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Magnetically driven flow of pseudoplastic fluid across a sensor surface

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Abstract

The current article addresses the unsteady squashing hydromagnetic transport of an electrically conductive pseudoplastic fluid traversing across a sensor surface. The fluid flow phenomenon is happening under the thermic radiation and heat origination effects. The sensor surface is positioned in the superficially free stream. The viscosity and thermic conductivity are taken as a concomitant of temperature. The magnetic field is acting transversely to the phenomenon. The energy equation is assimilated with the non-conventional heat transfer model. This type of assimilation is established instead of conventional Fourier’s law for expressing the heat generation, thermic radiation and especially thermal relaxation times. To construct the simpler non-dimensional structure of the arising energy, continuity and momentum equations, suitable controlling parameters have been utilized. A well-known numerical method has adopted to construct the solutions of the constructed equations. To check the convergence of the obtained numerical solutions, a comprehensive graphical analysis has been presented. The consequences of impressive parameters like heat origination parameter, radiation parameter, boundary layer, thermal relaxation times, magnetic factor and the squeezing number on the flow structure are deliberated graphically. Also, the things of engineering importance, such as the variation in squeezed flow index factor, Prandtl number, thermal conductivity, variable thickness, free stream velocity, Weissenberg number, have sturdy impacts on the flow and energy equation.

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Abbreviations

q w :

Heat flux

α ∞ :

Thermal conductivity

δ c :

Thermal relaxation time of heat transfer

V :

Velocity of the fluid

u, v :

Velocity component along x and y direction

ρ :

Density of fluid

α(T):

Variable thermal conductivity

ε :

A small quantity

t :

Time

T :

Temperature

Q 0 :

Heat generation

T ∞ :

Ambient temperature

q r :

Radiative heat flux

C p :

Specific heat

k*:

Coefficient of mean absorption

σ*:

Stefan–Boltzmann constant

U(x, t):

Free stream velocity

P :

Pressure of the fluid

n :

Power law index

σ :

Electrical conductivity

B o :

Magnetic field strength

μ o :

Variable viscosity

v o(t):

Sensor surface velocity

μ*:

Constant value of coefficient of viscosity

c, T r :

Constants

γ :

Thermal property of fluid (a constant)

b :

Squeezed flow index

ψ :

Wave function

s :

Arbitrary constant

A :

Squeezed strength

Pr :

Prandtl number

W e :

Weissenberg number

M :

Magnetic parameter

β :

Dimensionless heat relaxation parameter

Θr :

Fluid viscosity parameter

Q :

Heat sink/source parameter

R :

Radiation parameter

Referencesc

  1. Engmann J, Servais C, Burbidge AS (2005) Squeeze flow theory and applications to rheometry: a review. J Non-Newtonian Fluid Mech 132:1–27

    Article  Google Scholar 

  2. Salahuddin T, Hussain A, Bilal S, Awais M, Khan I, Malik MY (2017) MHD squeezed flow of Carreau–Yasuda fluid over a sensor surface. Alex Eng J 56:27–34

    Article  Google Scholar 

  3. Haq RU, Nadeem S, Khan ZH, Noor NFM (2015) MHD squeezed flow of water functionalized metallic nanoparticles over a sensor surface. Physica E 73:45–53

    Article  Google Scholar 

  4. Datskos PG, Oden PI, Thundat T, Wachter EA, Warmack RJ, Hunter SR (1996) Remote infrared radiation detection using piezoresistive microcantilevers. Appl Phys Lett 69:2986–2988

    Article  Google Scholar 

  5. Khan M, Malik MY, Salahuddin T, Khan I (2016) Heat transfer squeezed flow of Carreau fluid over a sensor surface with variable thermal conductivity: a numerical study. Results Phys 6:940–945

    Article  Google Scholar 

  6. Rashidi MM, Shahmohamadi H, Dinarvand S (2008) Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates. Math Problems Eng 35:935095

    MathSciNet  MATH  Google Scholar 

  7. Khaled ARA, Vafai K (2004) Hydromagnetic squeezed flow and heat transfer over a sensor surface. Int J Eng Sci 42:509–519

    Article  Google Scholar 

  8. Malik MY, Hussain A, Salahuddin T, Awais M, Bilal S, Khan F (2016) Flow of Sisko fluid over a stretching cylinder and heat transfer with viscous dissipation and variable thermal conductivity: a numerical study. AIP Adv 6:045118

    Article  Google Scholar 

  9. Malik MY, Bibi M, Khan F, Salahuddin T (2016) Numerical solution of Williamson fluid flow past a stretching cylinder and heat transfer with variable thermal conductivity and heat generation/absorption. AIP Adv 6:035101

    Article  Google Scholar 

  10. Rehman KU, Malik MY, Salahuddin T, Naseer M (2016) Dual stratified mixed convection flow of Eyring–Powell fluid over an inclined stretching cylinder with heat generation/absorption effect. AIP Adv 6:075112

    Article  Google Scholar 

  11. Malik MY, Hussain A, Salahuddin T, Awais M, Bilal S (2016) Numerical solution of Sisko fluid over a stretching cylinder and heat transfer with variable thermal conductivity. J Mech 32:593–601

    Article  Google Scholar 

  12. Malik MY, Bilal S, Salahuddin T, Awais M, Hussain A (2015) Homogeneous-heterogeneous reactions in Williamson fluid MHD squeezed flow of Carreau–Yasuda fluid model over a stretching cylinder by using Keller box method. AIP Adv 5:107227

    Article  Google Scholar 

  13. Khaled ARA, Vafai K (2004) Hydromagnetic squeezed flow and heat transfer over a sensor surface. Int J Eng Sci 42:509–519

    Article  Google Scholar 

  14. Salahuddin T, Malik MY, Hussain A, Bilal S, Awais M (2015) Effects of transverse magnetic field with variable thermal conductivity on tangent hyperbolic fluid with exponentially varying viscosity. AIP Adv 5:127103

    Article  Google Scholar 

  15. Fick A (1855) Ueber diffusion. Ann Phys 170:59–86

    Article  Google Scholar 

  16. Fourier JBJ (1822) TheorieAnalytique De La Chaleur, Paris, pp 499–508

  17. Cattaneo C (1948) Sulla Conduzione del calore. AttiSemin Mat Fis UnivModea Reggio Emilia 3:431

    MATH  Google Scholar 

  18. Christov CI (2009) On frame in different formulation of the Maxwell–Cattaneo model of finite speed heat conduction. Mech Res Commun 36:481–486

    Article  Google Scholar 

  19. Malik MY, Khan M, Salahuddin T, Khan I (2016) Variable viscosity and MHD flow in Casson fluid with Cattaneo–Christov heat flux model: using Keller box method. Eng Sci Technol Int J 19:1985–1992

    Article  Google Scholar 

  20. Salahuddin T, Malik MY, Hussain A, Bilal S, Awais M (2016) MHD flow of Cattaneo–Christov heat flux model for Williamson fluid over a stretching sheet with variable thickness: using numerical approach. J Magn Magn Mater 401:991–997

    Article  Google Scholar 

  21. Saleem S, Awais M, Nadeem S, Sandeep N, Mustafa MT (2017) Theoretical analysis of upper-convected Maxwell fluid flow with Cattaneo–Christov heat flux model. Chin J Phys 4:1615–1625

    Article  Google Scholar 

  22. Khan M, Shahid A, Malik MY, Salahuddin T (2018) Thermal and concentration diffusion in Jeffery nanofluid flow over an inclined stretching sheet: a generalized Fourier’s and Fick’s. J Mol Liq 251:7–14

    Article  Google Scholar 

  23. Sandeep N, Vangala S (2014) Radiation and inclined magnetic field effects on unsteady hydromagnetic free convection flow past an impulsively moving vertical plate in a porous medium. J Appl Fluid Mech 7:275–286

    MATH  Google Scholar 

  24. Kumar KA, Reddy JVR, Vangala S, Sandeep N (2018) MHD flow of chemically reacting Williamson fluid over a curved/flat surface with variable heat source/sink. Int J Fluid Mech Res 46(2):12486–12493

    Google Scholar 

  25. Kumar KA, Reddy JVR, Vangala S, Sandeep N (2018) Impact of cross diffusion on MHD viscoelastic fluid flow past a melting surface with exponential heat source. Multidiscip Model Mater Struct. https://doi.org/10.1108/MMMS-12-2017-0151

    Article  Google Scholar 

  26. Ramadevi B, Sugunamma V, Anantha Kumar K, Ramana Reddy JV (2017) MHD flow of Carreau fluid over a variable thickness melting surface subject to Cattaneo–Christov heat flux. Multidiscip Model Mater Struct 12:0169

    Google Scholar 

  27. Kumar KA, Reddy JVR, Vangala S, Sandeep N (2017) Impact of frictional heating on MHD radiative ferrofluid past a convective shrinking surface. Defect Diffus Forum 378:157–174

    Article  Google Scholar 

  28. Kumar KA, Reddy JVR, Vangala S, Sandeep N (2018) Effect of cross diffusion on MHD non-Newtonian fluids flow past a stretching sheet with non-uniform heat source/sink: a comparative study. Eng J, Alex. https://doi.org/10.1016/j.aej.2017.03.008

    Book  Google Scholar 

  29. Reddy JVR, Vangala S, Sandeep N, Ramandevi B (2017) Combined influence of viscous dissipation and non-uniform heat source/sink on MHD non-Newtonian fluid flow with Cattaneo–Christov heat flux. Eng J, Alex. https://doi.org/10.1016/j.aej.2017.01.026

    Book  Google Scholar 

  30. Kumar KA, Reddy JVR, Vangala S, Sandeep N (2016) Influence of thermal radiation on stagnation flow towards a stretching sheet with induced magnetic field. Adv Phys Theor Appl 53:23–28

    Google Scholar 

  31. Ananth P, Dinesh A, Sugunamma V, Sandeep N (2015) Effect of nonlinear thermal radiation on stagnation flow of a Casson fluid towards a stretching sheet. Ind Eng Lett 5:70–79

    Google Scholar 

  32. Kumar KA, Reddy JVR, Vangala S, Sandeep N (2016) Dual solutions for thermo diffusion and diffusion thermo effects on 3D MHD casson fluid flow over a stretching surface. Res J Pharm Technol 9:1187–1194

    Article  Google Scholar 

  33. Lakshmi KB, Kumar A, Reddy JVR, Vangala S (2019) Influence of nonlinear radiation and cross diffusion on MHD flow of Casson and Walters-B nanofluids past a variable thickness sheet. J Nanofluids 8:73–83

    Article  Google Scholar 

  34. Anantha Kumar K, Reddy JVR, Sugunamma V, Sandeep N (2018) Magnetohydrodynamic Cattaneo–Christov flow past a cone and a wedge with variable heat source/sink. Alex Eng J 57:435–443

    Article  Google Scholar 

  35. Anantha Kumar K, Ramadevi B, Sugunamma V (2018) Impact of Lorentz force on unsteady bio convective flow of Carreau fluid across a variable thickness sheet with non-Fourier heat flux model. Defect Diffus Forum 387:474–497

    Article  Google Scholar 

  36. Reddy T, Rallabandi SR, Anand Rao J (2017) Influence of viscous dissipation on unsteady MHD natural convective flow of Casson fluid over an oscillating vertical plate via FEM. Ain Shams Eng J 9:4–21

    Google Scholar 

  37. Sheri SR, Rallabandi SR (2016) Transient MHD free convective flow past an infinite vertical plate embedded in a porous medium with viscous dissipation. Meccanica 51:1057–1068

    Article  MathSciNet  Google Scholar 

  38. Jithender Reddy R, Srinivasa Raju J, Rao Anand, Rashidi MM (2016) Analytical and numerical study of unsteady MHD free convection flow over an exponentially moving vertical plate with heat absorption. Int J Therm Sci 107:303–315

    Article  Google Scholar 

  39. Gorla RSR, Rao JA, Raju RS, Reddy GJ (2017) Unsteady MHD Couette flow of water at 4 °C in a rotating system in presence of heat transfer with ramped temperature via finite element method. Int J Appl Mech Eng (Indexed in Google Scholar & SCOPUS) 22:145–161

    Article  Google Scholar 

  40. Rallabandi SR, Reddy J, Anitha G (2017) MHD Casson viscous dissipative fluid flow past a vertically inclined plate in presence of heat and mass transfer: a finite element technique. Front Heat Mass Transf 8:27

    Google Scholar 

  41. Raju RS (2017) Transfer effects on an unsteady MHD free convective flow past a vertical plate with chemical reaction. Eng Trans J 65:221–249

    MathSciNet  Google Scholar 

  42. Raju RS, Reddy BM, Reddy GJ (2017) Finite element solutions of MHD free convective Casson fluid flow past an vertically inclined plate submitted in magnetic field in presence of heat and mass transfer. Int J Comput Methods Eng Sci Mech 8:250–265

    Article  Google Scholar 

  43. Ramya D, Raju RS, Rao JA (2016) Influence of chemical reaction on MHD boundary layer flow of nano fluids over a nonlinear stretching sheet with thermal radiation. J Nanofluids 5:880–888

    Article  Google Scholar 

  44. Srinivasa Raju R, Mahesh Reddy B, Rashidi MM, Gorla RSR (2016) Application of finite element method to unsteady MHD free convection flow past a vertically inclined porous plate including thermal diffusion and diffusion thermo effects. J Porous Media 8:701–722

    Article  Google Scholar 

  45. Lai FC, Kulacki FA (1990) The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium. Int J Heat Mass Transf 33:1028–1031

    Article  Google Scholar 

  46. Vajravelu K, Prasad KV, Ng C-O (2013) The effect of variable viscosity on the flow and heat transfer of a viscous Ag- water and Cu-water nanofluids. J Hydrodyn Ser B 25:1–9

    Article  Google Scholar 

  47. Abel MS, Khan SK, Prasad KV (2002) Study of visco-elastic fluid and heat transfer over a stretching sheet with variable viscosity. Int J Non-Linear Mech 37:81–83

    Article  Google Scholar 

  48. Saleem AM (2002) Variable viscosity and thermal conductivity on MHD flow and heat transfer in viscoelastic fluid over a stretching sheet. Phys Lett A 369:315–322

    Article  Google Scholar 

  49. Knezevic D, Svic V (2006) Mathematical modelling of changing of dynamical viscosity, as a function of temperature and pressure, of mineral oils for hydraulic systems. Facta Univ 6:27–34

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan

    Azad Hussain, Rabia Zetoon & Shoaib Ali

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

    S. Nadeem

Authors
  1. Azad Hussain
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  2. Rabia Zetoon
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  3. Shoaib Ali
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  4. S. Nadeem
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Correspondence to Azad Hussain.

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Technical Editor: Cezar Negrao, PhD.

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Hussain, A., Zetoon, R., Ali, S. et al. Magnetically driven flow of pseudoplastic fluid across a sensor surface. J Braz. Soc. Mech. Sci. Eng. 41, 185 (2019). https://doi.org/10.1007/s40430-019-1691-1

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