Comment on Khan et al. Impact of Irregular Heat Sink/Source on the Wall Jet Flow and Heat Transfer in a Porous Medium Induced by a Nanofluid with Slip and Buoyancy Effects. Symmetry 2022, 14, 2212

Abstract

Many errors exist in the above paper.

• First Error

In Equation (10) in [1], the dimensionless similarity variable $\xi$ is presented as follows:

$$\xi ={\left({\alpha }_f^2{x}^3\right)}^{-1/4}y$$

(1)

where ${\alpha }_f(m^2{\sec }^{-1})$ is the fluid thermal diffusivity and $x,y(m)$ are the Cartesian coordinates. From Equation (1), it is found that the units of $\xi$ are $m^{-3/4}{\sec }^{1/2}$ and the parameter $\xi$ is dimensional and wrong.

• Second Error

In Equation (10) in [1], the stream function $\psi$ is presented as follows:

$$\psi ={\left({\alpha }_f^{2}x\right)}^{1/4}F(\xi )$$

(2)

where $F(\xi )$ is a dimensionless function. From Equation (2), it is found that the units of $\psi$ are $m^{5/4}{\sec }^{-1/2}$ instead of $m^2{\sec }^{-1}$.

• Third Error

In Equation (11) in [1], the following equation is presented:

$$u={\displaystyle \frac{4}{\sqrt{x}}}F\prime (\xi )$$

(3)

where $u(m{\sec }^{-1})$ is the fluid velocity. Equation (3) is wrong because the units of the LHS are $m{\sec }^{-1}$, whereas the units of the RHS are $m^{-1/2}$. In a physics equation, all terms must have the same units.

• Fourth Error

In Equation (11) in [1], the following equation is presented:

$$\upsilon =-\sqrt{{\alpha }_f}{x}^{-3/4}\left(F(\xi )-3\xi F\prime (\xi )\right)$$

(4)

where $\upsilon (m{\sec }^{-1})$ is the fluid velocity. Equation (4) is wrong because the units of the LHS are $m{\sec }^{-1}$, whereas the units of the RHS are $m^{1/4}{\sec }^{-1/2}$.

• Fifth Error

The dimensionless mixed convection parameter is as follows:

$$\lambda ={\displaystyle \frac{g{\beta }_f{T}_0}{4}}$$

(5)

where $g(\mathrm{m}\mathrm{s}\mathrm{e}{\mathrm{c}}^{-2})$ is the gravity acceleration, ${\beta }_f(\mathrm{K}\mathrm{e}\mathrm{l}\mathrm{v}\mathrm{i}{\mathrm{n}}^{-1})$ is the thermal expansion coefficient and $T_0({\mathrm{m}}^2\mathrm{K}\mathrm{e}\mathrm{l}\mathrm{v}\mathrm{i}\mathrm{n})$. From Equation (5), it is found that the units of $\lambda$ are ${\mathrm{m}}^3{\sec }^{-2}$.

• Sixth Error

In Equations (5), (13) and (14) in [1], the term $e^{\xi }$ appears. In mathematics, $e^x$ with x dimensional is meaningless. Taking into account that $\xi (m^{-3/4}{\sec }^{1/2})$ is dimensional, Equations (5), (13) and (14) in [1] are wrong.

• Seventh Error

In the dimensionless Equation (15) in [1], the velocity slip parameter ${\Sigma }_a={\displaystyle \frac{A{\mu }_f}{\sqrt{{\alpha }_f}}}$ appears. The parameter A is included in ${\gamma }_1(x)=A{x}^{3/4}$ and the parameter ${\gamma }_1(x)$ is included in Equation (4) in [1]. From these equations, it is found that the units of ${\Sigma }_a$ are $m^{-3/4}{\sec }^{1/2}$. Therefore Equation (15) in [1] is wrong because in a dimensionless equation, all terms must be dimensionless.

• Eighth Error

Below Equation (12) in [1], the parameter $K_a={\displaystyle \frac{{\nu }_f{\epsilon }_a^2}{K_0}}$ appears. However the parameter $K_0$ is unknown.