Skip to main content
SpringerLink
Log in

Characteristics of Homogeneous Heterogeneous Reaction on Flow of Walters’ B Liquid Under the Statistical Paradigm

  • Conference paper
  • First Online:
Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 272))

Abstract

In this article, significance of inclined MHD stagnant point flow of Walters B liquid because of stretched surface is investigated. Flow phenomenon is studied with Newtonian heating, homogeneous heterogeneous reactions, Joule heating and viscous dissipation. The nonlinear PDEs are converted to get nonlinear system of ODEs by invoking suitable transformations and solved by utilizing OHAM. Statistical methodology is used to check the significance and insignificance of the physical parameters via correlation coefficients and probable error. Characteristics of various sundry parameters on velocity, concentration and temperature fields are studied. Friction and Nusselt numbers are calculated and discuss in detail.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ahmed, J., Shahzad, A., Khan, M., Ali, R.: A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet. AIP Adv. 5(11), 1–11 (2015)

    Article  Google Scholar 

  2. Zeeshan, A., Ellahi, R.: Series solutions of nonlinear partial differential equations with slip boundary conditions for non-Newtonian MHD fluid in porous space. J. Appl. Math. Inf. Sci. 7(1), 253–261 (2013)

    MathSciNet  Google Scholar 

  3. Nejad, M.M., Javaherdeh, K., Moslemi, M.: MHD mixed convection flow of power law non-Newtonian fluids over an isothermal vertical wavy plate. J. Magn. Magn. Mater. 389, 66–72 (2015)

    Article  Google Scholar 

  4. Shehzad, S.A., Abdullah, Z., Alsaedi, A., Abbasi, F.M., Hayat, T.: Thermally radiative three-dimensional flow of Jeffrey nanofluid with internal heat generation and magnetic field. J. Magn. Magn. Mater. 397, 108–114 (2016)

    Article  Google Scholar 

  5. Das, K., Acharya, N., Kumar Kundu, P.: Radiative flow of MHD Jeffrey fluid past a stretching sheet with surface slip and melting heat transfer. Alexandria Eng. J. 54, 815–821 (2015)

    Article  Google Scholar 

  6. Venkateswarlu, B., Satya Narayana, P.V.: MHD viscoelastic fluid flow over a continuously moving vertical surface with chemical reaction. Walailak J. Sci. Eng. 12(9), 775–783 (2015)

    Google Scholar 

  7. Rashidi, S., Dehghan, M., Ellahi, R., Riaz, M., Jamal-Abad, M.T.: Study of stream wise transverse magnetic fluid flow with heat transfer around a porous obstacle. J. Magn. Magn. Mater. 378, 128–137 (2015)

    Article  Google Scholar 

  8. Sheikholeslami, M., Bandpy, M.G., Ellahi, R., Zeeshan, A.: Simulation of CuO-water nanofluid flow and convective heat transfer considering Lorentz forces. J. Magn. Magn. Mater. 369, 69–80 (2014)

    Article  Google Scholar 

  9. Ellahi, R., Hussain, F.: Simultaneous effects of MHD and partial slip on peristaltic flow of Jeffery fluid in a rectangular duct. J. Magn. Magn. Mater. 393, 284–292 (2015)

    Article  Google Scholar 

  10. Hayat, T., Shafiq, A., Alsaedi, A.: Effect of Joule heating and thermal radiation in flow of third-grade fluid over radiative surface. PLOS ONE 9(1), e83153 (2014)

    Article  Google Scholar 

  11. Merkin, J.H.: A model for isothermal homogeneous-heterogeneous reactions in boundary layer flow. Math. Comput. Model. 24, 125–136 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chaudhary, M.A., Merkin, J.H.: A simple isothermal model for homogeneous heterogeneous reactions in boundary layer flow: I. Equal diffusivities. Fluid Dyn. Res. 16, 311–333 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. Bachok, N., Ishak, A., Pop, I.: On the stagnation-point flow towards a stretching sheet with homogeneous-heterogeneous reactions effects. Commun. Nonlinear Sci. Numer. Simul. 16, 4296–4302 (2011)

    Article  MATH  Google Scholar 

  14. Khan, W.A., Pop, I.: Effects of homogeneous-heterogeneous reactions on the viscoelastic fluid towards a stretching sheet. ASME J. Heat Transfer 134(064506), 1–5 (2012)

    Google Scholar 

  15. Shaw, S., Kameswaran, P.K., Sibanda, P.: Homogeneous-heterogeneous reactions in micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium. Bound. Value Probl. 2013, 77 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kameswaran, P.K., Shaw, S., Sibanda, P., Murthy, P.V.S.N.: Homogeneous heterogeneous reactions in a nanofluid flow due to porous stretching sheet. Int. J. Heat Mass Transfer 57, 465–472 (2013)

    Article  Google Scholar 

  17. Hayat, T., Farooq, M., Alsaedi, A.: Homogeneous-heterogeneous reactions in the stagnation point flow of carbon nanotubes with Newtonian heating. AIP Adv. 5, 027130 (2015)

    Article  Google Scholar 

  18. Hayat, T., Imtiaz, M., Alsaedi, A.: MHD flow of nanofluid with homogeneous heterogeneous reactions and velocity slip. Therm. Sci., 67 (2015)

    Google Scholar 

  19. Hayat, T., Imtiaz, M., Alsaedi, A.: Effects of homogeneous-heterogeneous reactions in flow of Powell-Eyring fluid. J. Centr. South Univ. 22(8), 3211–3216 (2015)

    Article  Google Scholar 

  20. Hayat, T., Imtiaz, M., Alsaedi, A., Almezal, S.: On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous heterogeneous reactions. J. Magn. Magn. Mater. 401, 296–303 (2016)

    Article  Google Scholar 

  21. Hayat, T., Imtiaz, M., Alsaedi, A.: Impact of magnetohydrodynamics in bidirectional flow of nanofluid subject to second order slip velocity and homogeneous-heterogeneous reactions. J. Magn. Magn. Mater. 395, 294–302 (2015)

    Article  Google Scholar 

  22. Sahoo, B.: Effects of partial slip, viscous dissipation and Joule heating on Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid. Commun. Nonlinear Sci. Numer. Simul. 14, 2982–2998 (2009)

    Article  Google Scholar 

  23. Salleh, M.Z., Nazar, R., Pop, I.: Boundary layer flow and heat transfer over a stretching sheet with Newtonian heating. J. Taiwan Inst. Chem. Eng. 41, 651–655 (2010)

    Article  Google Scholar 

  24. Hayat, T., Iqbal, Z., Mustafa, M.: Flow of second grade fluid over a stretching surface with Newtonian heating. J. Mech. 28, 209–216 (2012)

    Article  Google Scholar 

  25. Makinde, O.D.: Computational modelling of MHD unsteady flow and heat transfer towards a flat plate with Navier slip and Newtonian heating. Braz. J. Chem. Eng. 29, 159–166 (2012)

    Article  Google Scholar 

  26. Uddin, M.J., Khan, W.A., Ismail, A.I.: MHD free convective boundary layer flow of nanofluid past a flat vertical plate with Newtonian heating boundary condition. PLOS ONE 7(11), e49499 (2012)

    Article  Google Scholar 

  27. Sarif, N.M., Salleh, M.Z., Nazar, R.: Numerical solution of flow and heat transfer over a stretching sheet with Newtonian heating using the Keller Box Method. Procedia Eng. 53, 542–554 (2013)

    Article  Google Scholar 

  28. Ramzan, M., Farooq, M., Alsaedi, A., Hayat, T.: MHD three dimensional flow of couple stress fluid with Newtonian heating. Eur. Phys. J. Plus 128, 49 (2013)

    Article  Google Scholar 

  29. Makinde, O.D.: Effects of viscous dissipation and Newtonian heating on boundary layer flow of nanofluids over a flat plate. Int. J. Numer. Methods Heat Fluids Flow 23, 1291–1303 (2013)

    Google Scholar 

  30. Hayat, T., Shafiq, A., Mustafa, M., Alsaedi, A.: Boundary layer flow of Walters’ B fluid with Newtonian heating. Z. Naturforsch. 70(5), 333–341 (2015)

    Article  Google Scholar 

  31. Liao, S.J.: Notes on the homotopy analysis method: some definitions and theorems. Commun. Nonlinear Sci. Numer. Simul. 14, 983–997 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  32. Hayat, T., Shafiq, A., Alsaedi, A.: Melting heat transfer in a stagnation point flow of Tangent-hyperbolic fluid over a vertical surface. J. Magn. Magn. Mater. 405, 97–106 (2016)

    Article  Google Scholar 

  33. Hayat, T., Muhammad, T., Shehzad, S.A., Chen, G.Q., Abbas, I.A.: Interaction of magnetic field in flow of Maxwell nanofluid with convective effect. J. Magn. Magn. Mater. 389, 48–55 (2015)

    Article  Google Scholar 

  34. Hayat, T., Muhammad, T., Alsaedi, A., Alhuthali, M.S.: Magnetohydrodynamic three dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation. J. Magn. Magn. Mater. 385, 222–229 (2015)

    Article  Google Scholar 

  35. Hayat, T., Shafiq, A., Alsaedi, A.: Hydromagnetic boundary layer flow of Williamson fluid in the presence of thermal radiation and Ohmic dissipation. Alexandria Eng. J. 3(55), 2229–2240 (2016)

    Article  Google Scholar 

  36. Farooq, U., Zhao, Y.L., Hayat, T., Alsaedi, A., Liao, S.J.: Application of the HAM based mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nanofluid. Comput. Fluids 111, 69–75 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  37. Guedda, M., Hammouch, Z.: On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers. Fluid Dyn. Res. 38(4), 211 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  38. Zakia, H.: Etude mathématique et numérique de quelques problemes issus de la dynamique des fluides. Diss, Amiens (2006)

    Google Scholar 

  39. Khan, Z.H., Hussain, S.T., Hammouch, Z.: Flow and heat transfer analysis of water and ethylene glycol based Cu nanoparticles between two parallel disks with suction/injection effects. J. Mol. Liq. 221, 298–304 (2016)

    Article  Google Scholar 

  40. Amkadni, M., Azzouzi, A., Hammouch, Z.: On the exact solutions of laminar MHD flow over a stretching flat plate. Commun. Nonlinear Sci. Numer. Simul. 13(2), 359–368 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  41. Rizwan-ul-Haq, Soomro, F.A., Hammouch, Z.: Heat transfer analysis of CuO-water enclosed in a partially heated rhombus with heated square obstacle. Int. J. Heat Mass Transfer 118, 773–784 (2018)

    Article  Google Scholar 

  42. Bedjaoui, N., Guedda, M., Hammouch, Z.: Similarity solutions of the Rayleigh problem for Ostwald-de Wael electrically conducting fluids. Anal. Appl. 9(02), 135–159 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  43. Haq, R.U., Hammouch, Z., Waqar Khan, A.: Water-based squeezing flow in the presence of carbon nanotubes between two parallel disks. Therm. Sci., 148 (2014)

    Google Scholar 

  44. Shafiq, A., Hammouch, Z., Sindhu, T.N.: Bioconvective MHD flow of tangent hyperbolic nanofluid with Newtonian heating. Int. J. Mech. Sci. 133, 759–766 (2017)

    Article  Google Scholar 

  45. Shafiq, A., Hammouch, Z., Turab, A.: Impact of radiation in a stagnation point flow of Walters’ B fluid towards a Riga plate. Therm. Sci. Eng. Prog. 6, 27–33 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Anum Shafiq

  2. Department of Statistics, Quaid-i-Azam University, 45320, Islamabad, 44000, Pakistan

    T. N. Sindhu

  3. Département de Mathématiques, FST Errachidia, Université Moulay Ismail, Meknes, Morocco

    Z. Hammouch

Authors
  1. Anum Shafiq
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. N. Sindhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Z. Hammouch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Z. Hammouch .

Editor information

Editors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, Rajasthan, India

    Jagdev Singh

  2. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, India

    Devendra Kumar

  3. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  4. Department of Mathematics, Cankaya University, Balgat, Ankara, Turkey

    Dumitru Baleanu

  5. Department of Mathematics, Rajasthan Technical University, Kota, Rajasthan, India

    Sunil Dutt Purohit

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Shafiq, A., Sindhu, T.N., Hammouch, Z. (2019). Characteristics of Homogeneous Heterogeneous Reaction on Flow of Walters’ B Liquid Under the Statistical Paradigm. In: Singh, J., Kumar, D., Dutta, H., Baleanu, D., Purohit, S. (eds) Mathematical Modelling, Applied Analysis and Computation. ICMMAAC 2018. Springer Proceedings in Mathematics & Statistics, vol 272. Springer, Singapore. https://doi.org/10.1007/978-981-13-9608-3_20

Download citation

Publish with us

Policies and ethics

Search

Navigation