Effects of aggregation on TiO2–ethylene glycol nanoliquid over an inclined cylinder with exponential space-based heat source: sensitivity analysis


The current study investigates the impact of nanoparticle (NP) aggregation on nanoliquid flow over an inclined elongating cylinder with an exponential space-related heat source. The dynamic viscosity and thermal conductivity for aggregation structure are modeled by utilizing the Modified Krieger-Dougherty Model and Bruggeman Model correspondingly. The governing equations are solved numerically. Further, the regression model for friction coefficient and heat transport rate is obtained by utilizing the Response Surface Methodology for various space-based heat source parameter (\(0.5 \le Q_{\text{E}} \le 1.5\)), mixed convection parameter (\(1 \le \lambda \le 3\)) and NPs volume fraction (\(0.01 \le \phi \le 0.05\)). The velocity profile exhibited dual features for different values of curvature parameter and NPs volume fraction. The space-based exponential heat source and mixed convection have an enhancing impact on the skin friction coefficient. It is noticed that the heat transport augments with the addition of nanoparticles. The coefficient of friction is found to be more sensitive to the NPs volume fraction. Further, the heat transport rate is more sensitive toward exponential heat source than NP’s volume fraction and mixed convection.

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a :

Radius of the cylinder (m)

x :

Axial direction

r :

Radial coordinate

u :

Velocity along axial direction (m s−1)

v :

Velocity along radial direction (m s−1)

\(U_{\text{w}} \left( x \right)\) :

Free stream velocity (m s−1)

D :

Fractal index

R :

Radius of aggregates (m)

R p :

Radius of primary nanoparticle (m)

Pr :

Prandtl number

Gr :

Grashof number

l :

Characteristic length (m)

n :

Exponential index

T :

Temperature (K)

T :

Ambient temperature (K)

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

Constant temperature along the stretching cylinder

c 1 :

Positive constant

g :

Acceleration due to gravity (m s−2)

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

Exponential space-related heat source parameter

Sf :

Skin friction coefficient

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

Specific heat (J kg−1 K−1)

k :

Thermal conductivity (W m−1 K−1)

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

Nusselt number

\(Re_{\text{x}}\) :

Local Reynolds number

β 0 :

Thermal expansion coefficient (K−1)

\(\varTheta\) :

Angle of inclination

λ :

Mixed convection parameter

μ :

Dynamic viscosity (kg m s−1)

ρ :

Density (kg m−3)

ν :

Kinematic viscosity (m2 s−1)

γ :

Curvature parameter

ϕ :

Nanoparticle volume fraction


Nanoparticle volume fraction within the aggregate




Base liquid




Nanoparticle aggregation


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The authors are grateful to the Management of CHRIST (Deemed to be University), Bangalore, India, for their kind support. The authors also thank the Editor and the anonymous reviewers for their valuable and constructive comments.

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Correspondence to B. Mahanthesh.

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Mahanthesh, B., Thriveni, K. Effects of aggregation on TiO2–ethylene glycol nanoliquid over an inclined cylinder with exponential space-based heat source: sensitivity analysis. J Therm Anal Calorim (2021). https://doi.org/10.1007/s10973-020-10516-1

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  • Nanoparticle aggregation
  • Nanoliquid
  • Inclined cylinder
  • Exponential space-based heat source
  • Response surface methodology
  • Sensitivity analysis