreau fluid in rectangular duct. Advances in Mathematical Physics, 2020, 1-14(2020)
[10] NADEEM, S., AKRAM, S., HAYAT, T., and HENDI, A. A. Peristaltic flow of a Carreau fluid in a rectangular duct. Journal of Fluids Engineering, 134, 041201(2012)
[11] BUTT, A. W., AKBAR, N. S., and MIR, N. A. Heat transfer analysis of peristaltic flow of a Phan-Thien-Tanner fluid model due to metachronal wave of cilia. Biomechanics and Modeling in Mechanobiology, 19, 1925-1933(2020)
[12] KHAN, L. A., RAZA, M., MIR, N. A., and ELLAHI, R. Effects of different shapes of nanoparticles on peristaltic flow of MHD nanofluids filled in an asymmetric channel. Journal of Thermal Analysis and Calorimetry, 140, 879-890(2020)
[13] SCHENK, J. and HAN, B. S. Heat transfer from laminar flow in ducts with elliptic cross-section. Applied Scientific Research, 17, 96-114(1967)
[14] DONG, Z. F. and EBADIAN, M. A. A numerical analysis of thermally developing flow in elliptic ducts with internal fins. International Journal of Heat and Fluid Flow, 12, 166-172(1991)
[15] SAKALIS, V. D., HATZIKONSTANTINOU, P. M., and KAFOUSIAS, N. Thermally developing flow in elliptic ducts with axially variable wall temperature distribution. International Journal of Heat and Mass Transfer, 45, 25-35(2002)
[16] SHARIAT, M., AKBARINIA, A., NEZHAD, A. H., BEHZADMEHR, A., and LAUR, R. Numerical study of two phase laminar mixed convection nanofluid in elliptic ducts. Applied Thermal Engineering, 31, 2348-2359(2011)
[17] RAGUEB, H. and MANSOURI, K. A numerical study of viscous dissipation effect on nonNewtonian fluid flow inside elliptical duct. Energy Conversion and Management, 68, 124-132(2013)
[18] SALEEM, A., AKHTAR, S., NADEEM, S., ALHARBI, F. M., GHALAMBAZ, M., and ISSAKHOV, A. Mathematical computations for peristaltic flow of heated non-Newtonian fluid inside a sinusoidal elliptic duct. Physica Scripta, 95, 105009(2020)
[19] ZHANG, L., ARAIN, M. B., BHATTI, M. M., ZEESHAN, A., and HAL-SULAMI, H. Effects of magnetic Reynolds number on swimming of gyrotactic microorganisms between rotating circular plates filled with nanofluids. Applied Mathematics and Mechanics (English Edition), 41(4), 637-654(2020) https://doi.org/10.1007/s10483-020-2599-7
[20] ARAIN, M. B., BHATTI, M. M., ZEESHAN, A., SAEED, T., and HOBINY, A. Analysis of arrhenius kinetics on multiphase flow between a pair of rotating circular plates. Mathematical Problems in Engineering, 2020, 1-7(2020)
[21] BHATTI, M. M. and ABDELSALAM, S. I. Thermodynamic entropy of a magnetized Ree-Eyring particle-fluid motion with irreversibility process:a mathematical paradigm. Zeitschrift für Angewandte Mathematik und Mechanik, e202000186(2020) https://doi.org/10.1002/zamm.202000186
[22] ZHANG, L. J., BHATTI, M. M., MARIN, M., and Mekheimer, K. S. Entropy analysis on the blood flow through anisotropically tapered arteries filled with magnetic zinc-oxide (ZnO) nanoparticles. Entropy, 22, 1070(2020)
[23] AKBAR, N. S. and BUTT, A. W. Heat transfer analysis of viscoelastic fluid flow due to metachronal wave of cilia. International Journal of Biomathematics, 7, 1450066(2014)
[24] YANG, Z. H., CHU, Y. M., and ZHANG, W. Monotonicity of the ratio for the complete elliptic integral and Stolarsky mean. Journal of Inequalities and Applications, 2016, 1-10(2016)