Comment on Alruwaele, W.H.R.; Gajjar, J.S.B. Lid-Driven Cavity Flow Containing a Nanofluid. Dynamics 2024, 4, 671–697

Pantokratoras, Asterios

doi:10.3390/dynamics6020015

First error

In ref. [1], the base fluid is water, and Table 1 in ref. [1] shows that the water density is

ρ = 997.1 (k g / m^{3})

and the thermal expansion coefficient is

β = 2.1 \times 10^{- 4} (K^{- 1})

(the term thermal conductivity coefficient in Table 1 in ref. [1] is wrong; the correct term is thermal expansion coefficient).

However, from Table 1, it can be seen that the density

ρ = 997.1 (k g / m^{3})

corresponds to a temperature of 25 °C, and at this temperature, the corresponding thermal expansion coefficient is

β = 2.6 \times 10^{- 4} (K^{- 1})

.

Table 1. Water properties at different temperatures (Bejan [2]).

The error is 19%. Equation (9) in ref. [1] is as follows:

{(ρ β)}_{m} = ϕ ρ_{p} β_{p} + (1 - ϕ) ρ_{f} β_{f}

(1)

The wrong thermal expansion coefficient of water (

β_{f}

) influences the expansion coefficient

β_{m}

in Equation (1) and both

β_{m}, β_{f}

influence the last term

R i \frac{β_{m}}{β_{f}} \frac{\partial T}{\partial x}

in Equation (4) in ref. [1]. Thus, the error is transferred to the results.

Second error

Above Section 4, in the Results and Discussion section in ref. [1], it is written that the results in ref. [1] were produced for the Prandtl number Pr = 6.9. However, from Table 1, it can be seen that at the density

ρ = 997.1 (k g / m^{3})

, the corresponding Prandtl number is Pr = 6.21. The error is 11%.

Conflicts of Interest

The author declares that he has no competing interests.

References

Alruwaele, W.H.R.; Gajjar, J.S.B. Lid-Driven Cavity Flow Containing a Nanofluid. Dynamics 2024, 4, 671–697. [Google Scholar] [CrossRef] [Scilit]
Bejan, A. Convection Heat Transfer, 4th ed.; John Wiley & Sons: Hoboken, NJ, USA, 2013. [Google Scholar]

Table 1. Water properties at different temperatures (Bejan [2]).

T (°C)	$ρ$ (g/cm³)	$μ$ (g/cm·s)	$c_{p}$ (kJ/kg·K)	$k$ (W/m·K)	Pr	β (K⁻¹)
0	0.9999	0.01787	4.217	0.56	13.44	−0.6 × 10⁻⁴
5	1	0.01514	4.202	0.57	11.13	+0.1 × 10⁻⁴
10	0.9997	0.01304	4.192	0.58	9.45	0.9 × 10⁻⁴
15	0.9991	0.01137	4.186	0.59	8.13	1.5 × 10⁻⁴
20	0.9982	0.01002	4.182	0.59	7.07	2.1 × 10⁻⁴
25	0.9971	0.00891	4.179	0.60	6.21	2.6 × 10⁻⁴
30	0.9957	0.00798	4.178	0.61	5.49	3.0 × 10⁻⁴
35	0.9941	0.00720	4.178	0.62	4.87	3.4 × 10⁻⁴
40	0.9923	0.00654	4.178	0.63	4.34	3.8 × 10⁻⁴
50	0.9881	0.00548	4.180	0.64	3.57	4.5 × 10⁻⁴
60	0.9832	0.00467	4.184	0.65	3.01	5.1 × 10⁻⁴
70	0.9778	0.00405	4.189	0.66	2.57	5.7 × 10⁻⁴
80	0.9718	0.00355	4.196	0.67	2.23	6.2 × 10⁻⁴
90	0.9653	0.00316	4.205	0.67	1.98	6.7 × 10⁻⁴
100	0.9584	0.00283	4.216	0.68	1.78	7.1 × 10⁻⁴

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