Comment on the paper: “Thermal radiation and chemical reaction effects on boundary layer slip flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet, M.R. Krishnamurthy, B.J. Gireesha, B.C. Prasannakumara, and Rama Subba Reddy Gorla, Nonlinear Engineering 2016, 5(3), 147-159”

Asterios Pantokratoras

doi:10.1515/nleng-2018-0183

Article Open Access

Comment on the paper: “Thermal radiation and chemical reaction effects on boundary layer slip flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet, M.R. Krishnamurthy, B.J. Gireesha, B.C. Prasannakumara, and Rama Subba Reddy Gorla, Nonlinear Engineering 2016, 5(3), 147-159”

Asterios Pantokratoras

Published/Copyright: July 12, 2019

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From the journal Nonlinear Engineering Volume 8 Issue 1

Abstract

The present comment concerns some doubtful results included in the above paper.

In the above paper the concentration equation is as follows (equation 4 in [1])

u∂C∂x+v∂C∂y=DB∂2C∂y2+DTT∞∂2T∂y2−k0(C−C∞)(1)

In the above equation the units of each term are sec^–1C. Therefore the units of k₀ must be sec^–1 in order that the term k₀(C – C_∞) is compatible with the other terms in equation (1).

The non-dimensional chemical reaction parameter is defined as (equation 15 in [1])

y(y)=k0Lea(2)

Taking into account that the symbol used in figures is y it is clear that in equation (2) the correct symbol is y and y is a misprint. In equation (2)Le=νfDB is the dimensionless Lewis number and a is a constant which appears in the following equation

uw(x)=axn(3)

From equation (3) it is found that the units of a are

[a]=m1−n(length)1−nsec−1(time)−1

Therefore the units of chemical reaction parameter are

[y]=mn−1(length)n−1

This means that the chemical reaction parameter is dimensional, not dimensionless, as the authors claim. The chemical reaction parameter is dimensionless and correct only for the case n = 1. However, there are many results with n ≠ 1 in [1]. It is reminded here that the physical phenomena are treated with universal dimensionless numbers, not dimensional. See for example the view of Paul Dirac (Nobel Prize in Physics 1933) about dimensionless numbers in Buckley and Peat [2].

"Now, there is another dimensionless number which is of importance. If you have an electron and a proton, the electric force between them is inversely proportional to the square of the distance; the gravitational force is also inversely proportional to the square of the distance; the ratio of those two forces does not depend on the distance. The ratio gives you a dimensionless number. Of course it doesn’t depend on what units you’re using. It’s a number provided by nature and we should expect that a theory will some day provide a reason for it."

In conclusion the results in Krishnamurthy et al. [1] for n ≠ 1 are not correct.

References

[1] M.R. Krishnamurthy, B.J. Gireesha, B.C. Prasannakumara, and Rama Subba Reddy Gorla, “Thermal radiation and chemical reaction effects on boundary layer slip flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet”, Nonlinear Engineering, 5(3) (2016) 147-159.10.1515/nleng-2016-0013Search in Google Scholar

[2] P. Buckley(ed.), F.D. Peat(ed.) (1996) Glimpsing Reality: Ideas in Physics and Link to Biology, University of Toronto Press.Search in Google Scholar

Received: 2018-12-02

Accepted: 2018-12-14

Published Online: 2019-07-12

Published in Print: 2019-01-28

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