Skip to main content
SpringerLink
Log in

Physical significance of chemical processes and Lorentz’s forces aspects on Sisko fluid flow in curved configuration

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Current determination is committed to characterize the features of curved surface for Sisko fluid in the presence of Lorentz’s forces. Heat–mass relocation exploration is conducted in the presence of homogeneous–heterogeneous processes and non-uniform heat sink/source. Similarity variables are designated to transmute nonlinear PDEs into ODEs. These intricate ordinary differential expressions assessing the flow situation are handled efficaciously by manipulating bvp4c scheme. Graphical demonstration is deliberated to scrutinize the variation in pressure, velocity, temperature and concentration profiles with respect to flow regulating parameters. Numerical data are displayed through tables in order to surmise variation in surface drag force and heat transport rate. It is noted that radius of curvature and temperature-dependent heat sink/source significantly affect heat–mass transport mechanisms for curved surface. Furthermore, graphical analysis reveals that velocity profile of Sisko magneto-fluid enhances for augmented values of curvature parameter. Additionally, it is evaluated that increasing values of heat source parameter and Lorentz’s forces, pressure profile exhibited the diminishing behavior.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

r, s :

Curvilinear coordinates

\( a, b, n \) :

Material constants

E, F :

Autocatalysts

\( G_{a} ,G_{b} \) :

Concentration of chemical species E and F

\( k_{1} ,k_{s} \) :

Rate coefficient of homogeneous and heterogeneous reactions

\( G_{a0} \) :

Uniform concentration

\( B_{0} \) :

Applied magnetic field

R :

Radius of curvature

V :

Velocity vector

u,v :

Velocity components

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

Fluid density

K :

Thermal conductivity

T :

Temperature of fluid

\( T_{\text{w}} \) :

Temperature at the wall

\( T_{\infty } \) :

Ambient temperature

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

Radiative heat flux

\( D_{A} ,D_{B} \) :

Diffusion coefficients of two species (E, F)

\( q^{\prime \prime \prime } \) :

Heat sink/source

C :

Constant

\( \alpha_{1} \) :

Thermal diffusivity

\( U_{w} \) :

Stretching velocity

P :

Pressure

\( A^{*} \) :

Space dependent

\( B^{*} \) :

Temperature dependent

\( \eta \) :

Dimensionless variable

\( \psi \) :

Stream function

P :

Dimensionless pressure

\( R_{d} \) :

Radiation parameter

F :

Dimensionless velocity

\( \theta \) :

Dimensionless temperature

\( \varphi \) :

Dimensionless concentration

\( \delta \) :

Unsteadiness parameter

M :

Magnetic parameter

\( \varepsilon \) :

Diffusion coefficient

Pr:

Generalized Prandtl number

\( k_{2} \) :

Strength coefficient homogenous reaction

Sc:

Generalized Schmidt number

K :

Dimensionless radius of curvature

A :

Material parameter of the Sisko fluid

\( \gamma \) :

Generalized Biot number

\( \tau_{w} \) :

Surface shear stress

\( q_{w} \) :

Surface heat flux

\( C_{\text{f}} \) :

Skin friction coefficient

\( {\text{Nu}}_{s} \) :

Local Nusselt number

\( \text{Re}_{a} ,\text{Re}_{b} \) :

Local Reynolds numbers

References

  • Ali M, Khan WA, Irfan M, Sultan F, Shahzed M, Khan M (2019a) Computational analysis of entropy generation for cross-nanofluid flow. Appl Nanosci. https://doi.org/10.1007/s13204-019-01038-w

    Article  Google Scholar 

  • Ali M, Sultan F, Khan WA, Shahzad M (2019b) Exploring the physical aspects of nanofluid with entropy generation. Appl Nanosci. https://doi.org/10.1007/s13204-019-01173-4

    Article  Google Scholar 

  • Ali M, Sultan F, Khan WA, Shahzad M, Arif H (2020) Important features of expanding/contracting cylinder for cross magneto-nanofluid flow. Chaos, Solitons Fractals 133:109656

    Article  MathSciNet  Google Scholar 

  • Anwar MS, Rasheed A (2018) Joule heating in magnetic resistive flow with fractional Cattaneo–Maxwell model. J Braz Soc Mech Sci Eng. https://doi.org/10.1007/s40430-018-1426-8

    Article  Google Scholar 

  • Asghar Z, Ali N, Ahmed R, Waqas M, Khan WA (2019) A mathematical framework for peristaltic flow analysis of non-Newtonian Sisko fluid in an undulating porous curved channel with heat and mass transfer effects. Comput Methods Program Biomed 182:105040

    Article  Google Scholar 

  • Chaudhary MA, Merkin JH (1995) A simple isothermal model for homogeneous–heterogeneous reactions in boundary-layer flow. I. Equal diffusivities. Fluid Dyn Res 16:311–333

    Article  MathSciNet  Google Scholar 

  • Deng W, Yao R, Zhao H, Yang X, Li G (2017a) A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm. Soft Comput. https://doi.org/10.1007/s00500-017-2940-9

    Article  Google Scholar 

  • Deng W, Zhao H, Zou L, Li G, Yang X, Wu D (2017b) A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput 21(15):4387–4398

    Article  Google Scholar 

  • Deng W, Zhao H, Yang X, Xiong J, Sun M, Li B (2017c) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302

    Article  Google Scholar 

  • Deng W, Xu J, Zhao H (2019) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292

    Article  Google Scholar 

  • Haq I, Shahzad M, Khan WA, Irfan M, Mustafa S, Ali M, Sultan F (2019) Characteristics of chemical processes and heat source/sink with wedge geometry. Case Stud Therm Eng 14:100432

    Article  Google Scholar 

  • Hayat T, Rashid M, Alsaedi A (2018) Three dimensional radiative flow of magnetite-nanofluid with homogeneous–heterogeneous reactions. Results Phys 8:268–275

    Article  Google Scholar 

  • Hei Y, Zhang C, Song W, Kou Y (2019) Energy and spectral efficiency tradeoff in massive MIMO systems with multi-objective adaptive genetic algorithm. Soft Comput 23:7163–7179

    Article  Google Scholar 

  • Imtiaz M, Mabood F, Hayat T, Alsaedi A (2019) Homogeneous–heterogeneous reactions in MHD radiative flow of second grade fluid due to a curved stretching surface. Int J Heat Mass Transf 145:118781

    Article  Google Scholar 

  • Irfan M, Khan M, Khan WA (2018) Interaction between chemical species and generalized Fourier’s law on 3D flow of Carreau fluid with variable thermal conductivity and heat sink/source: a numerical approach. Results Phys 10:107–117

    Article  Google Scholar 

  • Khan WA, Khan M, Alshomrani AS, Ahmad L (2016) Numerical investigation of generalized Fourierís and Fickís laws for Sisko fluid flow. J Mol Liq 224:1016–1021

    Article  Google Scholar 

  • Khan M, Irfan M, Khan WA, Alshomrani AS (2017) A new modeling for 3D Carreau fluid flow considering nonlinear thermal radiation. Results Phys 7:2692–2704

    Article  Google Scholar 

  • Khan M, Irfan M, Khan WA, Ayaz M (2018) Aspects of improved heat conduction relation and chemical processes on 3D Carreau fluid flow. Pramana J Phys. https://doi.org/10.1007/s12043-018-1579-0

    Article  Google Scholar 

  • Khan WA, Ali M, Sultan F, Shahzad M, Khan M, Irfan M (2019a) Numerical interpretation of autocatalysis chemical reaction for nonlinear radiative 3D flow of cross magnetofluid. Pramana J Phys. https://doi.org/10.1007/s12043-018-1678-y

    Article  Google Scholar 

  • Khan WA, Sultan F, Ali M, Shahzad M, Khan M, Irfan M (2019b) Consequences of activation energy and binary chemical reaction for 3D fow of Cross-nanofluid with radiative heat transfer. J Braz Soc Mech Sci 41:4. https://doi.org/10.1007/s40430-018-1482-0

    Article  Google Scholar 

  • Khan WA, Ali M, Sultan F, Shahzad M, Khan M, Irfan M (2019c) Numerical interpretation of autocatalysis chemical reaction for nonlinear radiative 3D flow of cross magnetofluid. Pramana J Phys 92:16. https://doi.org/10.1007/s12043-018-1678-y

    Article  Google Scholar 

  • Mahanthesh B, Gireesha BJ, Shashikumar NS, Hayat T, Alsaedi A (2018) Marangoni convection in Casson liquid flow due to an infinite disk with exponential space dependent heat source and cross-diffusion effects. Results Phys 9:78–85

    Article  Google Scholar 

  • Mahdy A (2019) Aspects of homogeneous-heterogeneous reactions on natural convection flow of micropolar fluid past a permeable cone. Appl Math Comput 352:59–67

    MathSciNet  MATH  Google Scholar 

  • Malik R, Khan M (2018) Numerical study of homogeneous-heterogeneous reactions in Sisko fluid flow past a stretching cylinder. Results Phys 8:64–70

    Article  Google Scholar 

  • Merkin JH (1996) A model for isothermal homogenous-heterogeneous reactions in boundarylayer flow. Math Comput Model 24:125–136

    Article  MathSciNet  Google Scholar 

  • Muhammad S, Ali G, Shah SIA, Irfan M, Khan WA, Ali M, Sultan F (2019) Numerical treatment of activation energy for the three-dimensional flow of a cross magnetonanoliquid with variable conductivity. Pramana J Phys 93:40. https://doi.org/10.1007/s12043-019-1800-9

    Article  Google Scholar 

  • Rashid M, Hayat T, Rafique K, Alsaedi A (2019) Chemically reactive flow of thixotropic nanofluid with thermal radiation. Pramana J Phys. https://doi.org/10.1007/s12043-019-1837-9

    Article  Google Scholar 

  • Shahzad M, Ali M, Sultan F, Khan WA, Hussain Z (2020) Computational investigation of magneto-cross fluid flow with multiple slip along wedge and chemically reactive species. Results Phys 16:102972

    Article  Google Scholar 

  • Shen M, Chen L, Zhang M, Liu F (2018) A renovated Buongiorno’s model for unsteady Sisko nanofluid with fractional Cattaneo heat flux. Int J Heat Mass Transf 126:277–286

    Article  Google Scholar 

  • Soomro FA, Usman M, Haq RU, Wang W (2018) Melting heat transfer analysis of Sisko fluid over a moving surface with nonlinear thermal radiation via collocation method. Int J Heat Mass Transf 126:1034–1042

    Article  Google Scholar 

  • Sultan F, Khan WA, Ali M, Shahzad M, Irfan M, Khan M (2019a) Theoretical aspects of thermophoresis and Brownian motion for three-dimensional flow of the cross fluid with activation energy. Pramana J Phys 92:21. https://doi.org/10.1007/s12043-018-1676-0

    Article  Google Scholar 

  • Sultan F, Khan WA, Ali M, Shahzad M, Sun H, Irfan M (2019b) Importance of entropy generation and infinite shear rate viscosity for non-Newtonian nanofluid. Int J Mech Sci 41:439. https://doi.org/10.1007/s40430-019-1950-1

    Article  Google Scholar 

  • Toghraie D, Esfahani NN, Zarringhalam M, Shirani N, Rostami S (2020) Blood flow analysis inside different arteries using non-Newtonian Sisko model for application in biomedical engineering. Comput Methods Program Biomed. https://doi.org/10.1016/j.cmpb.2020.105338

    Article  Google Scholar 

  • Waqas M (2020) A mathematical and computational framework for heat transfer analysis of ferromagnetic non-Newtonian liquid subjected to heterogeneous and homogeneous reactions. J Mag Mag Mater 493:165646

    Article  Google Scholar 

  • Waqas M, Jabeen S, Hayat T, Khan MI, Alsaedi A (2019) Modeling and analysis for magnetic dipole impact in nonlinear thermally radiating Carreau nanofluid flow subject to heat generation. J Magn Magn Mater. https://doi.org/10.1016/j.jmmm.2019.03.040

    Article  Google Scholar 

  • Xu NL, Xu H, Raees A (2018) Homogeneous–heterogeneous reactions in flow of nanofluids near the stagnation region of a plane surface: the Buongiorno’s model. Int J Heat Mass Transf 125:604–609

    Article  Google Scholar 

  • Zhang S, Zhao H, Xu J, Deng W (2019) A novel fault diagnosis method based on improved adaptive VMD energy entropy and PNN. Trans Can Soc Mech Eng. https://doi.org/10.1139/tcsme-2018-0195

    Article  Google Scholar 

  • Zhao H, Deng W, Li G, Lifeng Y, Bing Y (2016) Research on a new fault diagnosis method based on WT, improved PSO and SVM for motor. Recent Patents Mech Eng 9:289–298

    Article  Google Scholar 

  • Zhao H, Sun D, Deng W, Yang X (2017) A new feature extraction method based on EEMD and multi-scale fuzzy entropy for motor bearing. Entropy. https://doi.org/10.3390/e19010014

    Article  Google Scholar 

  • Zhao H, Zheng J, Xu J, Deng W (2019a) Fault diagnosis method based on principal component analysis and broad learning system. IEEE Access 7:99263–99272

    Article  Google Scholar 

  • Zhao H, Liu H, Xu J, Deng W (2019b) performance prediction using high-order differential mathematical morphology gradient spectrum entropy and extreme learning machine. IEEE Trans Instrum Meas. https://doi.org/10.1109/TIM.2019.2948414

    Article  Google Scholar 

  • Zhao H, Zheng J, Deng W, Song Y (2020) Semi-supervised broad learning system based on manifold regularization and broad network. IEEE Trans Circuits Syst I Regul Pap 67(3):983–994

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This project was funded by the postdoctoral international exchange program for incoming postdoctoral students, at Beijing Institute of Technology, Beijing, China.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, Pakistan

    M. Ali, F. Sultan & M. Shahzad

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

    M. Irfan & M. Khan

  3. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    W. A. Khan

  4. Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Kashmir, 12010, Pakistan

    W. A. Khan

Authors
  1. M. Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Irfan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. A. Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. Sultan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Shahzad
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. A. Khan.

Ethics declarations

Conflict of interest

All authors declare that they have no conflict of interest.

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ali, M., Irfan, M., Khan, W.A. et al. Physical significance of chemical processes and Lorentz’s forces aspects on Sisko fluid flow in curved configuration. Soft Comput 24, 16213–16223 (2020). https://doi.org/10.1007/s00500-020-04935-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-04935-3

Keywords

Search

Navigation