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

Alam et al. [1] investigated hybrid nanofluid flow with heterogeneous-homogeneous reactions past a rotating disc. They presented the governing equation of temperature (Equation (5) in [1]) as:

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

(1)

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

Alam et al. [1] used these transformations (Equation (9) in [1]):

$$\eta =\sqrt{\frac{\Omega }{{\nu }_f}}z$$

(2)

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

(3)

From Equation (2), η depends on z only.

From Equation (3), θ(η) depends on z only because $\eta =\sqrt{\frac{\Omega }{{\nu }_f}}z$ whereas RHS $\frac{T(r,z)-T_{\infty }}{T_w-T_{\infty }}$ depends on r, z. Hence, Equation (3) is inappropriate.

Pantokratoras [2,3,4,5,6] indicated that the θ(η) expression is inappropriate. In [6], he presented the correct η form in Minkowycz and Sparrow [7] as:

$$\eta =\left[\frac{g\beta (T_w-T_{\infty })}{4{\nu }^2}\right]\frac{y}{x^{1/4}}$$

(4)

From Equation (4), η depends on x, y only, which is in agreement with the governing equation of temperature in Minkowycz and Sparrow [7]:

$$u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}=\alpha \frac{{\partial }^{2}T}{\partial y^2}$$

(5)

However, Alam et al. [1] expressed their governing equation of temperature (Equation (1) in these comments) as a function of both r, z.

In 2021, Awad [8] indicated that the θ(η) expression is inappropriate.

In their results, Alam et al. [1] presented graphically the various variables effects on the temperature and velocity.

However, many profiles in figures in this paper are truncated and wrong. Pantokratoras [9,10] discussed these common errors. Examples of these figures where profiles are truncated and wrong include:

i

The 3rd figure about ϕ₁ impact on f′(η);

ii

The 10th figure about K_s impact on g(η);

iii

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