1 Introduction

In the paper^[1], the transformed equations that have been solved are as follows (see Eqs. (12) and (13) in Ref. [1]):

(1)

(2)

where is the local inertia parameter, M=σ B₀² (1 - αt)/(ρc) is the magnetic parameter, K₁ = ν² Re_x/(KU²) is the permeability parameter, Re_x =Ux/ν is the local Reynolds number, and E_c =U²/(c_p(T_s - T₀))=c²x²/((1 - αt)²(c_p(T_s - T₀))) is the Eckert number (see Page 1618 in Ref. [1]). In order to make sure that E_c is constant, (T_s - T₀) should have the form of (T_s - T₀)=Tx²/(1 - αt)². Thus, the results work only for m=2.

It is clear that the dimensionless parameters F, M, K₁, and E_c are functions of the independent variable x, and this means that the problem treated in Ref. [1] is non-similar. However, the authors ignored this fact and treated the problem as a similar one. In other words, the partial differential equations (5)-(7) in Ref. [1] cannot be reduced to the ordinary (similarity) differential equations (12) and (13), and they should be solved as non-similar equations (see Ref. [2]).

By taking into account all the above, the results presented in Ref. [1] are doubtful.