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Falkner-Skan flow analysis for ohmic heated nanofluid toward moving surface with thermal jump

欧姆加热纳米流体中具有热跳现象移动表面的Falkner-Skan 流分析

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Abstract

The analysis upon Falkner-Skan flows under the assumption of boundary layer has attracted more interests due to their widespread applications in the industrial fields and in many engineering processes, such as percolation, thermal pad, heat exchangers, oil bed retrieval, and geothermal analysis. Therefore, this article focuses on the Falkner-Skan hydromagnetic wedge flow of graphene oxide-water nanofluid. The analysis is adopted near the stagnation point. Velocity and thermal slip phenomena are examined in the stretchable wall. Viscous dissipation and ohmic heating impacts are employed in the exploration of heat transport. The problem is computed analytically via homotopy method. The results are illustrated by velocity and heat transport mechanism against relevant parameters. Impacts of Nusselt number and skin friction are mathematically elaborated. The results report that temperature grows by increasing Brinkman number. Further thermal jump decreases the temperature field. Increasing the rates of Hartmann number improves the thickness of thermal field, while increasing Hartmann number contracts the thickness of momentum profile. This research has considerable implications in medical treatment, devices of relatively high-temperature, heat exchangers, mechanical structures, etc.

摘要

边界层假设下的Falkner-Skan流分析因其在渗流、导热垫、热交换器、油层检测和地热分析等 许多工业领域和过程中的广泛应用引起了越来越多的关注。本文主要研究了氧化石墨烯-水纳米流体的 Falkner-Skan 磁楔流。通过对驻点附近进行分析, 研究了可拉伸壁面的速度和热滑现象, 以及黏性耗 散和欧姆加热对热传输的影响。利用同伦算法说明了相关参数与速度和热传输机理的关系, 阐述了 Nusselt 数和表面摩擦因数的影响。结果表明:温度随着Brinkman 数的增长而升高, 进一步的热跳则使 温度场减小;Hartmann 数的增加使热场厚度增大, 动量谱厚度减小。该研究对医疗、高温设施、热交 换器和机械结构有极大意义。

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Abbreviations

u, v :

Velocity components, m/s

U e :

Ambient velocity, m/s

μ nf :

Nanofluid absolute viscosity, kg/(m·s)

ρ nf :

Density of nanofluid, kg/m3

σ nf :

Electric conductivity of nanofluid, A2/(kg·m3·s3)

B :

Magnetic field, kg/(m·s2·A)

k nf :

Nanofluid thermal conductivity, W/(m·K)

τ w :

Shear stress, kg/(m·s2)

β :

Pressure gradient

Pr :

Prandtl number

Ec :

Eckert number

λ :

Velocity ratio parameter

φ :

Nanofluid volume fraction

C f :

Skin friction coefficient

T :

Temperature, K

U w :

Stretching velocity, m/s

(c p)nf :

Nanofluid heat capacity, J/(kg·K)

α nf :

Thermal diffusivity, m2/s

T ∞ :

Ambient temperature, K

T w :

Wall temperature, K

q w :

Heat flux, W/m2

η :

Similarity variable

Ha :

Hartmann number

Br :

Brinkman number

Re :

Reynold number

Nu :

Nusselt number

S 1 :

Velocity slip parameter

S 2 :

Thermal slip parameter

References

  1. DEY D, SAHU D S. A review on the application of the nanofluids [J]. Heat Transfer, 2021, 50(2): 1113–1155. DOI: https://doi.org/10.1002/htj.21920.

    Article  Google Scholar 

  2. CHOI S U, EASTMAN J A. Enhancing thermal conductivity of fluids with nanoparticles [C]//Proceedings of the ASME International Mechanical Engineering Congress and Exposition. New York, USA: ASME, 1995, 66: 99–105.

  3. LI Chun-quan, HUANG Jian, SHANG Yu-ling, et al. Study on the flow and heat dissipation of water-based alumina nanofluids in microchannels [J]. Case Studies in Thermal Engineering, 2020, 22: 100746. DOI: https://doi.org/10.1016/j.csite.2020.100746.

    Article  Google Scholar 

  4. AMAR N, KISHAN N. Viscous dissipation and heat transfer effect on MHD boundary layer flow past a wedge of nano fluid embedded in a porous media [J]. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021, 12(4): 1352–1366. DOI: https://doi.org/10.17762/turcomat.v12i4.1208.

    Article  Google Scholar 

  5. AHMAD S, SHERIFF S, FAROOQ M. Characteristics of modified diffusion analysis of squeezed hydro-magnetic nanofluid flow [J]. Journal of Magnetics, 2021, 26(3): 347–355. DOI:https://doi.org/10.4283/JMAG.2021.26.3.347.

    Article  Google Scholar 

  6. MUNTAZIR R M, MUSHTAQ M, SHAHZADI S, et al. MHD nanofluid flow around a permeable stretching sheet with thermal radiation and viscous dissipation [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2022, 236(1): 137–152. DOI: https://doi.org/10.1177/09544062211023094.

    Google Scholar 

  7. RAMA DEVI S V V, GNANESWARA REDDY M. Parametric analysis of MHD flow of nanofluid in stretching sheet under chemical sensitivity and thermal radiation [J]. Heat Transfer, 2022, 51(1): 948–975. DOI: https://doi.org/10.1002/htj.22337.

    Article  Google Scholar 

  8. ANWAR M S, IRFAN M, HUSSAIN M, et al. Heat transfer in a fractional nanofluid flow through a permeable medium [J]. Mathematical Problems in Engineering, 2022: e3390478. DOI: https://doi.org/10.1155/2022/3390478.

  9. ELBASHBESHY E M A, ASKER H G. Fluid flow over a vertical stretching surface within a porous medium filled by a nanofluid containing gyrotactic microorganisms [J]. The European Physical Journal Plus, 2022, 137(5): 541. DOI: https://doi.org/10.1140/epjp/s13360-022-02682-y.

    Article  Google Scholar 

  10. ALI A, KHAN H S, SALEEM S, et al. EMHD nanofluid flow with radiation and variable heat flux effects along a slandering stretching sheet [J]. Nanomaterials (Basel, Switzerland), 2022, 12(21): 3872. DOI: https://doi.org/10.3390/nano12213872.

    Article  Google Scholar 

  11. WAHID N S, ARIFIN N M, POP I, et al. MHD stagnationpoint flow of nanofluid due to a shrinking sheet with melting, viscous dissipation and Joule heating effects [J]. Alexandria Engineering Journal, 2022, 61(12): 12661–12672. DOI: https://doi.org/10.1016/j.aej.2022.06.041.

    Article  Google Scholar 

  12. HSIAO K L. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet [J]. Applied Thermal Engineering, 2016, 98: 850–861. DOI: https://doi.org/10.1016/j.applthermaleng.2015.12.138.

    Article  Google Scholar 

  13. HSIAO K L. To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-Nanofluid with parameters control method [J]. Energy, 2017, 130: 486–499. DOI: https://doi.org/10.1016/j.energy.2017.05.004.

    Article  Google Scholar 

  14. HSIAO K L. Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects [J]. Applied Thermal Engineering, 2017, 112: 1281–1288. DOI:https://doi.org/10.1016/j.applthermaleng.2016.08.208.

    Article  Google Scholar 

  15. HSIAO K L. Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature [J]. International Journal of Heat and Mass Transfer, 2017, 112: 983–990. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.042.

    Article  Google Scholar 

  16. BALAJI T, SELVAM C, LAL D M, et al. Enhanced heat transport behavior of micro channel heat sink with graphene based nanofluids [J]. International Communications in Heat and Mass Transfer, 2020, 117: 104716. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2020.104716.

    Article  Google Scholar 

  17. MASOOD S, FAROOQ M, AHMAD S. Description of viscous dissipation in magnetohydrodynamic flow of nanofluid: Applications of biomedical treatment [J]. Advances in Mechanical Engineering, 2020, 12(6): 168781402092635. DOI: https://doi.org/10.1177/1687814020926359.

    Article  Google Scholar 

  18. ABD ELAZEM N Y. Numerical results for influence the flow of MHD nanofluids on heat and mass transfer past a stretched surface [J]. Nonlinear Engineering, 2021, 10(1): 28–38. DOI:https://doi.org/10.1515/nleng-2021-000.

    Article  Google Scholar 

  19. BERREHAL H, SOWMYA G, MAKINDE O. Shape effect of nanoparticles on MHD nanofluid flow over a stretching sheet in the presence of heat source/sink with entropy generation [J]. International Journal of Numerical Methods For Heat & Fluid Flow, 2022, 32(5): 1643–1663. DOI: https://doi.org/10.1108/HFF-03-2021-0225.

    Article  Google Scholar 

  20. ANWAR M I, FIRDOUS H, AL ZUBAIDI A, et al. Computational analysis of induced magnetohydrodynamic non-Newtonian nanofluid flow over nonlinear stretching sheet [J]. Progress in Reaction Kinetics and Mechanism, 2022, 47: 146867832110727. DOI: https://doi.org/10.1177/14686783211072712.

    Article  Google Scholar 

  21. ASJAD M I, ZAHID M, JARAD F, et al. Bioconvection flow of MHD viscous nanofluid in the presence of chemical reaction and activation energy [J]. Mathematical Problems in Engineering, 2022: e1707894. DOI: https://doi.org/10.1155/2022/1707894.

  22. SRINIVASACHARYA D, JAGADEESHWAR P. Effect of Joule heating on the flow over an exponentially stretching sheet with convective thermal condition [J]. Mathematical Sciences, 2019, 13(3): 201–211. DOI: https://doi.org/10.1007/s40096-019-0290-8.

    Article  MathSciNet  MATH  Google Scholar 

  23. SWAIN B K, PARIDA B C, KAR S, et al. Viscous dissipation and joule heating effect on MHD flow and heat transfer past a stretching sheet embedded in a porous medium [J]. Heliyon, 2020, 6(10): e05338. DOI: https://doi.org/10.1016/j.heliyon.2020.e05338.

    Article  Google Scholar 

  24. MISHRA A, KUMAR M. Velocity and thermal slip effects on MHD nanofluid flow past a stretching cylinder with viscous dissipation and Joule heating [J]. SN Applied Sciences, 2020, 2(8): 1350. DOI: https://doi.org/10.1007/s42452-020-3156-7.

    Article  Google Scholar 

  25. ZHANG Xiao-hong, ABIDI A, AHMED A E S, et al. MHD stagnation point flow of nanofluid over a curved stretching/shrinking surface subject to the influence of Joule heating and convective condition [J]. Case Studies in Thermal Engineering, 2021, 26: 101184. DOI: https://doi.org/10.1016/j.csite.2021.101184.

    Article  Google Scholar 

  26. ZEESHAN A, MAJEED A, AKRAM M J, et al. Numerical investigation of MHD radiative heat and mass transfer of nanofluid flow towards a vertical wavy surface with viscous dissipation and Joule heating effects using Keller-box method [J]. Mathematics and Computers in Simulation, 2021, 190: 1080–1109. DOI:https://doi.org/10.1016/j.matcom.2021.07.002.

    Article  MathSciNet  MATH  Google Scholar 

  27. NASEEM T, FATIMA U, MUNIR M, et al. Joule heating and viscous dissipation effects in hydromagnetized boundary layer flow with variable temperature [J]. Case Studies in Thermal Engineering, 2022, 35: 102083. DOI: https://doi.org/10.1016/j.csite.2022.102083.

    Article  Google Scholar 

  28. KHAN S A, IMRAN KHAN M, ALSALLAMI S A M, et al. Irreversibility analysis in hydromagnetic flow of Newtonian fluid with Joule heating: Darcy-Forchheimer model [J]. Journal of Petroleum Science and Engineering, 2022, 212: 110206. DOI: https://doi.org/10.1016/j.petrol.2022.110206.

    Article  Google Scholar 

  29. KOTNURKAR A, KALLOLIKAR N. Effect of Joule heating and entropy generation on multi-slip condition of peristaltic flow of Casson nanofluid in an asymmetric channel [J]. Journal of Biological Physics, 2022, 48(3): 273–293. DOI: https://doi.org/10.1007/s10867-022-09603-1.

    Article  Google Scholar 

  30. ULLAH H, KHAN H, FIZA M, et al. Comparative analysis of the effect of joule heating and slip velocity on unsteady squeezing nanofluid flow [J]. Mathematical Problems in Engineering, 2022: e8452862. DOI: https://doi.org/10.1155/2022/8452862.

  31. SHARMA B K, GANDHI R. Combined effects of Joule heating and non-uniform heat source/sink on unsteady MHD mixed convective flow over a vertical stretching surface embedded in a Darcy-Forchheimer porous medium [J]. Propulsion and Power Research, 2022, 11(2): 276–292. DOI: https://doi.org/10.1016/j.jppr.2022.06.001.

    Article  Google Scholar 

  32. SHANKAR GOUD B, DHARMENDAR REDDY Y, MISHRA S. Joule heating and thermal radiation impact on MHD boundary layer Nanofluid flow along an exponentially stretching surface with thermal stratified medium [J]. Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 2022, 4: 239779142211009. DOI: https://doi.org/10.1177/23977914221100961.

    Google Scholar 

  33. ABDELMALEK Z, KHAN I, KHAN M W A, et al. Computational analysis of nano-fluid due to a non-linear variable thicked stretching sheet subjected to Joule heating and thermal radiation [J]. Journal of Materials Research and Technology, 2020, 9(5): 11035–11044. DOI: https://doi.org/10.1016/j.jmrt.2020.07.085.

    Article  Google Scholar 

  34. HAYAT T, SHAH F, ALSAEDI A, et al. Entropy optimized dissipative flow of effective Prandtl number with melting heat transport and Joule heating [J]. International Communications in Heat and Mass Transfer, 2020, 111: e104454. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2019.104454.

    Article  Google Scholar 

  35. MORTEZA MOUSAVI S, EHTESHAMI B, ALI RABIENATAJ DARZI A. Two-and-three-dimensional analysis of Joule and viscous heating effects on MHD nanofluid forced convection in microchannels [J]. Thermal Science and Engineering Progress, 2021, 25: 100983. DOI: https://doi.org/10.1016/j.tsep.2021.100983.

    Article  Google Scholar 

  36. RAMESH K, RIAZ A, DAR Z A. Simultaneous effects of MHD and Joule heating on the fundamental flows of a Casson liquid with slip boundaries [J]. Propulsion and Power Research, 2021, 10(2): 118–129. DOI: https://doi.org/10.1016/j.jppr.2021.05.002.

    Article  Google Scholar 

  37. REHMAN S, ANJUM A, FAROOQ M, et al. Melting heat phenomenon in thermally stratified fluid reservoirs (Powell-Eyring fluid) with joule heating [J]. International Communications in Heat and Mass Transfer, 2022, 137: e106196. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2022.106196.

    Article  Google Scholar 

  38. WAHID N S, ARIFIN N M, POP I, et al. MHD stagnationpoint flow of nanofluid due to a shrinking sheet with melting, viscous dissipation and Joule heating effects [J]. Alexandria Engineering Journal, 2022, 61(12): 12661–12672. DOI: https://doi.org/10.1016/j.aej.2022.06.041.

    Article  Google Scholar 

  39. LIAO S J. Homotopy analysis method in non-linear differential equations [M]. Heidelberg: Springer and Higher Education Press, 2012.

    Book  Google Scholar 

  40. LIAO S J. Advances in the homotopy analysis method [M]. Singapore: World Scientific, 2014.

    Book  MATH  Google Scholar 

  41. FAROOQ M, ANJUM A, HAYAT T, et al. Melting heat transfer in the flow over a variable thicked Riga plate with homogeneous-heterogeneous reactions [J]. Journal of Molecular Liquids, 2016, 224: 1341–1347. DOI: https://doi.org/10.1016/j.molliq.2016.10.123.

    Article  Google Scholar 

  42. AHMAD S, FAROOQ M, JAVED M, et al. Slip analysis of squeezing flow using doubly stratified fluid [J]. Results in Physics, 2018, 9: 527–533. DOI: https://doi.org/10.1016/j.rinp.2018.02.066.

    Article  Google Scholar 

  43. TLILI I, SHAHMIR N, RAMZAN M, et al. A novel model to analyze Darcy Forchheimer nanofluid flow in a permeable medium with Entropy generation analysis [J]. Journal of Taibah University for Science, 2020, 14(1): 916–930. DOI: https://doi.org/10.1080/16583655.2020.1790171.

    Article  Google Scholar 

  44. WAQAS M, AKRAM N, ASGHAR Z, et al. An improved Darcian analysis for chemically reacted Maxwell liquid toward convectively heated moving surface with magnetohydrodynamics [J]. Journal of Thermal Analysis and Calorimetry, 2021, 143(3): 2069–2074. DOI: https://doi.org/10.1007/s10973-020-09613-y.

    Article  Google Scholar 

  45. BERREHAL H. Thermodynamics second law analysis for MHD boundary layer flow and heat transfer caused by a moving wedge [J]. Journal of Mechanical Science and Technology, 2019, 33(6): 2949–2955. DOI: https://doi.org/10.1007/s12206-019-0542-4.

    Article  Google Scholar 

  46. PANDEY A K, KUMAR M. Chemical reaction and thermal radiation effects on boundary layer flow of nanofluid over a wedge with viscous and Ohmic dissipation [J]. St Petersburg Polytechnical University Journal: Physics and Mathematics, 2017, 3(4): 322–332. DOI: https://doi.org/10.1016/j.spjpm.2017.10.008.

    Article  Google Scholar 

  47. AZIMI M, RIAZI R. Go-water nanofluid inside semi porous channel: Analytical investigation [J]. World Journal of Engineering, 2015, 12(2): 103–108. DOI: https://doi.org/10.1260/1708-5284.12.2.103.

    Article  Google Scholar 

  48. DANIEL Y S. The solution of Falkner-Skan flow and heat transfer over a wedge with slip boundary condition using homotopy analysis method (HAM) [J]. Journal of Basic and Applied Research International, 2015, 10(2): 117–126. https://www.ikppress.org/index.php/JOBARI/article/view/3487.

    Google Scholar 

  49. ANJUM A, MIR N A, FAROOQ M, et al. Entropy generation under the influence of melting heat transfer in stratified polystyrene-water/kerosene nanofluid flow with velocity slip [J]. Materials Research Express, 2020, 6(12): 1250h6. DOI: https://doi.org/10.1088/2053-1591/ab5510.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Riphah International University, Islamabad, 44000, Pakistan

    Ahmad Shakeel & Farooq Hina

  2. Department of Pure and Applied Mathematics, The University of Haripur, Haripur, 22600, Pakistan

    Farooq Muhammad

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  1. Ahmad Shakeel
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Correspondence to Ahmad Shakeel.

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Contributors

Ahmad SHAKEEL developed the overarching research goals and edited the draft of manuscript. Farooq HINA conducted the literature review and wrote the manuscript. Farooq MUHAMMAD validated the proposed method with analysis and wrote the first draft of manuscript.

Conflict of interest

Ahmad SHAKEEL, Farooq HINA, and Farooq MUHAMMAD declare that they have no conflict of interest.

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Shakeel, A., Hina, F. & Muhammad, F. Falkner-Skan flow analysis for ohmic heated nanofluid toward moving surface with thermal jump. J. Cent. South Univ. 30, 834–843 (2023). https://doi.org/10.1007/s11771-023-5277-9

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