Reply to Awad, M.M. Comment on “Alam et al. Numerical Simulation of Homogeneous–Heterogeneous Reactions through a Hybrid Nanofluid Flowing over a Rotating Disc for Solar Heating Applications. Sustainability 2021, 13, 8289”

Abstract

This write-up presents a closure to the comments of Awad, M.M. (2021) on the paper “Numerical Simulation of Homogeneous–Heterogeneous Reactions through a Hybrid Nanofluid Flowing over a Rotating Disc for Solar Heating Applications” (Alam et al., 2021). The authors have addressed each of the comments in detail to uphold the correctness of the mathematical formulation together with the pertinent results presented in our published article.

Response to the Comments

The author Mohamed M. Awad [1] commented that,

Alam et al. [2] investigated hybrid nanofluid flow with heterogeneous-homogeneous reactions past a rotating disc. They presented the governing equation of temperature (Equation (5) in ref. [2]) as:

$$\left[u\frac{\partial T}{\partial r}+w\frac{\partial T}{\partial z}\right]=\left[\frac{k_h{}_{nf}}{{\left(\rho cp\right)}_{hnf}}+\frac{16{\sigma }^{*}{T}_{\infty }^3}{3k^{*}{\left(\rho cp\right)}_{hnf}}\right]\left[\frac{{\partial }^{2}T}{\partial r^2}+\frac{{\partial }^{2}T}{\partial z^2}+\frac{1}{r}\frac{\partial T}{\partial r}\right]$$

(1)

From Equation (1), temperature (T) depends on r, z.

Alam et al. [2] used these transformations (Equation (9) in Ref. [2]):

$$\eta =\sqrt{\frac{\mathsf{\Omega }}{{\upsilon }_f}}z$$

(2)

$$\theta (\eta )=\frac{T(r,z)-T_{\infty }}{T_w-T_{\infty }},$$

(3)

From Equation (2), $\eta$ depends on z only.

From Equation (3), $\theta (\eta )$ depends on z only, whereas RHS $\frac{T(r,z)-T_{\infty }}{T_w-T_{\infty }}$ depends on r, z. Hence, Equation (3) is inappropriate.

Response:

In this regard, we would like to clarify that we disagree with author’s comments. The y variation in temperature can be neglected: If the variation in temperature in the y direction is much smaller than the variation in the x direction. The assumption will be valid and consistent with the general interpretation of a small Biot condition. The temperature in an object will essentially be uniform (here in the y direction) because the dominant resistance to heat transfer occurs at the surface from convection. “This means that the energy equation is correct and valid and hence, we disagree with Author Mohamed M. Awad’s comments” [3,4].

Other comments:

However, many profiles in figures in this paper are truncated and wrong. Pantokra [5,6] discussed these common errors. Examples of these figures where profiles are truncated and wrong include:

i.

The 3rd figure about 1 impact on f’(η).

ii.

The 10th figure about Ks impact on g(η).

iii.

The 11th figure about δ* impact on g(η).

Response:

We again disagree with the author’s comments. The results and figures presented in our paper are clear based on the literature available without any error [3,4,7].