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Entropy generation approach with heat and mass transfer in magnetohydrodynamic stagnation point flow of a tangent hyperbolic nanofluid

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Abstract

This work examines the entropy generation with heat and mass transfer in magnetohydrodynamic (MHD) stagnation point flow across a stretchable surface. The heat transport process is investigated with respect to the viscous dissipation and thermal radiation, whereas the mass transport is observed under the influence of a chemical reaction. The irreversibe factor is measured through the application of the second law of thermodynamics. The established non-linear partial differential equations (PDEs) have been replaced by acceptable ordinary differential equations (ODEs), which are solved numerically via the bvp4c method (built-in package in MATLAB). The numerical analysis of the resulting ODEs is carried out on the different flow parameters, and their effects on the rate of heat transport, friction drag, concentration, and the entropy generation are considered. It is determined that the concentration estimation and the Sherwood number reduce and enhance for higher values of the chemical reaction parameter and the Schmidt number, although the rate of heat transport is increased for the Eckert number and heat generation/absorption parameter, respectively. The entropy generation augments with boosting values of the Brinkman number, and decays with escalating values of both the radiation parameter and the Weissenberg number.

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Abbreviations

u, v :

fluid velocity components

M :

Hartmann number

τ :

capacity ratio

θ :

dimensionless temperature

ρ :

density

γ :

chemical reaction parameter

σ :

electrical conductivity

q m :

wall mass flux

ν :

kinematic viscosity

D :

coefficient of diffusion

η :

similarity variable

δ :

heat generation/absorption

B 0 :

strength of magnetic field

T w :

surface temperature

a, c :

constants

Ec :

Eckert number

T :

temperature

n :

power law index

C :

concentration

ϕ :

nanoparticle volume fraction

C p :

specific heat

C w :

surface concentration

T ∞ :

ambient temperature

u w :

stretching velocity

C ∞ :

ambient concentration

u e :

free stream velocity

K 1 :

chemical reaction parameter

μ :

dynamic viscosity

q w :

wall heat flux

k :

thermal conductivity

τ w :

shear stress

S :

suction parameter

Le :

Lewis number

A :

ratio parameter

f :

dimensionless stream function

Sc :

Schmidt number

C fx :

skin friction coefficient

R :

radiation parameter

\(N{u_x}\) :

Nusselt number

N G :

entropy generation

Sh x :

local Sherwood number

B r :

Brinkman number

We :

Weissenberg number

L :

diffusion parameter

Re x :

Reynolds number

α 1 :

temperature difference variable

Pr :

Prandtl number

α 2 :

concentration difference parameter.

References

  1. CRANE, L. J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 21(4), 645–647 (1970)

    Article  Google Scholar 

  2. ATIF, S. M., HUSSAIN, S., and SAGHEER, M. Effect of viscous dissipation and Joule heating on MHD radiative tangent hyperbolic nanofluid with convective and slip conditions. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(4), 1–17 (2019)

    Article  Google Scholar 

  3. HSU, J. P., HUNG, S. H., and YU, H. Y. Electrophoresis of a sphere at an arbitrary position in a spherical cavity filled with Carreau fluid. Journal of Colloid and Interface Science, 280(1), 256–263 (2004)

    Article  Google Scholar 

  4. ANDERSSON, H. I., BECH, K. H., and DANDAPAT, B. S. Magnetohydrodynamic flow of a power-law fluid over a stretching sheet. International Journal of Non-Linear Mechanics, 27(6), 929–936 (1992)

    Article  MATH  Google Scholar 

  5. KHAN, M. R., PAN, K., KHAN, A. U., and ULLAH, N. Comparative study on heat transfer in CNTs-water nanofluid over a curved surface. International Communications in Heat and Mass Transfer, 116, 104707 (2020)

    Article  Google Scholar 

  6. DOGHNCHI, A. S., WAQAS, M., SEYYED, S. M., HASHEMI-TILEHNOEE, M., and GANJI, D. D. A modified Fourier approach for analysis of nanofluid heat generation within a semi-circular enclosure subjected to MFD viscosity. International Communications in Heat and Mass Transfer, 111, 104430 (2020)

    Article  Google Scholar 

  7. GAO, T., LI, C., JIA, D., ZHANG, Y., YANG, M., WANG, X., and XU, X. Surface morphology assessment of CFRP transverse grinding using CNT nanofluid minimum quantity lubrication. Journal of Cleaner Production, 277, 123328 (2020)

    Article  Google Scholar 

  8. KHAN, M. R., PAN, K., KHAN, A. U., and NADEEM, S. Dual solutions for mixed convection flow of SiO2-Al2O3/water hybrid nanofluid near the stagnation point over a curved surface. Physica A: Statistical Mechanics and Its Applications, 547, 123959 (2020)

    Article  Google Scholar 

  9. DU, X., QIU, J., DENG, S., DU, Z., CHENG, X., and WANG, H. Flame-retardant and solid-solid phase change composites based on dopamine-decorated BP nanosheets/polyurethane for efficient solar-to-thermal energy storage. Renewable Energy, 164, 1–10 (2021)

    Article  Google Scholar 

  10. KHAN, M. R. Numerical analysis of oblique stagnation point flow of nanofluid over a curved stretching/shrinking surface. Physica Scripta, 95(10), 105704 (2020)

    Article  Google Scholar 

  11. VAJRAVELU, K. Viscous flow over a nonlinearly stretching sheet. Applied Mathematics and Computation, 124(3), 281–288 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. HAYAT, T., MUMTAZ, M., SHAFIQ, A., and ALSAEDI, A. Stratified magnetohydrodynamic flow of tangent hyperbolic nanofluid induced by inclined sheet. Applied Mathematics and Mechanics (English Edition), 38(2), 271–288 (2017) https://doi.org/10.1007/s10483-017-2168-9

    Article  MathSciNet  Google Scholar 

  13. LIU, I. C., WANG, H. H., and PENG, Y. F. Flow and heat transfer for three-dimensional flow over an exponentially stretching surface. Chemical Engineering Communications, 200(2), 253–268 (2013)

    Article  Google Scholar 

  14. ASHRAFI, N. and MOHAMADALI, M. Transient flow and heat transfer of pseudoplastic fluids on a stretching sheet. Applied Mathematics and Computation, 228, 153–161 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. HAYAT, T., ASAD, S., MUSTAFA, M., and ALSAEDI, A. Boundary layer flow of Carreau fluid over a convectively heated stretching sheet. Applied Mathematics and Computation, 246, 12–22 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. MEGAHED, A. M. Carreau fluid flow due to nonlinearly stretching sheet with thermal radiation, heat flux, and variable conductivity. Applied Mathematics and Mechanics (English Edition), 40(11), 1615–1624 (2019) https://doi.org/10.1007/s10483-019-2534-6

    Article  MathSciNet  Google Scholar 

  17. MACHIREDDY, G. R. and NARAMGARI, S. Heat and mass transfer in radiative MHD Carreau fluid with cross diffusion. Ain Shams Engineering Journal, 9(4), 1189–1204 (2018)

    Article  Google Scholar 

  18. VAJRAVELU, K. and HADJINICOLAOU, A. Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream. International Journal of Engineering Science, 35(12–13), 1237–1244 (1997)

    Article  MATH  Google Scholar 

  19. POP, I. and NA, T. Y. A note on MHD flow over a stretching permeable surface. Mechanics Research Communications, 25(3), 263–269 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  20. ISHAK, A., NAZAR, R., and POP, I. Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet. Heat and Mass Transfer, 44(8), 921–927 (2008)

    Article  Google Scholar 

  21. NADEEM, S., KHAN, M. R., and KHAN, A. U. MHD stagnation point flow of viscous nanofluid over a curved surface. Physica Scripta, 94(11), 115207 (2019)

    Article  Google Scholar 

  22. NADEEM, S. and KHAN, A. U. MHD oblique stagnation point flow of nanofluid over an oscillatory stretching/shrinking sheet: existence of dual solutions. Physica Scripta, 94(7), 075204 (2019)

    Article  Google Scholar 

  23. KHAN, M., MALIK, R., and ANJUM, A. Exact solutions of MHD second Stokes flow of generalized Burgers fluid. Applied Mathematics and Mechanics (English Edition), 36(2), 211–224 (2015) https://doi.org/10.1007/s10483-015-1906-7

    Article  MathSciNet  MATH  Google Scholar 

  24. ALI, F. M., NAZAR, R., ARIFIN, N. M., and POP, I. MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field. Applied Mathematics and Mechanics (English Edition), 32(4), 409–418 (2011) https://doi.org/10.1007/s10483-011-1426-6

    Article  MathSciNet  MATH  Google Scholar 

  25. ZHANG, X. and ZHANG, Y. Heat transfer and flow characteristics of Fe3O4-water nanofluids under magnetic excitation. International Journal of Thermal Sciences, 163, 106826 (2021)

    Article  Google Scholar 

  26. UDDIN, I., ULLAH, I., ALI, R., KHAN, I., and NISAR, K. S. Numerical analysis of nonlinear mixed convective MHD chemically reacting flow of Prandtl-Eyring nanofluids in the presence of activation energy and Joule heating. Journal of Thermal Analysis and Calorimetry, 145, 495–505 (2021)

    Article  Google Scholar 

  27. GAO, T., LI, C., ZHANG, Y., YANG, M., JIA, D., JIN, T., and LI, R. Dispersing mechanism and tribological performance of vegetable oil-based CNT nanofluids with different surfactants. Tribology International, 131, 51–63 (2019)

    Article  Google Scholar 

  28. ZHU, J., ZHENG, L. C., and ZHANG, Z. G. Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet. Applied Mathematics and Mechanics (English Edition), 31 (4), 439–448 (2010) https://doi.org/10.1007/s10483-010-0404-z

    Article  MathSciNet  MATH  Google Scholar 

  29. SADEGHI, M. S., TAYEBI, T., DOGONCHI, A. S., NAYAK, M. K., and WAQAS, M. Analysis of thermal behavior of magnetic buoyancy-driven flow in ferrofluid-filled wavy enclosure furnished with two circular cylinders. International Communications in Heat and Mass Transfer, 120, 104951 (2021)

    Article  Google Scholar 

  30. ZHANG, X. and ZHANG, Y. Experimental study on enhanced heat transfer and flow performance of magnetic nanofluids under alternating magnetic field. International Journal of Thermal Sciences, 164, 106897 (2021)

    Article  Google Scholar 

  31. RAUF, A., ABBAS, Z., and SHEHZAD, S. A. Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium. Applied Mathematics and Mechanics (English Edition), 40(6), 837–850 (2019) https://doi.org/10.1007/s10483-019-2488-9

    Article  MathSciNet  Google Scholar 

  32. ZHANG, Y., LI, C., JIA, D., ZHANG, D., and ZHANG, X. Experimental evaluation of the lubrication performance of MoS2/CNT nanofluid for minimal quantity lubrication in Ni-based alloy grinding. International Journal of Machine Tools and Manufacture, 99, 19–33 (2015)

    Article  Google Scholar 

  33. KHAN, M. R., LI, M., MAO, S., ALI, R., and KHAN, S. Comparative study on heat transfer and friction drag in the flow of various hybrid nanofluids effected by aligned magnetic field and nonlinear radiation. Scientific Reports, 11(1), 1–14 (2021)

    Google Scholar 

  34. ZHU, J., ZHENG, L., ZHENG, L., and ZHANG, X. Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction. Applied Mathematics and Mechanics (English Edition), 36(9), 1131–1146 (2015) https://doi.org/10.1007/s10483-015-1977-6

    Article  MathSciNet  MATH  Google Scholar 

  35. BEJAN, A. A study of entropy generation in fundamental convective heat transfer. Journal Heat Transfer, 101(4), 718–725 (1979)

    Article  Google Scholar 

  36. BEJAN, A. and KESTIN, J. Entropy generation through heat and fluid flow. Journal of Applied Mechanics, 50, 475 (1983)

    Article  Google Scholar 

  37. BHATTI, M. M., SHEIKHOLESLAMI, M., SHAHID, A., HASSAN, M., and ABBAS, T. Entropy generation on the interaction of nanoparticles over a stretched surface with thermal radiation. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 570, 368–376 (2019)

    Article  Google Scholar 

  38. ELLAHI, R., ALAMRI, S. Z., BASIT, A., and MAJEED, A. Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation. Journal of Taibah University for Science, 12(4), 476–482 (2018)

    Article  Google Scholar 

  39. KHAN, M. I., KHAN, T. A., QAYYUM, S., HAYAT, T., KHAN, M. I., and ALSAEDI, A. Entropy generation optimization and activation energy in nonlinear mixed convection flow of a tangent hyperbolic nanofluid. The European Physical Journal Plus, 133(8), 1–20 (2018)

    Article  Google Scholar 

  40. ULLAH, I., ALI, R., KHAN, I., and NISAR, K. S. Insight into kerosene conveying CNTs and Fe3O4 nanoparticles through a porous medium: significance of Coriolis force and entropy generation. Physica Scripta, 96(5), 055705 (2021)

    Article  Google Scholar 

  41. HAYAT, T., YAQOOB, R., QAYYUM, S., and ALSAEDI, A. Entropy generation optimization in nanofluid flow by variable thicked sheet. Physica A: Statistical Mechanics and Its Applications, 551, 124022 (2020)

    Article  MathSciNet  Google Scholar 

  42. HAYAT, T., KHAN, M. I., WAQAS, M., and ALSAEDI, A. Stagnation point flow of hyperbolic tangent fluid with Soret-Dufour effects. Results in Physics, 7, 2711–2717 (2017)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 311121, China

    Tiehong Zhao

  2. LSEC and ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    M. R. Khan

  3. School of Mathematical Science, University of Chinese Academy of Sciences, Beijing, 100190, China

    M. R. Khan

  4. Department of Mathematics, Huzhou University, Huzhou, Zhejiang Province, 313000, China

    Yuming Chu

  5. Department of Mathematical and Computer Modeling, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan

    A. Issakhov

  6. Department of Mathematical and Computer Modeling, Kazakh British-Technical University, Almaty, 050000, Kazakhstan

    A. Issakhov

  7. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    R. Ali & S. Khan

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  1. Tiehong Zhao
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  2. M. R. Khan
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  3. Yuming Chu
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  4. A. Issakhov
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  5. R. Ali
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  6. S. Khan
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Correspondence to M. R. Khan.

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Citation: ZHAO, T. H., KHAN, M. R., CHU, Y. M., ISSAKHOV, A., ALI, R., and KHAN, S. Entropy generation approach with heat and mass transfer in magnetohydrodynamic stagnation point flow of a tangent hyperbolic nanofluid. Applied Mathematics and Mechanics (English Edition), 42(8), 1205–1218 (2021) https://doi.org/10.1007/s10483-021-2759-5

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Zhao, T., Khan, M.R., Chu, Y. et al. Entropy generation approach with heat and mass transfer in magnetohydrodynamic stagnation point flow of a tangent hyperbolic nanofluid. Appl. Math. Mech.-Engl. Ed. 42, 1205–1218 (2021). https://doi.org/10.1007/s10483-021-2759-5

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  • DOI: https://doi.org/10.1007/s10483-021-2759-5

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