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Analysis of activation energy and entropy generation in mixed convective peristaltic transport of Sutterby nanofluid

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Abstract

Peristalsis of nanofluid is significant in cancer treatment, ulcer treatment and industrial equipment. This study simulated the MHD peristaltic transport of Sutterby nanofluid with mixed convection and Hall current. Partial slip and convective conditions are imposed for flexible channel walls. Energy and concentration equations are modeled by considering the effects of Joule heating, thermal radiation, viscous dissipation and activation energy. Buongiorno nanofluid model is employed which features thermophoresis and Brownian movement aspects. The resulting nonlinear system of equations is numerically solved after employing the large wavelength and small Reynolds number supposition. Graphical analysis for the velocity, temperature, concentration, heat transfer coefficient and entropy generation is analyzed. It is observed that velocity has opposite behavior for mixed convection parameters. Temperature and heat transfer rate enhanced for Brownian movement and thermophoresis parameters. Concentration rises against larger activation energy and radiation variables. Further entropy declines against higher diffusion parameter.

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Abbreviations

\((u,v)\) :

Velocity components \(\left( {{\text{m}}\;{\text{s}}^{{ - 1}} } \right)\)

\(\left( {x,y} \right)\) :

Cartesian coordinates \(\left( {\text{m}} \right)\)

\(c\) :

Wave speed \(\left( {{\text{m}}\;{\text{s}}^{{ - 1}} } \right)\)

\(g\) :

Gravitational acceleration \(\left( {{\text{m}}\;{\text{s}}^{{ - 2}} } \right)\)

\(a\) :

Wave amplitude \(({\text{m}})\)

\(\mu\) :

Dynamic viscosity \(\left( {{\text{kg}}\;{\text{m}}^{{ - 1}} {\text{s}}^{{ - 1}} } \right)\)

\(d_{1}\) :

Half channel width \(\left( {\text{m}} \right)\)

\(p\) :

Pressure \(\left( {{\text{N}}\;{\text{m}}^{{ - 2}} } \right)\)

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

Density of nanofluid \(\left( {{\text{kg}}\;{\text{m}}^{{ - 3}} } \right)\)

\(\alpha\) :

Thermal diffusivity \(\left( {{\text{m}}^{2} \;{\text{s}}^{{ - 1}} } \right)\)

\(\lambda\) :

Wave length \(\left( {\text{m}} \right)\)

\(k\) :

Thermal conductivity \(\left( {{\text{kg}}\;{\text{mK}}^{{ - 1}} \;{\text{s}}^{{ - 3}} } \right)\)

\(c_{p}\) :

Specific heat \(\left( {{\text{m}}^{2} \;{\text{s}}^{{ - 2}} \;{\text{K}}^{{ - 1}} } \right)\)

\(\nu\) :

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

\(\beta_{T}\) :

Thermal expansion coefficient \(\left( {{\text{K}}^{ - 1} } \right)\)

\(\beta_{C}\) :

Concentration expansion coefficient \(\left( {\left( {{\text{kg}}} \right)^{{ - 1}} \;{\text{m}}^{{ - 3}} } \right)\)

\(m_{1}\) :

Mass per unit area \(\left( {{\text{kg}}\;{\text{m}}^{{ - 2}} } \right)\)

\(g\) :

Gravitational acceleration \(\left( {{\text{m}}\;{\text{s}}^{{ - 2}} } \right)\)

\(h_{1}\) :

Heat transfer rate \(\left( {{\text{kg}}\;{\text{m}}^{{ - 2}}\, {\text{K}}} \right)\)

\(\tau_{1}\) :

Elastic tension \(\left( {{\text{kg}}\;{\text{s}}^{{ - 2}} } \right)\)

\(t\) :

Time \(\left( {\text{s}} \right)\)

\(\sigma\) :

Electric conductivity \(\left( {\left( {{\text{kg}}} \right)^{{ - 1}} {\text{m}}^{{ - 2}} \;{\text{s}}^{3} \;{\text{A}}^{2} } \right)\)

\(T\) :

Fluid temperature \(\left( {\text{K}} \right)\)

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

Mean temperature \(\left( {\text{K}} \right)\)

\(C\) :

Fluid concentration \(\left( {{\text{kg}}\;{\text{m}}^{{ - 3}} } \right)\)

\(B_{0}\) :

Applied magnetic field \(\left( {{\text{kg}}\;{\text{s}}^{{ - 2}} \;{\text{A}}^{{ - 1}} } \right)\)

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

Thermophoretic diffusion coefficient \(\left( {{\text{m}}^{2} \;{\text{s}}^{1} } \right)\)

θ :

Temperature

ϕ :

Concentration

\(\psi\) :

Stream function

\(\varepsilon\) :

Amplitude ratio

\(m\) :

Hall parameter

\(Re\) :

Reynolds number

\(\delta\) :

Wave number

\(Br\) :

Brinkman number

\({ \Pr }\) :

Prandtl number

\(Ec\) :

Eckert number

\(E_{1} ,E_{2} ,E_{3}\) :

Wall parameters

\(M\) :

Hartman number

\(Rn\) :

Radiation parameter

\(\varOmega\) :

Temperature ratio parameter

\(B\) :

Fluid parameter

\(Nb\) :

Brownian motion parameter

\(Nt\) :

Thermophoresis parameter

\(Gr\) :

Thermal Grashof number

\(Gc\) :

Mass Grashof number

\(Bi_{1}\) :

Thermal Biot number

\(Bi_{2}\) :

Mass Biot number

\(\beta\) :

Slip parameter

\(Sc\) :

Schmidt number

\(\zeta\) :

Chemical reaction parameter

\(E\) :

Activation energy parameter

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Acknowledgement

We are grateful to Higher Education Commission (HEC) of Pakistan for financial Support of this work under the project No. 20-3088/NRPU/R & D/HEC/13.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    T. Hayat & Z. Nisar

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    T. Hayat, A. Alsaedi & B. Ahmad

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Hayat, T., Nisar, Z., Alsaedi, A. et al. Analysis of activation energy and entropy generation in mixed convective peristaltic transport of Sutterby nanofluid. J Therm Anal Calorim 143, 1867–1880 (2021). https://doi.org/10.1007/s10973-020-09969-1

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