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Investigation for mixed convection flow of physiological fluid due to non-uniform vertical complex channel with entropy generation effects

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Abstract

A theoretical mathematical model has been proposed to analyze the combined heat and mass transfer impact due to peristaltic flow of Carreau-Yasuda nanofluid model. The flow is causing by non-uniform complex wavy channel with convergent and divergent characterization. The analysis is updated with applications of entropy generation applications. The investigation for enhancement in heat transfer is visualized by adopting the nonlinear radiated impact. Furthermore, the mixed convection and activation energy effects. Both surfaces of non-uniform channel are specified at distinct zeta potential. The utilization of governing theories along with the Poisson Boltzmann equation have been incorporated to model the problem. The simplification of problem is incorporated via Debye–Huckel linearization. The numerical method based on shooting technique is suggested to simulates the problem. The physical characteristics of flow problem in view of involved parameters is presented.

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Abbreviations

\({\overline{E}}_{\overline{{\text{X}}}}\) :

Axial electric field

\(\overline{C}\) :

Nanoparticle concentration

\({\in }_{1}\) :

Dielectric constant

\({\text{Sh}}\) :

Sherwood number

\({C}_{0},{C}_{1}\) :

Concentration at walls

\(v\) :

Radial (transverse) velocity component in dimensionless form

\({D}_{{\text{B}}}\) :

Brownian diffusion coefficient

\(\overline{P}\) :

Pressure in wave frame

\({D}_{{\text{c}}}\) :

Diffusivity of chemical species

\(y\) :

Transverse coordinate in dimensionless form

\({E}_{S}\) :

Entropy generation number

\({\text{We}}\) :

Weissenberg number

\({K}_{{\text{B}}}\) :

Boltzmann constant

\(\Phi \) :

Phase difference

\({S}_{\mathrm{i j}},\mathrm{ i},{\text{j}}=\mathrm{1,2},3\) :

Extra stress tensor

\({\xi }_{1},{\xi }_{2}\) :

Zeta potentials at walls

\(\overline{U}\) :

Axial velocity component in wave frame

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

Nusselt number

\(\overline{X}\) :

Axial coordinate in wave frame

\({U}_{{\text{hs}}}\) :

Helmholtz-Smoluchowski velocity

\({e}_{{\text{i}}},{\text{i}}=\mathrm{1,2},\mathrm{3,4}\) :

Amplitude of the peristaltic wave

\({a}_{1},{a}_{2}\) :

Half widths of the channel

\(\overline{t}\) :

Time

\(\overline{T}\) :

Temperature

\({\lambda }_{{\text{d}}}\) :

Debye-length of electric double layer

\({C}_{{\text{p}}}\) :

Specific heat capacity of nano-particles

\({\rho }_{{\text{e}}}\) :

Density of net ionic energy

\({C}_{{\text{f}}}\) :

Specific heat capacity of fluid

\({\rho }_{{\text{f}}}\) :

Fluid density

\({R}_{\upxi }\) :

Zeta potential ratio parameter

\({\text{Gr}}\) :

Thermal Grashof number

\({\text{Gc}}\) :

Concentration Grashof number

\({\sigma }_{{\text{e}}}\) :

Electric conductivity

\({H}_{1},{H}_{2}\) :

Lower and upper walls

\({\text{Be}}\) :

Bejan number

\({\text{Br}}\) :

Brinkman number

\(n\) :

Power law index

\({\text{Ec}}\) :

Eckert number

\(\overline{Y}\) :

Transverse coordinate in wave frame

\({\text{Nb}}\) :

Brownian motion parameter

\(\overline{V}\) :

Radial (transverse) velocity component in wave frame

\({\text{Nt}}\) :

Dimensionless Thermophoresis parameter

\({D}_{{\text{T}}}\) :

Thermophoresis diffusion coefficient

\(T{\prime}\) :

Averaging temperature of electrolyte

\(S\) :

Joule heating parameter

\(e\) :

Electronic charge

\(\delta \) :

Wave number

\(k\) :

Electro-osmotic parameter

\({h}_{1},{h}_{2}\) :

Lower and upper walls in dimensionless form

\(u\) :

Axial velocity component in dimensionless form

\({\text{Pe}}\) :

Peclet number

\(x\) :

Axial coordinate in dimensionless form

\({T}_{{\text{m}}}\) :

Mean temperature of fluid

\(z\) :

Charge balance

\({\text{Re}}\) :

Reynolds number

\(\alpha \) :

Dimensionless fluid parameter

\({T}_{0},{T}_{1}\) :

Temperature at walls

\({\text{Rd}}\) :

Thermal radiation parameter

\(\Omega \) :

Temperature ratio parameter

\(\theta \) :

Dimensionless temperature

\({K}_{f}\) :

Thermal conductivity

\(E\) :

Dimensionless potential distribution

\(\psi \) :

Steam fuction

\(\phi \) :

Dimensionless concentration

\(F\) :

Flow rate in wave frame

\({K}_{r}\) :

Chemical reaction parameter

\({E}_{\alpha }\) :

Activation energy parameter

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Authors and Affiliations

  1. Department of Mechanical Engineering, Prince Mohammad Bin Fahd University, P. O. Box 1664, 31952, Al-Khobar, Kingdom of Saudi Arabia

    M. Ijaz Khan

  2. Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 13100, Pakistan

    A. Abbasi

  3. Department of Mathematics, Namal University, Mianwali, 42250, Pakistan

    Sami Ullah Khan

  4. Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah, Saudi Arabia

    Hala A. Hejazi

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  1. M. Ijaz Khan
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Khan, M.I., Abbasi, A., Khan, S.U. et al. Investigation for mixed convection flow of physiological fluid due to non-uniform vertical complex channel with entropy generation effects. Eur. Phys. J. Plus 139, 349 (2024). https://doi.org/10.1140/epjp/s13360-024-05123-0

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