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Investigation on TiO2–Cu/H2O hybrid nanofluid with slip conditions in MHD peristaltic flow of Jeffrey material

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Abstract

Slippage impacton peristaltic transport of MHD hybrid nanofluids (TiO2–Cu/H2O) in an asymmetric channel is addressed. Impact of viscous dissipation and Hall current are analyzed in the modeling as well. Constitutive expressions for viscoelastic Jeffery fluid are employed. The mathematical expressions of the problem are transformed into a set of ordinary differential equations by employing appropriate quantities. Well-known long wavelength assumption is invoked. The obtained dimensionless model is then numerically solved with the help of Adams–Bashforth method. The effects of sundry parameters on flow distributions are demonstrated via plots.

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Abbreviations

\(h_{1} (x , {\text{ t)}}\) :

Right wall in fixed frame

\(h_{2} (x , {\text{ t)}}\) :

Left wall in fixed frame

\(a_{1}\) :

Right wall amplitude

\(a_{2}\) :

Left wall amplitude

\(d_{1} + d_{2}\) :

Width of the channel

\(\overline{p}\) :

Pressure (Pa)

\(T\) :

Temperature (K)

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

Mean temperature (K)

\(\left( {\overline{U} ,\overline{V} } \right)\) :

Velocity component in fixed frame (ms−1)

\(\varvec{S}\) :

Extra stress tensor (Pa)

\(c_{\text{p}}\) :

Specific heat (JK−1 kg−1)

\(M\) :

Hartmann number

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

Grashof number

\(Q_{\text{o}}\) :

Heat source/sink parameter (Wm−2 K−1)

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

Brinkman number

\(\text{Re}\) :

Reynolds number

\(\Pr\) :

Prandtl number

\(m\) :

Hall parameter

\(n\) :

Shape factor

\(\overline{\beta }_{1}\) :

Velocity slip parameter

\(\overline{{\beta_{2} }}\) :

Thermal slip parameter

\(\varPhi\) :

Nanoparticles volume fraction

\(\lambda\) :

Wavelength (m)

\(\delta\) :

Wave number (dimensionless)

\(\psi\) :

Stream function (m2 s−1)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\sigma\) :

Electric conductivity (m−3 kg−1 s3 A2)

\(\kappa\) :

Thermal conductivity (Wm−1 K−1)

\(\beta\) :

Thermal expansion (K−1)

\(\varepsilon\) :

Dimensionless heat source/sink parameter

\(\lambda_{1}\) :

Relaxation to Radiation time ratio

\(\lambda_{2}\) :

Retardation time

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

Base fluid

\({\text{nf}}\) :

Nanofluid

\({\text{hnf}}\) :

Hybrid nanofluid

\({\text{s}}_{1}\) :

First solid component

\({\text{s}}_{2}\) :

Second solid component

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock, 43600, Pakistan

    Aamir Ali, Sana Mumraiz & M. Awais

  2. Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia

    S. Saleem

  3. Mathematics and Its Applications in Life Sciences Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Anber Saleem

  4. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Anber Saleem

  5. Department of Mathematics, Faculty of Engineering and Technology, Islamia College Peshawar, Jamrod Road, University Campus, Peshawar, Khyber Pakhtunkhwa, 25120, Pakistan

    D. N. Khan Marwat

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  1. Aamir Ali
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  2. S. Saleem
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Ali, A., Saleem, S., Mumraiz, S. et al. Investigation on TiO2–Cu/H2O hybrid nanofluid with slip conditions in MHD peristaltic flow of Jeffrey material. J Therm Anal Calorim 143, 1985–1996 (2021). https://doi.org/10.1007/s10973-020-09648-1

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