Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

doi:10.1007/s10483-012-1624-6

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (10): 1313-1328.doi: https://doi.org/10.1007/s10483-012-1624-6

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

O. U. MEHMOOD, N. MUSTAPHA, S. SHAFIE

Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bharu, Malaysia

收稿日期:2011-09-22 修回日期:2012-05-04 出版日期:2012-10-10 发布日期:2012-10-10
通讯作者: N. MUSTAPHA, Ph.D., E-mail: norzieha@utm.my E-mail: norzieha@utm.my
基金资助:
Project supported by the Ministry of Higher Education (MOHE) and the Research Management Centre, UTM (Nos. 03J54, 78528, and 4F109)

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

O. U. MEHMOOD, N. MUSTAPHA, S. SHAFIE

Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bharu, Malaysia

Received:2011-09-22 Revised:2012-05-04 Online:2012-10-10 Published:2012-10-10
Supported by:
Project supported by the Ministry of Higher Education (MOHE) and the Research Management Centre, UTM (Nos. 03J54, 78528, and 4F109)

摘要/Abstract

摘要：

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic (MHD) fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.

关键词: peristaltic flow, shallow shell, nonlinear-stability, singular perturbation solutions, inclined channel, heat transfer, fourth grade fluid, slip condition

Abstract:

Key words: fourth grade fluid, inclined channel, heat transfer, shallow shell, nonlinear-stability, singular perturbation solutions, slip condition, peristaltic flow

中图分类号:

O. U. MEHMOOD;N. MUSTAPHA;S. SHAFIE. Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1313-1328.

参考文献

[1] Guyton, G. C. Text Book of Medical Physiology, Saunders, Philadelphia (1986)
[2] Shapiro, A. H., Jaffrin, M. Y., and Weinberg, S. L. Peristaltic pumping with long wavelength atlow Reynolds number. Journal of Fluid Mechanics, 37, 799-825 (1969)
[3] Fung, Y. C. and Yih, C. S. Peristaltic transport. Journal of Applied Mechanics, 33, 669-675(1968)
[4] Mekheimer, K. S. and Elmaboud, Y. A. The influence of heat transfer and magnetic field onperistaltic transport of a Newtonian fluid in a vertical annulus: application of an endoscope.Physics Letters A, 372, 1657-1665 (2008)
[5] Ebaid, A. Effects of magnetic field and wall slip conditions on the peristaltic transport of aNewtonian fluid in an asymmetric channel. Physics Letters A, 372, 4493-4499 (2008)
[6] Kothandapani, M. and Srinivas, S. Non-linear peristaltic transport of a Newtonian fluid in aninclined asymmetric channel through a porous medium. Physics Letters A, 372, 1265-1276 (2008)
[7] Joseph, D. D. Fluid Dynamics of Viscoelastic Fluids, Springer-Verlag, Berlin (1980)
[8] Pandey, S. K. and Tripathi, D. Unsteady peristaltic transport of Maxwell fluid through finitelength tube: application to oesophageal swallowing. Applied Mathematics and Mechanics (EnglishEdition), 33(1), 15-24 (2012) DOI 10.1007/s10483-012-1530-9
[9] Misra, J. C. and Maiti, S. Peristaltic transport of rheological fluid: model for movement of foodbolus through esophagus. Applied Mathematics and Mechanics (English Edition), 33(3), 315-332(2012) DOI 10.1007/s10483-012-1552-7
[10] Mehmood, O. U., Shafie, S., and Mustapha, N. Peristaltic transport of Walter’s B fluid in anasymmetric channel. International Journal of Applied Mathematics and Mechanics, 7, 1-19 (2011)
[11] Haroun, M. H. Effect of Deborah number and phase difference on peristaltic transport of a third-order fluid in an asymmetric channel. Communications in Nonlinear Science and Numerical Simulation, 8, 1464-1480 (2007)
[12] Wang, Y., Hayat, T., and Hutter, K. Peristaltic flow of a Johnson-Segalman fluid through adeformable tube. Theoretical and Computational Fluid Dynamics, 21, 369-380 (2007)
[13] Nadeem, S., Akbar, N. S., Hayat, T., and Hendi, A. A. Peristaltic flow of Walter’s B fluid inendoscope. Applied Mathematics and Mechanics (English Edition), 32(6), 689-700 (2011) DOI10.1007/s10483-011-1449-7
[14] El-Hakeem, A., Naby, A., and El-Shamy, I. I. E. Slip effects on peristaltic transport of power-lawfluid through an inclined tube. Applied Mathematical Sciences, 1, 2967-2980 (2007)
[15] Hayat, T., Qureshi, M. U., and Ali, N. The influence of slip on the peristaltic motion of a thirdorder fluid in an asymmetric channel. Physics Letters A, 372, 2653-2664 (2008)
[16] Ali, N., Wang, Y., Hayat, T., and Oberlack, M. Slip effects on the peristaltic flow of a third gradefluid in a circular cylindrical tube. ASME Journal of Applied Mechanics, 76, 1-10 (2009)
[17] Hayat, T. and Hina, S. Effects of heat and mass transfer on peristaltic flow of Williamson fluidin a non-uniform channel with slip conditions. International Journal for Numerical Methods inFluids, 67, 1590-1604 (2011)
[18] Ali, N., Sajid, M., Javed, T., and Abbas, Z. Heat transfer analysis of peristaltic flow in a curvedchannel. International Journal of Heat and Mass Transfer, 53, 3319-3325 (2010)
[19] Hayat, T. and Hina, S. The influence of wall properties on the MHD peristaltic flow of a Maxwellfluid with heat and mass transfer. Nonlinear Analysis: Real World Applications, 11, 3155-3169(2010)
[20] Hayat, T. and Mehmood, O. U. Slip effects on MHD flow of third order fluid in a planar channel.Communications in Nonlinear Science and Numerical Simulation, 16, 1363-1377 (2011)
[21] Nadeem, S. and Akbar, N. S. Influence of heat transfer on peristaltic transport of a Johnson-Segalman fluid in an inclined asymmetric channel. Communications in Nonlinear Science andNumerical Simulation, 15, 2860-2877 (2010)
[22] Nadeem, S. and Akbar, N. S. Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel. Applied Mathematics and Mechanics (EnglishEdition), 31(8), 969-978 (2010) DOI 10.1007/s10483-010-1332-6
[23] Nadeem, S. and Akbar, N. S. Influence of heat and mass transfer on the peristaltic flow of aJohnson-Segalman fluid in a vertical asymmetric channel with induced MHD. Journal of theTaiwan Institute of Chemical Engineers, 42, 58-66 (2011)
[24] Akbar, N. S., Hayat, T., Nadeem, S., and Hendi, A. A. Effects of slip and heat transfer on theperistaltic flow of a third order fluid in an inclined asymmetric channel. International Journal ofHeat and Mass Transfer, 54, 1654-1664 (2011)
[25] Akbar, N. S., Nadeem, S., Hayat, T., and Hendi, A. A. Effects of heat and mass transfer on theperistaltic flow of hyperbolic tangent fluid in an annulus. International Journal of Heat and MassTransfer, 54, 4360-4369 (2011)
[26] Hayat, T., Khan, M., Siddiqui, A. M., and Asghar, S. Non-linear peristaltic flow of a non-Newtonian fluid under effect of a magnetic field in a planar channel. Communications in NonlinearScience and Numerical Simulation, 12, 910-919 (2007)
[27] Hayat, T. and Noreen, S. Peristaltic transport of fourth grade fluid with heat transfer and inducedmagnetic field. Comptes Rendus Mecanique, 338, 518-528 (2010)
[28] Haroun, M. H. Non-linear peristaltic flow of a fourth grade fluid in an inclined asymmetric channel.Computational Materials Science, 39, 324-333 (2007)
[29] Hayat, T., Asghar, Z., Asghar, S., and Mesloub, S. Influence of inclined magnetic field on peri-staltic transport of fourth grade fluid in an inclined asymmetric channel. Journal of the TaiwanInstitute of Chemical Engineers, 41, 553-563 (2010)

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	N. HUMNEKAR, D. SRINIVASACHARYA. Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(3): 563-580.
[2]	S. I. ABDELSALAM, A. Z. ZAHER. Biomimetic amelioration of zirconium nanoparticles on a rigid substrate over viscous slime—a physiological approach[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1563-1576.
[3]	Fanming CAI, Zhaomiao LIU, Nan ZHENG, Yanlin REN, Yan PANG. Lattice Boltzmann simulation of the effects of cavity structures and heater thermal conductivity on nucleate boiling heat transfer[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 981-996.
[4]	Qingkai ZHAO, Longbin TAO, Hang XU. Analysis of periodic pulsating nanofluid flow and heat transfer through a parallel-plate channel in the presence of magnetic field[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(11): 1957-1972.
[5]	Hua WU, Xinyi LI, Yajun YU, Zichen DENG. A novel electron-phonon coupling thermoelasticity with Burgers electronic heat transfer[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(11): 1927-1940.
[6]	Hang XU. Mixed convective flow of a hybrid nanofluid between two parallel inclined plates under wall-slip condition[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(1): 113-126.
[7]	Tianyong YANG, Bofu WANG, Jianzhao WU, Zhiming LU, Quan ZHOU. Horizontal convection in a rectangular enclosure driven by a linear temperature profile[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(8): 1183-1190.
[8]	Yanlin REN, Zhaomiao LIU, Yan PANG, Xiang WANG, Yuandi XU. Lattice Boltzmann simulation of phase change and heat transfer characteristics in the multi-layer deposition[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(4): 553-566.
[9]	A. ROJA, B. J. GIREESHA, B. NAGARAJA. Irreversibility investigation of Casson fluid flow in an inclined channel subject to a Darcy-Forchheimer porous medium: a numerical study[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(1): 95-108.
[10]	C. REVNIC, T. GROŞAN, M. SHEREMET, I. POP. Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al₂O₃-water nanofluid with discrete heating[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(9): 1345-1358.
[11]	A. SALEEM, M. N. KIANI, S. NADEEM, A. ISSAKHOV. Heat transfer and Helmholtz-Smoluchowski velocity in Bingham fluid flow[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(8): 1167-1178.
[12]	T. HAYAT, F. HAIDER, T. MUHAMMAD, A. ALSAEDI. Darcy-Forchheimer flow by rotating disk with partial slip[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(5): 741-752.
[13]	Yingli SHI, Junyun JI, Yafei YIN, Yuhang LI, Yufeng XING. Analytical transient phase change heat transfer model of wearable electronics with a thermal protection substrate[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(11): 1599-1610.
[14]	T. G. FANG, F. J. WANG. Momentum and heat transfer of a special case of the unsteady stagnation-point flow[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 51-82.
[15]	H. SADAF. Bio-fluid flow analysis based on heat transfer and variable viscosity[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(7): 1029-1040.