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Natural Convection Immersion Cooling of the Cylinders in Nanofluids: Developing a New Nusselt Number Correlation

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

This study focuses on exploring the natural convection heat transfer within water-alumina nanofluids and its practical applications in immersion cooling. The aim is to improve the efficiency of this cooling method by utilizing fluids with improved thermal properties. The selected geometry is a vertical cylinder, which is of great significance in engineering applications and academic research. The used nanofluid consists of \({{\text{Al}}}_{2}{{\text{O}}}_{3}-{\text{water}}\) nanofluid, with varying volume fractions (0.1, 0.2, and 0.5%). Experimental assessments were carried out using a steady-state methodology. Numerical simulations employ the single-phase and two-phase mixture approaches. The results of this research reveal the impressive accuracy of the mixture method in simulating external natural convection when compared to concurrently obtained experimental data. Furthermore, in the present paper, the single-phase method has yielded results deemed acceptable and closely aligned with the outcomes from the two-phase method. This alignment was achieved through the utilization of appropriate relationships, ensuring the accurate estimation of thermophysical properties. Notably, it becomes evident that established correlations for the Nusselt number correlation of natural convection designed for conventional fluids and the mere incorporation of the thermophysical properties of nanofluids are insufficient for the accurate prediction of the Nusselt number for nanofluids. In response to this challenge, a novel Nusselt correlation is introduced, comprehensively considering the thermophysical properties of \({{\text{Al}}}_{2}{{\text{O}}}_{3}-{\text{water}}\) nanofluids, nanoparticle transport mechanisms, geometric attributes of the studied object, and nanoparticle volume fraction. Comparative assessments with previous correlations emphasize the enhanced predictive accuracy of the proposed innovative correlation.

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Abbreviations

\({A}_{s}\) :

Total surface area (\({{\text{m}}}^{2})\)

BGF :

Body gravity function

BFF :

Body fluid function

G :

BGF. Based on the characteristic length \(\sqrt{A}\)

\({G}_{dyn}\) :

Dynamic BGF. Based on the characteristic length \(\sqrt{A}\)

\({C}_{p}\) :

Specific heat capacity (J/kg K)

\({d}_{bf}\) :

Equivalent diameter of a base fluid molecule, m

\({d}_{p}\) :

Particle diameter (m)

g :

Gravitational acceleration vector (m/\({{\text{s}}}^{2}\))

\({G}_{up}\) :

Upper bound for BGF.

\({G}_{low}\) :

Lower bound for BGF.

h :

Heat transfer coefficient of nanofluid (W/\({{\text{m}}}^{2}\) K)

H :

Enthalpy (\({\text{J}}/{\text{kg}})\)

\({H}_{c}\) :

Characteristic length (m)

J :

Drift flux (\({\text{kg}}/{{\text{m}}}^{2}{\text{s}})\)

k :

Thermal conductivity (W/m K)

\({k}_{eff}\) :

Effective thermal conductivity of the nanofluid, \({\text{W}}/\mathrm{m K}\)

\({L}_{c}\) :

Characteristic length (m)

Nu :

Nusselt number (dimensionless)

\({Nu}_{0}\) :

Conduction limit (dimensionless)

\({Nu}_{\sqrt{A}}\) :

Nusselt number based on the characteristic length \(\sqrt{A}\) (dimensionless)

\({Nu}_{\sqrt{A}}^{0}\) :

Conduction limit based on the characteristic length \(\sqrt{A}\) (dimensionless)

P :

Pressure (Pa)

Pr :

Prandtl number (dimensionless)

q :

Heat flux (W/\({{\text{m}}}^{2}\))

Ra :

Rayleigh number (dimensionless)

Re :

Reynolds number (dimensionless)

\({S}_{T}\) :

Thermophoretic parameter (dimensionless)

T :

Temperature (K)

\({T}_{fr}\) :

Freezing point of the base fluid, K

\({T}_{s}\) :

Surface temperature, K

V :

Velocity vector \(({\text{m}}/{\text{s}})\)

\({V}_{pm}\) :

Drift velocity (\({\text{m}}/{\text{s}})\)

\(\alpha\) :

Thermal diffusivity (\({{\text{m}}}^{2}/{\text{s}})\)

\(\beta\) :

Thermal expansion coefficient (1/K)

\(\mu\) :

Viscosity (Pa s)

\(\rho\) :

Density (kg/\({{\text{m}}}^{3}\))

\(\tau\) :

Shear stress (Pa)

\(\upsilon\) :

Drift velocity (\(m/s)\)

\(\varphi\) :

Volume fraction (dimensionless)

bf:

Base fluid

nf:

Nanofluid

p:

Particle

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Authors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, Shiraz, 71936-16548, Iran

    Fatemeh Dehbozorgi, Khosrow Jafarpur & Ebrahim Goshtasbi Rad

Authors
  1. Fatemeh Dehbozorgi
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  2. Khosrow Jafarpur
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  3. Ebrahim Goshtasbi Rad
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Corresponding author

Correspondence to Ebrahim Goshtasbi Rad.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work report in this paper.

Appendices

Appendix

Uncertainty analysis

Uncertainty analysis is done according to the method given in (Moffat 1988). The result R is assumed to be calculated from a set of measurements as

$$R = R\left( {X_{1} ,X_{2} , \ldots ,X_{N} } \right)$$
(42)

where \(X_{1} ,X_{2} , \ldots ,X_{N}\). are independent variables in function R. If the uncertainty in each variable is \(\delta X_{i}\), then the overall uncertainty is calculated by the Eq. (33).

$$\delta R = \left[ {\left( {\frac{\partial R}{{\partial X_{1} }}} \right)^{2} \left( {\delta X_{1} } \right)^{2} + \left( {\frac{\partial R}{{\partial X_{2} }}} \right)^{2} \left( {\delta X_{2} } \right)^{2} + \ldots + \left( {\frac{\partial R}{{\partial X_{N} }}} \right)^{2} \left( {\delta X_{N} } \right)^{2} } \right]^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}}$$
(43)

Therefore, according to Eqs. (21) and (22), and \(Q = VI\). the uncertainty Nu number measurements has been calculated. The accuracy of measurements is listed in Table 6. Error estimation based on the experimental data of the present research can be seen in (Table 7).

Table 6 Measurements' accuracy
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Table 7 Error estimation based on the experimental data of the present research
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Dehbozorgi, F., Jafarpur, K. & Rad, E.G. Natural Convection Immersion Cooling of the Cylinders in Nanofluids: Developing a New Nusselt Number Correlation. Iran J Sci Technol Trans Mech Eng (2024). https://doi.org/10.1007/s40997-024-00759-w

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  • DOI: https://doi.org/10.1007/s40997-024-00759-w

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