Discussion on “Higher Order Chemical Reaction and Radiation Effects on Magnetohydrodynamic Flow of a Maxwell Nanofluid With Cattaneo–Christov Heat Flux Model Over a Stretching Sheet in a Porous Medium” (Reddy Vinodkumar, M. and Lakshminarayana, P., 2022, ASME J. Fluids Eng., 144(4), p. 041204)

Abstract

The most important development in Fluid Mechanics during the 20th century was the concept of boundary layer flow introduced by Prandtl in Ref. [1]. A boundary layer is that layer of fluid which forms in the vicinity of a surface bounding the fluid. Every time a fluid moves along a surface a boundary layer near the surface appears. Therefore, boundary layers exist in the interior of water pipes, in sewer pipes, in irrigation channels, near the earth's surface, and around buildings due to winds, near airplane wings, around a moving car, at the river bottom, inside the blood vessels and so on. Therefore, it is a popular field in Fluid Mechanics for engineers, physicists, and mathematicians. Hundreds of papers are published each year in this field. However, errors appear in many papers. Four usual errors made in investigation of boundary layer flows have been analyzed by Pantokratoras in Ref. [2]. The most usual error is that concerning the truncation of velocity and temperature profiles, and this kind of errors exist in Ref. [3]. The analysis of errors in Ref. [3] follows.In Ref. [3] the boundary conditions (11) are as follows: (1)f′=0,θ=0,ϕ=0 asη→∞where f′ is the nondimensional fluid velocity, θ is the nondimensional temperature, and ϕ is the nondimensional concentration. In Eq. (1), η→∞ means a very long η.In Fig. 1 of the present work, the dimensionless temperature profile taken from Fig. 11 of Ref. [3] is shown. It is seen that the temperature profile from Ref. [3] does not approach the ambient condition asymptotically but intersects the horizontal axis with a steep angle (the profile by Ref. [3] is a straight line). At the same figure, it is shown a correct profile (sketch), proposed by the present author, which extends to high values of transverse component η and approaches smoothly the ambient condition. In Fig. 11 of Ref. [3], the calculations have been restricted to a maximum η equal to 5. It is obvious that this calculation domain is insufficient to capture the real shape of profile and a higher value of η is needed.According to above analysis, most of the curves in Figs. 3, 5, 6, 8–16, 18–21 in Ref. [3] are incorrect.The temperature gradient θ′(0)=∂θ(0)∂η at point A, which lies at the sheet, is quite different in the work presented in Ref. [3] and the corrected profile. This means that ALL −θ′(0) values in Tables 1–4 in Ref. [3] are wrong. More information on the truncation error is given by Pantokratoras in Ref. [4]. Recently a similar paper with truncated profiles has been retracted [5].From Fig. 1 of Ref. [3], it is clear that the x axis is horizontal, and the y axis is vertical. The horizontal momentum equation (2) in Ref. [3] is as follows: (2)u∂u∂x+v∂u∂y=υ∂2u∂y2−λ1(u2∂2u∂x2+2uv∂2u∂x∂y+v2∂2u∂y2)−υku−σB02uρ+g(βT(T−T∞)+βC(C−C∞)It is well known that gravity acts in the vertical direction. Therefore, the gravity term g(βT(T−T∞)+βC(C−C∞) in Eq. (2) must be zero. For the same reason, the gravity terms Grθ and Gcϕ in the transformed equation (8) in Ref. [3] must be zero.