Experimental investigation of thermophysical properties of R718 based nanofluids at low temperatures

Abstract

An extensive experimental investigation on the thermophysical properties of two different types of R718 (water) based nanofluid was performed for particle volume fractions (ϕ) ranging from 0.25–2.5%. R718 (water) is used as a secondary refrigerant in refrigeration systems; therefore, it is important to measure the variation in the thermophysical properties of R718 due to the addition of nanoparticles. The major highlight of the current work is the measurement of the thermophysical properties at a temperature as low as 278 K. Most of the studies available in the open literature are based on the thermophysical property measurement of nanofluids at elevated temperatures (above 293 K). In the present work, the thermophysical properties such as thermal conductivity, viscosity and density of the nanofluids were measured at a temperature varying from 5 to 25 °C (278-298 K) and were later compared with the existing theoretical models and previous experimental results. The specific heat capacity of Al₂O₃ and CuO based nanofluids was predicted and analysed using a theoretical model. The thermal conductivity of the nanofluid was measured by the Transient hot-wire method and the viscosity of the nanofluid was measured using a Cannon-Fenske viscometer. Copper oxide (CuO) and aluminium oxide (Al₂O₃) nanoparticles were chosen for the present investigation. The average particle diameter of CuO and Al₂O₃ nanoparticles was 30 nm. It was observed that the enhancement in thermal conductivity of nanofluids at low temperature (~278 K) is considerably lower than the enhancements at elevated temperatures. The viscosity measurements also revealed that the classical models can be successfully applied for predicting the viscosity of Al₂O₃ –R718 nanofluids at low particle volume fractions (ϕ < 0.5%).

Appendix

1.1 Uncertainty in thermal conductivity measurement

$$ {\displaystyle \begin{array}{l}\varDelta T=\left(\frac{q}{4\pi k}\right)\ln (t)\\ {}k=\frac{q}{4\pi \varDelta T}\ln (t)\end{array}} $$

(12)

By replacing ΔT by Resistance terms in Eq. (12), we get

$$ {\displaystyle \begin{array}{l}\varDelta T=\frac{R_w-{R}_i}{\alpha}\\ {}k=\frac{I^2{R}_w\alpha\ \ln (t)}{4\pi \left(\varDelta R\right)}\end{array}} $$

(13)

where ΔR = R_w-R_i.

The uncertainty for the term (R_w-R_i) can be computed by adding the uncertainty of the individual resistance and the uncertainty in thermal conductivity can be determined as shown in Eq. (14):

$$ {\displaystyle \begin{array}{c}\delta \left(\varDelta R\right)=\delta {R}_w+\delta {R}_i\\ {}\delta k=\left|\frac{\partial k}{\partial {R}_w}\right|\delta {R}_w+\left|\frac{\partial k}{\partial \left(\varDelta R\right)}\right|\delta \left(\varDelta R\right)\end{array}} $$

(14)

$$ \frac{\partial k}{\partial {R}_w}=\frac{I^2\alpha\ \ln (t)}{4\pi \left(\varDelta R\right)}=\frac{\left({0.116}^2\right)(0.003727)\left(\ln (2)\right)}{(4)(3.14)(0.005)} $$

$$ \left|\frac{\partial k}{\partial {R}_w}\right|\delta {R}_w=0.000040 $$

$$ \frac{\partial k}{\partial \left(\varDelta R\right)}=-\frac{I^2{R}_w\alpha \ln (t)}{4\pi {\left(\varDelta R\right)}^2}=-\frac{\left({0.116}^2\right)(4.13)(0.003727)\left(\ln (2)\right)}{(4)(3.14){(0.01)}^2} $$

$$ \left|\frac{\partial k}{\partial \left(\varDelta R\right)}\right|\delta \left(\varDelta R\right)=0.01657 $$

Therefore, total uncertainty in k is as follows:

$$ \delta k=0.000040+0.01657=0.01661\ W/ mK $$

The uncertainty in thermal conductivity measurement is ±0.01661 W/mK (±2.6%).

1.2 Uncertainty in density measurement

The density of any substance is given by:

$$ \rho =\frac{m}{V} $$

(15)

Since mass and volume are two independent measurements, it is possible to apply the quadrature equation for predicting the uncertainty [65]. The equation is as follows:

$$ \delta \rho =\sqrt{{\left(\left(\frac{\partial \rho }{\partial m}\right)\delta m\right)}^2+{\left(\left(\frac{\partial \rho }{\partial V}\right)\delta V\right)}^2} $$

(16)

$$ \frac{\partial \rho }{\partial m}=\frac{1}{V}=0.01333 $$

$$ \left(\frac{\partial \rho }{\partial m}\right)\delta m=0.000013 $$

$$ \frac{\partial \rho }{\partial V}=-\frac{m}{V^2}=-\frac{40}{(75)^2}=0.00711 $$

$$ \left(\frac{\partial \rho }{\partial V}\right)\delta V=0.01777 $$

Substituting the above values in Eq. (16), the uncertainty in density measurement was found to be

$$ \delta \rho =\sqrt{(0.000013)^2+{(0.01777)}^2}=0.0177\ g/{cm}^3 $$

The uncertainty in density measurement is ±0.0177 g/cm³ or ± 17.7 kg/m³ (±1.7%).

C. Uncertainty in Viscosity measurement.

The dynamic viscosity (μ) is given by:

$$ \boldsymbol{\mu} =\rho \nu $$

(17)

The uncertainty in viscosity measurement is as follows:

$$ \delta \mu =\sqrt{{\left(\left(\frac{\partial \mu }{\partial \rho}\right)\delta \rho \right)}^2+{\left(\left(\frac{\partial \mu }{\partial \nu}\right)\delta \nu \right)}^2} $$

(18)

Before determining the uncertainty in dynamic viscosity measurement using Eq. (18), it is important to determine the partial uncertainties for density and kinematic viscosity measurement.

The kinematic viscosity equation is given by:

$$ \nu ={C}_1t-\left(\frac{C_2}{t^2}\right) $$

The uncertainty in kinematic viscosity measurement is as follows:

$$ \delta \nu =\sqrt{{\left(\left(\frac{\partial \nu }{\partial t}\right)\delta t\right)}^2} $$

$$ \frac{\partial \nu }{\partial t}={C}_1+\left(\frac{C_2}{t^3}\right)=0.00106+2.68.{10}^{-12}=0.00106 $$

Therefore, we get δν = 0.00106 cSt since δt = 1 s.

Now, uncertainty in Dynamic viscosity can be obtained by:

$$ \delta \mu =\sqrt{{\left(\left(\frac{\partial \mu }{\partial \rho}\right)\delta \rho \right)}^2+{\left(\left(\frac{\partial \mu }{\partial \nu}\right)\delta \nu \right)}^2} $$

$$ \frac{\partial \mu }{\partial \rho }=\nu =0.8\times {10}^{-6}\ {m}^2{s}^{-1} $$

$$ {\left(\left(\frac{\partial \mu }{\partial \rho}\right)\delta \rho \right)}^2=188.67\times {10}^{-12} $$

Similarly,

$$ {\left(\left(\frac{\partial \mu }{\partial \nu}\right)\delta \nu \right)}^2=1.12\times {10}^{-12} $$

Substituting in Eq. (18), δμ was found to be:

$$ \delta \mu =1.377\times {10}^{-5}\ Pa.s $$

The uncertainty in dynamic viscosity measurement was found to be ±1.377×10⁻⁵ Pa.s or ± 0.0137 cP (±1.5%).