Reply to Pantokratoras, A. Comment on “Saleem et al. Thermal Case Study of Cilia Actuated Transport of Radiated Blood-Based Ternary Nanofluid Under the Action of Tilted Magnetic Field. Coatings 2022, 12, 873”

Abstract

This reply presents a point-by-point response to the comments received from Pantokratoras in our previously published research article. The comments highlighted that the values of electrical conductivity assigned to alumina (Al₂O₃), silicon dioxide (SiO₂), and titanium dioxide (TiO₂) nanoparticles were not appropriate and the experimental value of the Prandtl number for blood should remain within the range of 29–32. In response the electrical conductivity values for each nanoparticle were corrected and revised the Prandtl number values accordingly. The recomputed findings revealed that only small changes appeared in quantitative results while the overall trends and insights remained same.

We sincerely thank the editor for giving us the opportunity to improve the quality and accuracy of our work. Below we provide a detailed point-by-point response to the four specific concerns raised [1].

Point 1: First error: The base fluid in [2] is blood and the nanoparticles are alumina (Al₂O₃), silicon dioxide (SiO₂) and titanium dioxide (TiO₂); their thermophysical properties are presented in Table 1 in [2], where the alumina (Al₂O₃) electrical conductivity is σ = 36.9 × 10⁶ (Ω⁻¹·m⁻¹ = S·m⁻¹). This value is wrong for the following reason: The values presented in references [3,4,5] are experimental and agree with the values 10⁻¹⁰ S·m⁻¹ − 10⁻¹² S·m⁻¹ given by UNIPRETEC, a ceramic company in China which produces alumina. A paper published recently in Chinese Journal of Physics [6] confirms that the value σ = 36.9 × 10⁶ S·m⁻¹ is wrong.

Response: We agree that the previously used value for Al₂O₃ electrical conductivity did not reflect the established experimental values for pure alumina. Based on literature data and experimental measurements from multiple sources, we have now corrected the electrical conductivity value of pure Al₂O₃ to the appropriate order of magnitude characteristic of insulating ceramics. The revised value has been incorporated into Table 1 of the manuscript and used consistently in all related nondimensional parameter calculations.

Table 1. Thermophysical properties of the blood-based trimetallic nanoliquid.

Physical Entities	Base Fluid		Solid Nanogranules
	(Blood)	TiO2	SiO2	Al2O3
ρ (kgm−3)	1063	4250	2200	3970
σ (S·m−1)	0.8	10−10	10−15	10−12
Cp (JK−1kg−1)	3594	686.2	754	765
k (Wm−1K−1)	0.492	8.9538	1.4013	40

Table 1. Thermophysical properties of the blood-based trimetallic nanoliquid.

Physical Entities	Base Fluid		Solid Nanogranules
	(Blood)	TiO2	SiO2	Al2O3
ρ (kgm−3)	1063	4250	2200	3970
σ (S·m−1)	0.8	10−10	10−15	10−12
Cp (JK−1kg−1)	3594	686.2	754	765
k (Wm−1K−1)	0.492	8.9538	1.4013	40

Point 2: In Table 1 in [2], the silicon dioxide (SiO₂) electrical conductivity is 3.5 × 10⁶ S·m⁻¹ [7]. This value is wrong for the following reason: Silicon dioxide (SiO₂) is an excellent electrical insulator, not a conductor, because it has no mobile electrons or ions to carry an electric current. In Table 1 the silicon dioxide electrical resistivity is 10⁻¹⁵ S·m⁻¹. The electrical conductivity is the inverse of electrical resistivity and is ${10}^{-15}{\mathsf{\Omega }}^{-1}·{\mathrm{m}}^{-1}$. This error is huge.

Response: We have updated the electrical resistivity value for SiO₂ in Table 1 using established literature values for insulators. All subsequent results and figures that depend on this parameter have been recalculated accordingly in the revised manuscript.

Point 3: In Table 1 in [1] the titanium dioxide (TiO₂) electrical conductivity is 2.4 × 10⁶ (Ω⁻¹·m⁻¹ = S·m⁻¹). This value is wrong for the following reasons: The Fraunhofer Gesellschaft in Germany is reliable leading applied research organization. In its annual report 2020, in section Titanium Oxides-Electrical All-Rounders in Fraunhofer [8] there is a table with electrical resistivity of different titanium oxides (TiO₂, Ti₉O₁₇, Ti₆O₁₁, Ti₅O₉, etc.). The electrical resistivity of (TiO₂) is 10¹² (Ωcm) = 10¹⁰ (Ωm). The electrical conductivity is the inverse of resistivity and the electrical conductivity of (TiO₂) is 10^-10 (S·m⁻¹). This value is completely different from that in [2]. AZoM [9] is an online publication for the Materials Science community. The error is huge. A paper with exactly the same error has been criticized, by the present author, in [10].

Response: We have revised the electrical conductivity value used for TiO₂ to reflect reliable materials data where TiO₂ is known to exhibit high resistivity and thus low conductivity. The updated value appears in the revised Table 1. All subsequent results and figures that depend on this parameter have been recalculated accordingly in the revised manuscript.

Point 4: The blood specific heat and thermal conductivity are presented in Table 1 in [2]. The blood dynamic viscosity is included in reference [11]. These Prandtl numbers agree with that calculated in reference [12]. However, in Figures 5–7 in [2], results are presented for Prandtl numbers Pr = 1, 1.2, 1.4 and 1.6, and in Table 3 in [2], results are presented for Pr = 1. All these results do not correspond to blood and are wrong.

Response: The thermophysical properties of blood have been re-evaluated from the established literature, yielding a physiologically realistic Prandtl number range of Pr = 29–32; Table 2 and all previously plotted figures/tables have been updated accordingly.

Table 2. The heat transfer rate for conventional blood, mono nanofluid, hybrid nanofluid, and tri-hybrid nanofluid with fixed values of Ec = 0.1, Pr = 29 and R_n = 1.

M	Conventional Blood	Mono Nanofluid	% Increase	Bi-Hybrid Nanofluid	% Increase	Ternary Nanofluid	% Increase
0.5	6.34074	6.51325	2.72	6.64594	4.81	6.87585	8.44
1	7.53337	7.69317	2.12	7.80526	3.61	8.06958	7.12
1.5	9.51133	9.65037	1.46	9.72860	2.28	10.0501	5.66
2	12.2617	12.3726	0.90	12.4043	1.16	12.8053	4.33
2.5	15.7698	15.8186	0.31	15.8454	0.48	16.3212	3.50

Table 2. The heat transfer rate for conventional blood, mono nanofluid, hybrid nanofluid, and tri-hybrid nanofluid with fixed values of Ec = 0.1, Pr = 29 and R_n = 1.

M	Conventional Blood	Mono Nanofluid	% Increase	Bi-Hybrid Nanofluid	% Increase	Ternary Nanofluid	% Increase
0.5	6.34074	6.51325	2.72	6.64594	4.81	6.87585	8.44
1	7.53337	7.69317	2.12	7.80526	3.61	8.06958	7.12
1.5	9.51133	9.65037	1.46	9.72860	2.28	10.0501	5.66
2	12.2617	12.3726	0.90	12.4043	1.16	12.8053	4.33
2.5	15.7698	15.8186	0.31	15.8454	0.48	16.3212	3.50

Figure 1a–c (corresponding to Figure 5a–c in [2]) indicate that ternary nanofluid temperature rises when the elevated values of the Hartmann number and the Prandtl number are considered, while the smaller values of radiation number further enhance the temperature distribution.

Figure 1. Alterations in temperature profile of trihybrid nanofluid for distinct values of (a) the Hartmann number Ha, (b) the thermal radiation number R_n, and (c) the Prandtl number Pr.

Figure 1. Alterations in temperature profile of trihybrid nanofluid for distinct values of (a) the Hartmann number Ha, (b) the thermal radiation number R_n, and (c) the Prandtl number Pr.

Figure 2a–c (corresponding to Figure 6a–c in [2]) reveal that entropy generation near the peripheral part of the channel can be minimized for smaller values of the Hartmann number and Prandtl number. In contrast, enhancing the radiation parameter substantially lowers entropy generation, implying that thermal radiation effects contribute effectively to curtail irreversibility in the fluid stream.

Figure 2. Variations in entropy generation number distribution for distinct values of (a) the Hartmann number Ha, (b) the thermal radiation number R_n, and (c) the Prandtl number Pr.

Figure 2. Variations in entropy generation number distribution for distinct values of (a) the Hartmann number Ha, (b) the thermal radiation number R_n, and (c) the Prandtl number Pr.

Figure 3a–c (corresponding to Figure 7a–c in [2]) show that the Bejan number increases with rising Hartmann number and Prandtl number values, but it decreases as the radiation parameter increases. It is further observed that, in Figure 3a (corresponding to Figure 7a in [2]), heat transfer irreversibility is the major source of total irreversibility. In contrast, Figure 3b,c (corresponding to Figure 7b,c in [2]) show that the contribution of heat transfer irreversibility reduces, and the system’s overall irreversibility becomes dominant.

Figure 3. Alterations in the Bejan number distribution for distinct values of (a) the Hartmann number Ha, (b) the thermal radiation number R_n, and (c) the Prandtl number Pr.

Figure 3. Alterations in the Bejan number distribution for distinct values of (a) the Hartmann number Ha, (b) the thermal radiation number R_n, and (c) the Prandtl number Pr.