Advertisement

Consequences of activation energy and binary chemical reaction for 3D flow of Cross-nanofluid with radiative heat transfer

  • W. A. Khan
  • F. Sultan
  • M. Ali
  • M. Shahzad
  • M. Khan
  • M. Irfan
Technical Paper

Abstract

In view of ecological concern and energy security, execution of refrigeration system should be enriched which can be done by improving the characteristics of working liquids. The nanoliquids have gained interest in industrial and engineering fields due to their outstanding thermophysical features. Researchers used nanoliquids as working liquid and detected substantial variations in thermal performance. In the present research work, our intention is to explore the impact of nonlinear thermal radiation and variable thermal conductivity on 3D flow of cross-nanofluid. Moreover, heat sink–source, chemical processes and activation energy are implemented. Zero mass flux relation with thermophoresis and Brownian motion mechanisms are scrutinized. The required system of ordinary ones is achieved by implementing appropriate transformations. The achieved system of ordinary ones is computed numerically by implementing bvp4c scheme. Graphs are plotted to explore the impact of various physical parameters on concentration, temperature and velocity fields. It is detected from obtained graphical data that thermophoresis and Brownian motion mechanisms significantly affect heat transport mechanism. Furthermore, graphical analysis reveals that concentration of cross-nanofluid enhances for augmented values of activation energy.

Keywords

3D flow Activation energy Cross-fluid model Nanoparticles Nonlinear thermal radiation New mass flux boundary conditions 

List of symbols

\(u,v,w\)

Velocity components (ms−1)

\(x,y,z\)

Space coordinates (ms−1)

\(n\)

Power law index

\(m\)

Fitted rate constant

\(\left( {\rho c} \right)_{\text{f}}\)

Heat capacity of fluid

\(T\)

Temperature of fluid (K)

\(k(T)\)

Variable thermal conductivity \(\left( {\frac{{\text{W}}}{{{\text{mK}}}}} \right)\)

\(\alpha_{1}\)

Thermal diffusivity (ms−1)

\(k^{*}\)

Boltzmann constant

\(D_{\text{B}}\)

Brownian diffusion coefficient

\(D_{\text{T}}\)

Thermophoresis diffusion coefficient \(\left( {\frac{{{\text{m}}^{2} }}{\text{s}}} \right)\)

\(C\)

Nanoparticles concentration (K)

\(Q_{0}\)

Dimensional heat source/sink parameter

\(E_{\text{a}}\)

Activation energy

\(a,b\)

Positive constants

\(B_{0}\)

Magnetic field strength \(\left( {\frac{{\text{A}}}{{\text{M}}}} \right)\)

\(C_{\infty }\)

Ambient concentration

\(T_{\infty }\)

Ambient fluid temperature (K)

\(k_{\infty }\)

Thermal conductivity far away from stretched surface

\(h_{\text{f}}\)

Heat conversion coefficient \(\left( {\frac{\text{W}}{{{\text{Km}}^{2} }}} \right)\)

\(f,g\)

Dimensionless velocities

\(C_{fx} ,C_{fy}\)

Skin fractions

\(Nu_{x}\)

Local Nusselt number

\(M\)

Magnetic parameter

\(U_{w} \left( {x,t} \right),V_{w} \left( {y,t} \right)\)

Stretching velocities (ms−1)

\(E\)

Activation energy

\(We_{1} ,We_{2}\)

Local Weissenberg numbers

\(Pr\)

Prandtl number

\(Le\)

Lewis number

\(q_{\text{r}}\)

Nonlinear radiative heat flux

\(N_{\text{b}}\)

Brownian motion parameter

\(N_{\text{t}}\)

Thermophoresis parameter

\(R_{\text{d}}\)

Radiation parameter

\(\left( {\rho c} \right)_{\text{p}}\)

Effective heat capacity of a nanoparticle

\(Re_{x}\)

Local Reynolds number

\(\alpha\)

Ratio of stretching rates parameter

\(k_{\text{c}}\)

Chemical reaction constant

Greek symbols

\(\gamma\)

Biot number

\(\tau\)

Effective heat capacity ratio

\(\lambda\)

Dimensionless heat source or sink parameter

\(\phi\)

Dimensionless concentration

\(\sigma\)

Stefan–Boltzmann constant \(\left( {\frac{{\text{S}}}{{\text{m}}}} \right)\)

\(\eta\)

Dimensionless variable

\(\theta_{\text{f}}\)

Temperature ratio parameter

\(\rho_{\text{f}}\)

Fluid density \(\left( {\frac{\text{kg}}{{{\text{m}}^{3} }}} \right)\)

\(\theta\)

Dimensionless temperature

\(\varepsilon\)

Thermal conductivity parameter

\(\nu\)

Kinematics viscosity \(\left( {{\text{m}}^{2} {\text{s}}^{ - 1} } \right)\)

References

  1. 1.
    Khan WA, Khan M, Malik R (2014) Three-dimensional flow of an Oldroyd-B nanofluid towards stretching surface with heat generation/absorption. PLoS ONE 9(8):e10510Google Scholar
  2. 2.
    Sheikholeslami M, Ellahi R (2015) Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid. Int J Heat Mass Transf 89:799–808CrossRefGoogle Scholar
  3. 3.
    Khan M, Khan WA (2015) Forced convection analysis for generalized Burgers nanofluid flow over a stretching sheet. AIP Adv 5:107138.  https://doi.org/10.1063/1.4935043 CrossRefGoogle Scholar
  4. 4.
    Sandeep N, Kumar BR, Kumar MSJ (2015) A comparative study of convective heat and mass transfer in non-Newtonian nanofluid flow past a permeable stretching sheet. J Mol Liq 212:585–591CrossRefGoogle Scholar
  5. 5.
    Rehman S, Haq RU, Khan ZH, Lee C (2016) Entropy generation analysis for non-Newtonian nanofluid with zero normal flux of nanoparticles at the stretching surface. J Taiwan Inst Chem Eng 63:226–235CrossRefGoogle Scholar
  6. 6.
    Khan M, Khan WA (2016) MHD boundary layer flow of a power-law nanofluid with new mass flux condition. AIP Adv 6:025211.  https://doi.org/10.1063/1.4942201 CrossRefGoogle Scholar
  7. 7.
    Haq RU, Khan ZH, Hussain ST, Hammouch Z (2016) Flow and heat transfer analysis of water and ethylene glycol based Cu nanoparticles between two parallel disks with suction/injection effects. J Mol Liq 221:298–304CrossRefGoogle Scholar
  8. 8.
    Khan M, Khan WA (2016) Steady flow of Burgers’ nanofluid over a stretching surface with heat generation/absorption. J Braz Soc Mech Sci Eng 38(8):2359–2367CrossRefGoogle Scholar
  9. 9.
    Khan M, Khan WA, Alshomrani AS (2016) Non-linear radiative flow of three-dimensional Burgers nanofluid with new mass flux effect. Int J Heat Mass Transf 101:570–576CrossRefGoogle Scholar
  10. 10.
    Rahman SU, Ellahi R, Nadeem S, Zaigham Zia QM (2016) Simultaneous effects of nanoparticles and slip on Jeffrey fluid through tapered artery with mild stenosis. J Mol Liq 218:484–493CrossRefGoogle Scholar
  11. 11.
    Raju CSK, Sandeep N, Sugunamma V (2016) Unsteady magneto-nanofluid flow caused by a rotating cone with temperature dependent viscosity: a surgical implant application. J Mol Liq 222:1183–1191CrossRefGoogle Scholar
  12. 12.
    Reddy JVR, Kumar KA, Sugunamma V, Sandeep N (2017) Effect of cross diffusion on MHD non-Newtonian fluids flow past a stretching sheet with non-uniform heat source/sink: a comparative study. Alex Eng J.  https://doi.org/10.1016/j.aej.2017.03.008 CrossRefGoogle Scholar
  13. 13.
    Hayat T, Rashid M, Imtiaz M, Alsaedi A (2017) Nanofluid flow due to rotating disk with variable thickness and homogeneous–heterogeneous reactions. Int J Heat Mass Transf 113:96–105CrossRefGoogle Scholar
  14. 14.
    Raju CSK, Hoque MM, Anika NN, Mamatha SU, Sharma P (2017) Natural convective heat transfer analysis of MHD unsteady Carreau nanofluid over a cone packed with alloy nanoparticles. Powder Technol 317:408–416CrossRefGoogle Scholar
  15. 15.
    Khan M, Ahmad L, Khan WA (2017) Numerically framing the impact of radiation on magnetonanoparticles for 3D Sisko fluid flow. J Braz Soc Mech Sci Eng 39(11):4475–4487CrossRefGoogle Scholar
  16. 16.
    Hayat T, Javed M, Imtiaz M, Alsaedi A (2017) Double stratification in the MHD flow of a nanofluid due to a rotating disk with variable thickness. Eur Phys J Plus 132:146CrossRefGoogle Scholar
  17. 17.
    Khan M, Irfan M, Khan WA (2017) Impact of forced convective radiative heat and mass transfer mechanisms on 3D Carreau nanofluid: a numerical study. Eur Phys J Plus.  https://doi.org/10.1140/epjp/i2017-11803-3 CrossRefGoogle Scholar
  18. 18.
    Kumar KA, Reddy JVR, Sugunamma V, Sandeep N (2017) Impact of frictional heating on MHD radiative ferrofluid past a convective shrinking surface. Defect Diffus Forum 378:157–174CrossRefGoogle Scholar
  19. 19.
    Sandeep N (2017) Effect of aligned magnetic field on liquid thin film flow of magnetic-nanofluids embedded with graphene nanoparticles. Adv Powder Technol 28:865–875CrossRefGoogle Scholar
  20. 20.
    Santhosh HB, Raju CSK (2018) Unsteady Carreau radiated flow in a deformation of graphene nanoparticles with heat generation and convective conditions. J Nanofluids 7:1130–1137CrossRefGoogle Scholar
  21. 21.
    Anantha Kumar K, Ramana Reddy JV, Sugunamma V, Sandeep N (2018) Magnetohydrodynamic Cattaneo-Christov flow past a cone and a wedge with variable heat source/sink. Alex Eng J 57(1):435–444CrossRefGoogle Scholar
  22. 22.
    Raju CSK, Saleem S, Mamatha SU, Hussain I (2018) Heat and mass transport phenomena of radiated slender body of three revolutions with saturated porous: Buongiorno’s model. Int J Therm Sci 132:309–315CrossRefGoogle Scholar
  23. 23.
    Khan WA, Alshomrani AS, Alzahrani AK, Khan M, Irfan M (2018) Impact of autocatalysis chemical reaction on nonlinear radiative heat transfer of unsteady three-dimensional Eyring–Powell magneto-nanofluid flow. Pramana J Phys.  https://doi.org/10.1007/s12043-018-1634-x CrossRefGoogle Scholar
  24. 24.
    Anantha Kumar K, Sugunamma V, Sandeep N, Ramana Reddy JV (2018) Impact of Brownian motion and thermophoresis on bio convective flow of nanoliquids past a variable thickness surface with slip effects. Multidiscip Model Mater Struct.  https://doi.org/10.1108/MMMS-02-2018-0023 CrossRefGoogle Scholar
  25. 25.
    Kumar KA, Reddy JVR, Sugunamma V, Sandeep N (2018) Impact of cross diffusion on MHD viscoelastic fluid flow past a melting surface with exponential heat source. Multi Mod Mat Str.  https://doi.org/10.1108/MMMS-12-2017-0151 CrossRefGoogle Scholar
  26. 26.
    Santhosh HB, Raju CSK (2018) Carreau fluid over a radiated shrinking sheet in a suspension of dust and titanium alloy nanoparticles with heat source. J Integr Neurosci.  https://doi.org/10.3233/jin-180083 CrossRefGoogle Scholar
  27. 27.
    Santhosh HB, Raju CSK (2018) Partial slip flow of radiated Carreau dusty nanofluid over exponentially stretching sheet with non-uniform heat source or sink. J Nanofluids 7:72–81CrossRefGoogle Scholar
  28. 28.
    Alshomrani AS, Ullah MZ, Capizzano SS, Khan WA, Khan M (2018) Interpretation of chemical reactions and activation energy for unsteady 3D flow of Eyring–Powell magneto-nanofluid. Arab J Sci Eng.  https://doi.org/10.1007/s1336 CrossRefGoogle Scholar
  29. 29.
    Anantha Kumar K, Ramana Reddy JV, Sugunamma V, Sandeep N (2018) Simultaneous solutions for MHD flow of Williamson fluid over a curved sheet with non-uniform heat source/sink. Heat Transf Res.  https://doi.org/10.1615/heattransres.2018025939 CrossRefGoogle Scholar
  30. 30.
    Durgaprasad P, Varma SVK, Hoque MM, Raju CSK (2018) Combined effects of Brownian motion and thermophoresis parameters on three-dimensional (3D) Casson nanofluid flow across the porous layers slendering sheet in a suspension of graphene nanoparticles. Neural Comput Appl.  https://doi.org/10.1007/s00521-018-3451-z CrossRefGoogle Scholar
  31. 31.
    Ramadevi B, Sugunamma V, Kumar KA, Reddy JVR (2018) MHD flow of Carreau fluid over a variable thickness melting surface subject to Cattaneo-Christov heat flux. Multi Mod Mat Str.  https://doi.org/10.1108/MMMS-12-2017-0169 CrossRefGoogle Scholar
  32. 32.
    Saleem S, Nadeem S, Rashidi MM, Raju CSK (2018) An optimal analysis of radiated nanomaterial flow with viscous dissipation and heat source. Microsyst Technol.  https://doi.org/10.1007/s00542-018-3996-x CrossRefGoogle Scholar
  33. 33.
    Anantha Kumar K, Reddy JVR, Sugunamma V, 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.  https://doi.org/10.1615/interjfluidmechres.2018025940 CrossRefGoogle Scholar
  34. 34.
    Upadhya SM, Raju CSK, Saleem S, Alderremy AA (2018) Modified Fourier heat flux on MHD flow over stretched cylinder filled with dust, graphene and silver nanoparticles. Results Phys 9:1377–1385CrossRefGoogle Scholar
  35. 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 387:474–497CrossRefGoogle Scholar
  36. 36.
    Irfan M, Khan M, Khan WA, Ayaz M (2018) Modern development on the features of magnetic field and heat sink/source in Maxwell nanofluid subject to convective heat transport. Phys Lett A 382(30):1992–2002CrossRefGoogle Scholar
  37. 37.
    Lakshmi KB, Kumar KA, Reddy JVR, Sugunamma V (2019) Influence of nonlinear radiation and cross diffusion on MHD flow of Casson and Walters-B nanofluids past a variable thickness sheet. J Nanofluids 8:73–83CrossRefGoogle Scholar
  38. 38.
    Khan WA, Khan M, Alshomrani AS (2016) Impact of chemical processes on 3D Burgers fluid utilizing Cattaneo-Christov double-diffusion: applications of non-Fourier’s heat and non-Fick’s mass flux models. J Mol Liq 223:1039–1047CrossRefGoogle Scholar
  39. 39.
    Khan WA, Alshomrani AS, Khan M (2016) Assessment on characteristics of heterogeneous–homogeneous processes in three-dimensional flow of Burgers fluid. Results Phys 6:772–779CrossRefGoogle Scholar
  40. 40.
    Khan MI, Waqas M, Hayat T, Imran Khan M, Alsaedi A (2017) Numerical simulation of nonlinear thermal radiation and homogeneous–heterogeneous reactions in convective flow by a variable thicked surface. J Mol Liq 246:259–267CrossRefGoogle Scholar
  41. 41.
    Khan MI, Waqas M, Hayat T, Imran Khan M, Alsaedi A (2017) Chemically reactive flow of upper-convected Maxwell fluid with Cattaneo-Christov heat flux model. J Braz Soc Mech Sci Eng 39(11):4571–4578CrossRefGoogle Scholar
  42. 42.
    Khan WA, Irfan M, Khan M, Alshomrani AS, Alzahrani AK, Alghamdi MS (2017) Impact of chemical processes on magneto nanoparticle for the generalized Burgers fluid. J Mol Liq 234:201–208CrossRefGoogle Scholar
  43. 43.
    Mustafa M, Khan JA, Hayat T, Alsaedi A (2017) Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy. Int J Heat Mass Transf 108:1340–1346CrossRefGoogle Scholar
  44. 44.
    Ariel PD (2007) The three-dimensional flow past a stretching sheet and the homotopy perturbation method. Comput Math Appl 54:920–925MathSciNetCrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • W. A. Khan
    • 1
  • F. Sultan
    • 1
    • 2
  • M. Ali
    • 1
  • M. Shahzad
    • 1
  • M. Khan
    • 3
  • M. Irfan
    • 3
  1. 1.Department of MathematicsHazara UniversityMansehraPakistan
  2. 2.Department of Mathematical AnalysisGhent UniversityGhentBelgium
  3. 3.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

Personalised recommendations