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Effects of aggregation kinetics on nanoscale colloidal solution inside a rotating channel

A thermal framework

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Abstract

The objective of the present investigation is to reveal the effects of aggregation kinetics on the nanofluid flow between two revolving plates. Additionally, we have presumed that the upper surface of the revolving structure is permeable while the lower one is blessed to move with variable speed. Here we have introduced Nimonic 80A alloy nanoparticles with water as a base liquid. Aggregation kinetics at molecular level has been introduced mathematically to model our work and to explore how aggregation features affect the thermal integrity of the system. Similarity technique guided us to avail non-dimensional form of leading equations. RK-4 method along with shooting technique aids us to solve nonlinear ODEs. Several features of aggregation parameters on velocity and temperature profile have been explored through graphs and tables. Results extract that effective thermal conductivity of aggregated composite increases for nanoparticle volume fraction. Heat transport drops off for radius of gyration factor at lower segment but rises at upper regime.

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Abbreviations

\({\varvec{\Omega}}\) :

Angular velocity

\(\left( {u,v,w} \right)\) :

Velocity along \(x,y,z\,{\text{axis}}\)

\(U_{\text{w}}\) :

Stretching velocity

\(T_{0}\) :

Temperature of the upper surface

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

Temperature of the lower surface

\(T\) :

Nanofluid temperature

\(\rho\) :

Density

\(\mu\) :

Dynamic viscosity

\(\kappa\) :

Thermal conductivity

\(\left( {C_{\text{p}} } \right)\) :

Heat capacitance

\(v_{\text{w}}\) :

Suction/injection parameter

\(\alpha_{\text{nf}} = \frac{{\kappa_{\text{nf}} }}{{\left( {\rho C_{\text{p}} } \right)_{\text{nf}} }}\) :

Nanofluid thermal diffusivity

\(\phi\) :

Nanoparticle volume fraction

\(\phi_{\text{int}}\) :

Nanoparticle volume fraction within aggregate

\(A_{\text{k}}\) :

Kapitza radius

\(p\) :

Aspect ratio

\(R\) :

Average radius of gyration

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

Fractal dimension

\(d_{\text{l}}\) :

Chemical dimension

\(N\) :

Number of particles

\(a\) :

Radius of primary particles

\(\delta = \frac{{bh^{2} }}{{\nu_{\text{f}} }}\) :

Reynolds number

\(Pr = \frac{{\mu_{\text{f}} \left( {\rho C_{p} } \right)_{\text{f}} }}{{\rho_{\text{f}} \kappa_{\text{f}} }}\) :

Prandtl number

\(S = \frac{{v_{\text{w}} }}{bh}\) :

Suction/injection parameter

\(\lambda = \frac{{\varOmega h^{2} }}{{\nu_{\text{f}} }}\) :

Rotation parameter

\(Nu\) :

Nusselt number

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

Skin friction

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

Reduced Nusselt number

\(C_{\text{fr}}\) :

Reduced skin friction

\({Re}_{\text{x}} = \frac{{U_{\text{w}} x}}{{\nu_{\text{f}} }}\) :

Local Reynold’s number

a:

Aggregate

c:

Backbone

nc:

Dead end

f:

Fluid

nf:

Nanofluid

s:

Nanoparticle

max:

Maximum

eff:

Effective

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, West Bengal, 700032, India

    Nilankush Acharya & Prabir Kumar Kundu

  2. Department of Mathematics, Krishnagar Govt. College, Krishnagar, Nadia, West Bengal, 741101, India

    Kalidas Das

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  1. Nilankush Acharya
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Acharya, N., Das, K. & Kundu, P.K. Effects of aggregation kinetics on nanoscale colloidal solution inside a rotating channel. J Therm Anal Calorim 138, 461–477 (2019). https://doi.org/10.1007/s10973-019-08126-7

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