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Magnetohydrodynamic mixed convection 3-D simulations for chemically reactive couple stress nanofluid over periodically moving surface with thermal radiation

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Abstract

In the recent advancement in growing nano-technology, the dynamic scientists have shown their interest toward the thermal aspects of nanoparticles due to their prestigious industrial, engineering, medical and modern sciences applications. The current exertion discloses unsteady three-dimensional chemically reactive couple stress nanofluid flow induced by bidirectional oscillatory stretching surface. The heat transfer analysis is explored by utilizing heat generation/absorption and thermal radiation features. Additionally, the mixed convection and magnetic effects are also encountered as novelty. The flow has been generated by bidirectional periodically accelerated surface. Apposite transformations are engaged to reduce formulated nonlinear problem into dimensionless form, and then analytic series solution is computed via homotopic technique. The physical aspect of involved flow parameters is graphically entertained. A complete graphical investigation for profiles of dimensionless velocities, temperature, concentration and skin friction coefficients is deliberated for various prominent flow parameters. Furthermore, the numerical calculations for local Nusselt and Sherwood numbers are presented and discussed. The results perceived that amplitude of oscillation increases in both components of velocities and skin friction coefficients for higher couple stress parameter. It is further reported that temperature distribution enhanced for higher values of Brownian motion parameter, thermophoresis constant and radiation parameter. Moreover, the concentration distribution decreases for enhancement of Brownian motion parameter and chemical reaction parameter.

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Abbreviations

\(u,v,w\) :

Velocity components along \(\tilde{x},\tilde{y}\)and \(\tilde{z}\) \(\left( {{\text{ms}}^{ - 1} } \right)\)

\(\tilde{x},\tilde{y},\tilde{z}\) :

Coordinate axes \(\left( {\text{m}} \right)\)

\(a\) :

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

\(\bar{T}\) :

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

\(\bar{C}\) :

Nanoparticles concentration \(\left( {{\text{kg}}\,{\text{m}}^{ - 3} } \right)\)

\(\bar{T}_{{{\bar{\text{w}}}}}\) :

Wall temperature \(({\rm K})\)

\(\bar{C}_{{{\bar{\text{w}}}}}\) :

Concentration at wall \(\left( {{\text{kg}}\;{\text{m}}^{ - 3} } \right)\)

\(\bar{T}_{\infty }\) :

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

\(\bar{C}_{\infty }\) :

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

\(t\) :

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

\(\omega\) :

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

\(\eta_{ * }\) :

Material constant for couple stress parameter \(\left( {{\text{kg}}\;{\text{m}}\;{\text{s}}^{ - 1} } \right)\)

\(\rho_{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\text{f}}}}\) :

Density of base fluid \(\left( {{\text{kg}}\,{\text{m}}^{ - 3} } \right)\)

\(\sigma\) :

Electrical conductivity of base fluid \(\left( {{\text{Sm}}^{ - 1} } \right)\)

\({\rm B}_{0}\) :

Strength of magnetic field \(\left( {{\text{kg}}\,{\text{s}}^{ - 2} \,{\text{A}}^{ - 1} } \right)\)

\(\bar{g}\) :

Gravitational acceleration \(\left( {{\text{ms}}^{ - 2} } \right)\)

\(\beta_{{{\bar{\text{T}}}}}\) :

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

\(\beta_{{\bar{C}}}\) :

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

\(\alpha_{0}\) :

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

\(\varGamma_{ * }\) :

Ratio among heat capacities \(( - )\)

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

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

\(\sigma^{ * }\) :

Stefan–Boltzmann constant \(\left( {{\text{Wm}}^{ - 2}\, {\text{K}}^{ - 4} } \right)\)

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

Brownian diffusion coefficient \(\left( {\text{m}^{2} \,{\text{s}}^{ - 1} } \right)\)

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

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

\(\mu\) :

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

\(\nu\) :

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

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

Heat capacity \(\left( {{\text{m}}^{2} \,{\text{s}}^{ - 2} \,{\text{K}}^{ - 1} } \right)\)

\(f_{\upxi} ,g_{\upxi}\) :

Dimensionless velocities \(( - )\)

\(\theta\) :

Dimensionless temperature \(( - )\)

\(\phi\) :

Dimensionless concentration \(( - )\)

\(\xi ,\tau\) :

Dimensionless parameters \(( - )\)

\(S\) :

Oscillating frequency to stretching rate ratio \(( - )\)

\({\rm K}_{\text{cs}}\) :

Couple stress parameter \(( - )\)

M :

Hartman number \(( - )\)

\(N_{\text{b}}\) :

Brownian motion parameter \(( - )\)

\(\delta\) :

Heat generation/absorption constant \(( - )\)

\(\Pr\) :

Prandtl number \(( - )\)

N :

Buoyancy ratio \(( - )\)

\(N_{\text{t}}\) :

Thermophoresis parameter \(( - )\)

\(\lambda\) :

Mixed convection parameter \(( - )\)

\(R_{ \oplus }\) :

Radiation parameter \(( - )\)

\({\text{Sc}}\) :

Schmidt number \(( - )\)

\(\kappa\) :

Chemical reaction parameter \(( - )\)

\(\text{Re}_{{{\tilde{\text{x}}}}}\) :

Renolds number \(( - )\)

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

Grashof number \(( - )\)

\({\text{Nu}}_{{{\tilde{\text{x}}}}}\) :

Local Nusselt number \(( - )\)

\({\text{Sh}}_{{{\tilde{\text{x}}}}}\) :

Local Sherwood number \(( - )\)

\(q_{ * }\) :

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

\(J_{ * }\) :

Mass flux \(\left( {{\text{kg}}\,{\text{s}}^{ - 1} \,{\text{m}}^{ - 2} } \right)\)

\(k\) :

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

\(Cf_{{{\tilde{\text{x}}}}} ,Cf_{{{\tilde{\text{y}}}}}\) :

Skin friction coefficients \(( - )\)

\({\mathbb{B}}_{j} \left( {j = 1 - 10} \right)\) :

Arbitrary constants

\(\hbar_{\text{f}} ,\hbar_{\text{g}} ,\hbar_{\uptheta} ,\hbar_{\upphi}\) :

Auxiliary parameters

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Authors and Affiliations

  1. Department of Mathematics, University of Azad Jammu & Kashmir, Muzaffarabad, 13100, Pakistan

    Samaira Aziz & Iftikhar Ahmad

  2. Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

    Nasir Ali

  3. Department of Mathematics, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    Sami Ullah Khan

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  1. Samaira Aziz
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Aziz, S., Ahmad, I., Ali, N. et al. Magnetohydrodynamic mixed convection 3-D simulations for chemically reactive couple stress nanofluid over periodically moving surface with thermal radiation. J Therm Anal Calorim 146, 435–448 (2021). https://doi.org/10.1007/s10973-020-09962-8

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