# Analysis of the effects of inclination angle, nanoparticle volume fraction and its size on forced convection from an inclined elliptic cylinder in aqueous nanofluids

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## Abstract

In this work, a detailed numerical investigation has been carried out to study the forced convection heat transfer from an inclined elliptic cylinder of a fixed aspect ratio of 0.5 immersed in a streaming water-based Al_{2}O_{3} nanofluid using the two-phase Buongiorno’s model. In particular, this study presents extensive numerical results on how the cylinder inclination angle, nanoparticle volume fraction and its size are going to influence the local flow, temperature and nanoparticle concentration fields in the vicinity of the cylinder surface as well as the gross engineering parameters like the drag coefficient and Nusselt number over the following ranges of conditions as: Reynolds number, \(0.01 \le Re \le 40\); cylinder inclination angle, \(0 \le \lambda \le 90\); nanoparticle volume fraction, \(0 \le \phi \le 0.06\) and two nanoparticle sizes (*d*_{np}), namely 30 nm and 60 nm. It has been found that both the Nusselt number and drag force increase with \(\phi\), but decrease with *d*_{np} under otherwise identical conditions. On the other hand, at a particular value of *Re*, \(\phi\) and *d*_{np}, the value of the average Nusselt number increases with the increasing values of \(\lambda\), whereas the value of the drag coefficient decreases. Finally, from an application standpoint, a simple analytical formula for the average Nusselt number is provided as a function of *Re*, \(\phi\) and \(\lambda\) which will facilitate the interpolation of the present results for the intermediate values of these governing parameters.

## Keywords

Nanofluids Elliptic cylinder Forced convection Buongiorno’s model Inclination angle## List of symbols

*a*Semi-minor axis (m)

*b*Semi-major axis (m)

- AR
Aspect ratio of the cylinder (=

*a*/*b*), dimensionless*C*_{p,bf}Specific heat capacity of base fluid (J kg

^{−1}K^{−1})*C*_{p,np}Specific heat capacity of nanoparticle (J kg

^{−1}K^{−1})*C*_{p,nf}Specific heat capacity of nanofluid (J kg

^{−1}K^{−1})*C*_{D}Total drag coefficient, dimensionless

*D*_{∞}Diameter of the outer domain (m)

*d*_{np}Diameter of the nanoparticle (nm)

*F*_{D}Total drag force (N)

*h*Heat transfer coefficient (W m

^{−2}K^{−1})*k*_{bf}Thermal conductivity of base fluid (W m

^{−1}K^{−1})*k*_{np}Thermal conductivity of nanoparticle (W m

^{−1}K^{−1})*k*_{nf}Thermal conductivity of nanofluid, (W m

^{−1}K^{−1})*n*_{s}Unit normal vector, dimensionless

*Nu*_{l}Local Nusselt number, dimensionless

*Nu*Average Nusselt number, dimensionless

*P*Pressure, dimensionless

*Pr*Prandtl number, dimensionless

*Re*Reynolds number, dimensionless

*S*Surface area of the cylinder, m

^{2}*T*Temperature, K

- ∆
*T* Temperature difference, (=

*T*_{w}−*T*_{∞}), K**U**Velocity vector, dimensionless

*U*_{∞}Velocity at the inlet (ms

^{−1})

## List of Greek symbols

*κ*Boltzmann constant (m

^{2}kg s^{−2}K^{−1})*ρ*_{bf}Density of base fluid (kg m

^{−3})*ρ*_{np}Density of nanoparticle (kg m

^{−3})*ρ*_{nf}Density of nanofluid (kg m

^{−3})*µ*_{bf}Viscosity of base fluid (Pa s)

*µ*_{nf}Viscosity of nanofluid (Pa s)

*θ*Temperature, dimensionless

- \(\phi\)
Volume fraction of nanoparticle, dimensionless

## Subscripts

- w
Condition at the cylinder surface

- ∞
Condition corresponds to far away from the cylinder surface

- bf
Base fluid

- np
Nanoparticle

- nf
Nanofluid

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