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Entropy generation analysis on zero mass flux effects of nonlinear mixed convective Williamson nanofluid flow with christov-Cattaneo heat flux

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Abstract

The passage of non-Newtonian fluids across the stretching plate exerts a significant impact and finds applications in various industrial sectors, such as fluidics networks, fluid agitation, thermal reactors, liquid chromatography, semiconductors, tissue regeneration, and gene delivery to organs. In this study, we investigated the hydrodynamic Williamson nanofluid flow over a stretchy surface with zero mass flux, Christov–Cattaneo (C–C) theory, non-linear mixed convection, and passive controls of nanomaterials. Thermophoresis and Brownian motion impressions are also taken in the present flow. The second law of thermodynamics is also used to determine the entropy generation. By using the proper similarity alterations, the PDEs (governing equations) are converted into non-linear ODEs. To crack the non-linear ODEs, the homotopy analysis method is used. There is a detailed discussion of the effects of magnetic, Weissenberg, radiation, Brownian motion, the Bejan parameter, and the entropy creation of various factors. Additionally, the heat, mass transfer rate, and skin friction are assessed. Also, compare skin friction and the Nusselt number with previous studies. The Weissenberg number and Brinkman parameter shows the opposite tendency in entropy generation and Bejan number profiles.

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Data availability

Data available upon request.

Abbreviations

\(\hat{a}\) :

Stretchy rate \(\left( {{\text{s}}^{ - 1} } \right)\)

\(Bi\) :

Biot parameter

\(Be\) :

Bejan parameter

\(Br\) :

Brinkman parameter

\(B_{0}\) :

Constant magnetic field \(\left( {{\text{kgs}}^{ = 2 } {\text{A}}^{ - 1} } \right)\)

\(C\) :

Concentration \(\left( {{\text{kgm}}^{ - 3} } \right)\)

\(Cr\) :

Reaction rate number

\(c_{p}\) :

Specific heat at constant pressure \(\left( {{\text{J kg}}^{ - 1} {\text{K}}^{ - 1} } \right)\)

\(C_{\infty }\) :

Free stream concentration \(\left( {{\text{kgm}}^{ - 3} } \right)\)

\(C_{w}\) :

Fluid concentration at wall \(\left( {{\text{kgm}}^{ - 3} } \right)\)

\(C_{f}\) :

Skin-friction coefficient

\(D_{B} \;{\text{and}}\;D_{T}\) :

Brownian and Thermophoresis diffusion coefficients \(\left( {{\text{m}}^{2} {\text{s}}^{ - 1} } \right)\)

\(E_{G}\) :

Entropy creation number

\(Ec\) :

Eckert parameter

\(f\left( \eta \right)\) :

Velocity similarity function

\(f_{w}\) :

Suction/blowing parameter

\(h_{f}\) :

Convective heat transmission coefficient \(\left( {{\text{W}} {\text{m}}^{ - 1} {\text{K}}^{ - 1} } \right)\)

\(k\) :

Thermal conductivity \(\left( {{\text{W}} {\text{m}}^{ - 1} {\text{K}}^{ - 1} } \right)\)

\(Le\) :

Lewis number

\(M\) :

Hartmann parameter

\(Nb\) :

Brownian motion number

\(Nt\) :

Thermophoresis number

\(Nu\) :

Nusselt parameter

\(N^{*}\) :

Ratio of concentration to thermal buoyancy forces

\(Pr\) :

Prandtl number

\(Q_{0}\) :

Heat source/sink coefficient

\(\hat{q}\) :

Heat flux \(\left( {{\text{W}} {\text{m}}^{ - 2} } \right)\)

\(Rd\) :

Radiation number

\(Re\) :

Reynolds parameter

\(Sh\) :

Sherwood parameter

\(S\) :

Heat source parameter

\(T\) :

Temperature \(\left( {\text{K}} \right)\)

\(T_{\infty }\) :

Free stream temperature \(\left( {\text{K}} \right)\)

\(T_{f}\) :

Convective surface temperature \(\left( {\text{K}} \right)\)

\(\hat{u}_{{\text{w}}}\) :

Sheet velocity \(\left( {{\text{m}} {\text{s}}^{ - 1} } \right)\)

\(\hat{u}, \hat{v}\) :

Velocity apparatuses in \(\left( {\widehat{x, }\hat{y}} \right)\) axes \(\left( {{\text{m}} {\text{s}}^{ - 1} } \right)\)

\(\hat{v}_{{\text{w}}} > 0\) :

Suction velocity

\(\hat{v}_{{\text{w}}} < 0\) :

Blowing velocity

\(We\) :

Weissenberg number

\(\widehat{x, }\hat{y}\) :

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

PDEs:

Partial differential equations

ODEs:

Ordinary differential systems

C–C:

Christov–Cattaneo heat flux

\(\beta\) :

Relaxation time

\(\beta_{t}\) :

Nonlinear mixed convection temperature component

\(\beta_{C}\) :

Nonlinear mixed convection concentration component

\(\phi \left( { \eta } \right)\;{\text{and}}\;\theta \left( { \eta } \right)\) :

Concentration and tedmperature similarity functions

\(\Gamma\) :

Non-dimensional velocity slip parameter

\(\gamma\) :

Non-dimensional thermal relaxation time

\(\eta\) :

Similarity parameter

\(\lambda_{T}\) :

Thermal relaxation time

\(\lambda\) :

Non-dimensional immovable

\({\upnu }\) :

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

\(\Omega\) :

Non-dimensional temperature variance

\(\tau\) :

Ratio of the effective heat capacity

\(\rho\) :

Density \(\left( {{\text{kgm}}^{ - 1} } \right)\)

\(\sigma\) :

Electrical conductance variable \(\left(\mathrm{S m}\right)\)

\(\psi\) :

Stream function \(\left({\text{m}}{ {\text{s}}}^{-1}\right)\)

\(\zeta\) :

Non-dimensional concentration variance

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Authors and Affiliations

  1. Department of Mathematics, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Chengalpattu, 603203, Tamil Nadu, India

    D. Mahalakshmi & B. Vennila

  2. Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, 303007, Rajasthan, India

    K. Loganathan

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  1. D. Mahalakshmi
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  2. B. Vennila
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  3. K. Loganathan
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Correspondence to B. Vennila.

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Mahalakshmi, D., Vennila, B. & Loganathan, K. Entropy generation analysis on zero mass flux effects of nonlinear mixed convective Williamson nanofluid flow with christov-Cattaneo heat flux. J. Appl. Math. Comput. 70, 1171–1192 (2024). https://doi.org/10.1007/s12190-024-02005-7

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