Skip to main content
SpringerLink
Log in

Transient analysis of Casson fluid thermo-convection from a vertical cylinder embedded in a porous medium: Entropy generation and thermal energy transfer visualization

多孔介质中垂直圆柱内 Casson 流体热对流的瞬态分析: 熵产和热能转移可视化

  • Article
  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

Thermal transport in porous media has stimulated substantial interest in engineering sciences due to increasing applications in filtration systems, porous bearings, porous layer insulation, biomechanics, geomechanics etc. Motivated by such applications, in this article, a numerical study of entropy generation impacts on the heat and momentum transfer in time-dependent laminar incompressible boundary layer flow of a Casson viscoplastic fluid over a uniformly heated vertical cylinder embedded in a porous medium is presented. Darcy’s law is used to simulate bulk drag effects at low Reynolds number for an isotropic, homogenous porous medium. Heat line visualization is also included. The mathematical model is derived and normalized using appropriate transformation variables. The resulting non-linear time-dependent coupled governing equations with associated boundary conditions are solved via an implicit finite difference method which is efficient and unconditionally stable. The outcomes show that entropy generation and Bejan number are both elevated with increasing values of Darcy number, Casson fluid parameter, group parameter and Grashof number. To analyze the heat transfer process in a two-dimensional domain, plotting heat lines provides an excellent approach in addition to streamlines and isotherms. It is remarked that as the Darcy number increases, the deviations of heat lines from the hot wall are reduced.

摘要

随着多孔介质在过滤系统、多孔轴承、多孔隔热层、生物力学、地质力学等方面的应用日益广 泛, 多孔介质中的热传输引起了工程科学领域的广泛兴趣。基于上述应用, 本文就熵产对 Casson 黏 塑性流体在多孔介质中均匀加热垂直圆柱上的分层不可压缩边界层流动中传热和动量传递的影响进 行了数值研究。采用 Darcy 定律模拟了各向同性均质多孔介质在低 Reynolds 数时的体阻力效应, 并进 行热线可视化。利用适当的变换变量, 推导了数学模型并进行归一化。利用隐式有限差分法求解了具 有相关边界条件的非线性时变耦合控制方程, 该方法有效且无条件稳定。结果表明, 随着 Darcy 数、 Casson 流体参数、群参数和 Grashof 数的增大, 熵产和 Bejan 数均增大。除了流线和等温线外, 绘制 热线为分析二维区域内的传热过程提供了一种很好的方法。结果表明, 随着Darcy 数的增加, 热壁之 间的传热线偏差减小。

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. SPARROW E M, GREGG J L. Laminar free convection heat transfer from the outer surface of a vertical circular cylinder [J]. ASME Journal of Heat Transfer, 1956, 78(8): 1823–1829.

    Google Scholar 

  2. LEE H R, CHEN T S, ARMALY B F. Natural convection along slender vertical cylinders with variable surface temperature [J]. ASME Journal of Heat Transfer, 1988, 110: 103–108.

    Article  Google Scholar 

  3. MAKANDA G, SHAW S, SIBANDA P. Diffusion of chemically reactive species in Casson fluid flow over an unsteady stretching surface in porous medium in the presence of a magnetic field [J]. Mathematical Problems in Engineering, 2015: Article ID 724596.

    Google Scholar 

  4. DASH R K, MEHTA K N, JAYARAMAN G. Casson fluid flow in a pipe filled with a homogeneous porous medium [J]. International Journal of Engineering Science, 1996, 34: 1145–1156.

    Article  MATH  Google Scholar 

  5. CASSON N. A flow equation for pigment oil suspensions of the printing ink type [M]// Rheology of Disperse Systems. Oxford: Pergamon Press, 1956: 84–102.

    Google Scholar 

  6. ABBAS Z, SHEIKH M, MOTSA S S. Numerical solution of binary chemical reaction on stagnation point flow of Casson fluid over a stretching/shrinking sheet with thermal radiation [J]. Energy, 2016, 95: 12–20.

    Article  Google Scholar 

  7. MUSTAFA M, HAYAT T, POP I, HENDI A. Stagnationpoint flow and heat transfer of a Casson fluid towards a stretching sheet [J]. Zeitschrift für Naturforschung A, 2012, 67: 70–76.

    Article  Google Scholar 

  8. MYTHILI D, SIVARAJ R. Influence of higher order chemical reaction and non-uniform heat source/sink on Casson fluid flow over a vertical cone and flat plate [J]. Journal of Molecular Liquids, 2016, 216: 466–475.

    Article  Google Scholar 

  9. DAS M, MAHATO R, NANDKEOLYAR R. Newtonian heating effect on unsteady hydromagnetic Casson fluid flow past a flat plate with heat and mass transfer [J]. Alexandria Engineering Journal, 2015, 54: 871–879.

    Article  Google Scholar 

  10. NADEEM S, HAQ R U, LEE C. Magnetohydrodynamic flow of a Casson fluid over an exponentially shrinking sheet [J]. Scientia Iranica, 2012, 19: 1550–1553.

    Article  Google Scholar 

  11. RAJU C S K, SANDEEP N, SUGUNAMMA V, BABU M J, REDDY J R. Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface [J]. Engineering Science and Technology, 2016, 19: 45–52.

    Google Scholar 

  12. GIANGASPERO G, SCIUBBA E. Application of the entropy generation minimization method to a solar heat exchanger: A pseudo-optimization design process based on the analysis of the local entropy generation maps [J]. Energy, 2013, 58: 52–65.

    Article  Google Scholar 

  13. BADESCU V. Optimal paths for minimizing lost available work during usual heat transfer processes [J]. Journal of Non-Equilibrium Thermodynamics, 2004, 29: 53–73.

    Article  MATH  Google Scholar 

  14. KOCKUM H, JERNQVIST A. Entropy generation in multifield flows: Equations and Examples of Applications [J]. Chemical Engineering Research and Design, 1998, 76: 210–222.

    Article  Google Scholar 

  15. BEJAN A. A study of entropy generation in fundamental convective heat transfer [J]. ASME Journal of Heat Transfer, 1979, 101: 718–725.

    Article  Google Scholar 

  16. BEJAN A. Second law analysis in heat transfer [J]. Energy, 1980, 5: 720–732.

    Article  Google Scholar 

  17. BEJAN A. Second law analysis in heat transfer and thermal design [J]. Advances in Heat Transfer, 1982, 15: 1–58.

    Article  Google Scholar 

  18. MAHIAN O, OZTOP H, POP I, MAHMUD S, WONGWISES S. Entropy generation between two vertical cylinders in the presence of MHD flow subjected to constant wall temperature [J]. International Communications Heat and Mass Transfer, 2013, 44: 87–92.

    Article  Google Scholar 

  19. MIRZAZADEH M, SHAFAEI A, RASHIDI F. Entropy analysis for non-linear viscoelastic fluid in concentric rotating cylinders [J]. International Journal of Thermal Science, 2008, 47: 1701–1711.

    Article  Google Scholar 

  20. MAHIAN O, MAHMUD S, HERIS SZ. Analysis of entropy generation between co-rotating cylinders using nanofluid [J]. Energy, 2012, 44: 438–446.

    Article  Google Scholar 

  21. BASSAM A K ABU-H, WALEED N H. Entropy generation due to laminar natural convection over a heated rotating cylinder [J]. International Journal of Heat and Mass Transfer, 1999, 42: 4225–4233.

    Article  MATH  Google Scholar 

  22. JIA Q, MUHAMMAD M B, MUNAWWAR A A, MOHAMMAD M R, MOHAMED EL-S A. Entropy generation on MHD Casson nano fluid flow over a porous stretching/shrinking surface [J]. Entropy, 2016, 18(4): 1–14.

    Google Scholar 

  23. ASMA K, ILYAS K, ARSHAD K, SHARIDAN S. Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium [J]. Engineering Science and Technology, 2015, 18(3): 309–317.

    Google Scholar 

  24. RAMACHANDRA P V, SUBBA R A, ANWAR B O. Flow and heat transfer of Casson fluid from a horizontal circular cylinder with partial slip in non-Darcy porous medium [J]. Journal of Applied & Computational Mathematics, 2013, 2(2): 1–12.

    Google Scholar 

  25. HARI R, KATARIA, HARSHAD R P. Radiation and chemical reaction effects on MHD Casson fluid flow past an oscillating vertical plate embedded in porous medium [J]. Alexandria Engineering Journal, 2016, 55: 583–595.

    Article  Google Scholar 

  26. KIMURA S, BEJAN A. The heatline visualization of convective heat transfer [J]. ASME Journal of Heat Transfer, 1983, 105: 916–919.

    Article  Google Scholar 

  27. BEJAN A. Convection heat transfer [M]. New York: John Wiley and Sons, 1984.

    MATH  Google Scholar 

  28. RANI H P, REDDY G J. Heatline visualization for conjugate heat transfer of a couple stress fluid from a vertical slender hollow cylinder [J]. International Communications in Heat and Mass Transfer, 2013, 48: 46–52.

    Article  Google Scholar 

  29. RANI H P, REDDY G J, KIM C N, RAMESHWAR Y. Transient couple stress fluid past a vertical cylinder with Bejan's heat and mass flow visualization for steady state [J]. ASME Journal of Heat Transfer, 2015, 137: 032501.

    Article  Google Scholar 

  30. MOREGA A. The heat function approach to the thermomagnetic convection of electroconductive melts [J]. Revue Roumaine des Sci Tech. Electrot et Energ, 1998, 33: 359–368.

    Google Scholar 

  31. MABOOD F, ABDEL-RAHMAN R G, LORENZINI G. Effect of melting heat transfer and thermal radiation on Casson fluid flow in porous medium over moving surface with magnetohydrodynamics [J]. Journal of Engineering Thermophysics, 2016, 25: 536–547.

    Article  Google Scholar 

  32. RANI H P, JANARDHANA R G, KIM C N. Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder [J]. Applied Mathematics and Mechanics (English Edition), 2013, 34: 985–1000.

    Article  MathSciNet  Google Scholar 

  33. QING J, BHATTI M M, ABBAS M A, RASHIDI M M, ALI M EL-S. Entropy generation on MHD Casson nanofluid flow over a porous stretching/shrinking surface [J]. Entropy, 2016, 18: 1–24.

    Article  Google Scholar 

  34. BUTT A S, ALI A, MEHMOOD A. Numerical investigation of magnetic field effects on entropy generation in viscous flow over a stretching cylinder embedded in a porous medium [J]. Energy, 2016, 99: 237–249.

    Article  Google Scholar 

  35. MAHDAVI M, SAFFAR- AVVAL M, TIARI S, MANSOORI S. Entropy generation and heat transfer numerical analysis in pipes partially filled with porous medium [J]. International Journal of Heat and Mass Transfer, 2014, 79: 496–506.

    Article  Google Scholar 

  36. BEJAN A. Entropy Generation Minimization [M]. New York, USA: CRC Press, 1996.

    MATH  Google Scholar 

  37. REDDY G J, KUMAR M, KETHIREDDY B, CHAMKHA A J. Colloidal study of unsteady magnetohydrodynamic couple stress fluid flow over an isothermal vertical flat plate with entropy heat generation [J]. Journal of Molecular Liquids, 2018, 252: 169–179.

    Article  Google Scholar 

  38. REDDY G J, HIREMATH A, KUMAR M. Computational modeling of unsteady third-grade fluid flow over a vertical cylinder: A study of heat transfer visualization [J]. Results in Physics, 2018, 8: 671–682.

    Article  Google Scholar 

  39. REDDY G J, KETHIREDDY B, KUMAR M, RANI H P, GORLA R S. Effect of Prandtl number for Casson fluid flow over a vertical cylinder: Heatline approach [J]. International Journal of Applied and Computational Mathe matics 2018, 4: 1–19.

    MathSciNet  MATH  Google Scholar 

  40. SHEHZAD S A, HAYAT T, ALSAEDI A. Three-dimensional MHD flow of Casson fluid in porous medium with heat generation [J]. Journal of Applied Fluid Mechanics, 2016, 9: 215–223.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Central University of Karnataka, Kalaburagi, 585367, India

    G. Janardhana Reddy, Kethireddy Bhaskerreddy & Kumar Mahesh

  2. Fluid Mechanics, Aeronautical and Mechanical Engineering Department, School of Computing, Science and Engineering, University of Salford, Manchester, M54WT, UK

    O. Anwar Bég

Authors
  1. G. Janardhana Reddy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kethireddy Bhaskerreddy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kumar Mahesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. O. Anwar Bég
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Janardhana Reddy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Janardhana Reddy, G., Bhaskerreddy, K., Mahesh, K. et al. Transient analysis of Casson fluid thermo-convection from a vertical cylinder embedded in a porous medium: Entropy generation and thermal energy transfer visualization. J. Cent. South Univ. 26, 1342–1361 (2019). https://doi.org/10.1007/s11771-019-4091-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-019-4091-x

Key words

关键词

Search

Navigation