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Discussion

# Discussion: “Numerical Study of Unsteady Jeffery Fluid Flow With Magnetic Field Effect and Variable Fluid Properties” (Mabood, F., Abdel-Rahman, R. G., and Lorenzini, G., 2016, ASME J. Therm. Sci. Eng. Appl., 8(4), p. 041003)OPEN ACCESS

[+] Author and Article Information
Asterios Pantokratoras

School of Engineering,
Democritus University of Thrace,
Xanthi 67100, Greece
e-mail: apantokr@civil.duth.gr

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received October 28, 2016; final manuscript received December 23, 2016; published online April 12, 2017. Assoc. Editor: Giulio Lorenzini.

J. Thermal Sci. Eng. Appl 9(4), 045501 (Apr 12, 2017) (1 page) Paper No: TSEA-16-1308; doi: 10.1115/1.4036013 History: Received October 28, 2016; Revised December 23, 2016

In the above paper, the energy equation (see Eq. (3) in Ref. [1]) is as follows: Display Formula

(1)$∂T∂t+u∂T∂x+v∂T∂y=1ρcp∂∂y(κ∂T∂y)+Φρcp$

where $T$ is the fluid temperature, $t$ is the time, $u$ and $v$ are the velocity components in the $x$ and $y$ directions, respectively, $ρ$ is the fluid density, $cp$ is the specific heat, $κ$ is the thermal conductivity, and $Φ$ is the heat source.

The units of temperature are

$[T]=Kelvin (temperature)$

The units of time are

$[t]=sec(time)$

Therefore, the units of $(Φ/ρcp)$ are $K s−1$ in order that this term is compatible with the other terms in Eq. (1).

The units of specific heat are

$[cp]=K−1(Kelvin−1) m2(length2) sec−2(time−2)$

The units of density are

$[ρ]=kg(mass) m−3(length−3)$

Therefore, the units of $Φ$ are Display Formula

(2)$[Φ]=kg(mass) m−1(length−1) sec−3(time−3)$

The heat source $Φ$ is given by the following equation (see p. 2 in Ref. [1]): Display Formula

(3)$Φ=κ∞ρus(x,t)μ∞xQ0[T−T∞]$

where $κ∞$ is the ambient thermal conductivity, $us(x,t)$ is the suction velocity, and $μ∞$ is the ambient dynamic viscosity. The units of thermal conductivity are

$[κ∞]=kg(mass)K−1(Kelvin−1)m(length) sec−3(time−3)$

The units of velocity are

$[us(x,t)]=m(length) sec−1(time−1)$

The units of dynamic viscosity are

$[μ∞]=kg(mass)m−1(length−1) sec−1(time−1)$

From Eqs. (2) and (3), it is found that the quantity $Q0$ is dimensionless. The heat source parameter is (see p. 3 in Ref. [1])

$γ=Q0μ∞ρcpκ∞$

and its units are

$[γ]=kg−1(mass−1)K2(Kelvin2)m−1(length−1) sec4(time4)$

This means the heat source parameter $γ$ is dimensional and not dimensionless as the authors claim. Taking into account that the heat source parameter is one of the basic parameters, the results presented by Mabood et al. [1] are doubtful.

## References

Mabood, F. , Abdel-Rahman, R. G. , and Lorenzini, G. , 2016, “ Numerical Study of Unsteady Jeffery Fluid Flow With Magnetic Field Effect and Variable Fluid Properties,” ASME J. Therm. Sci. Eng. Appl., 8(4), p. 041003.
View article in PDF format.

## References

Mabood, F. , Abdel-Rahman, R. G. , and Lorenzini, G. , 2016, “ Numerical Study of Unsteady Jeffery Fluid Flow With Magnetic Field Effect and Variable Fluid Properties,” ASME J. Therm. Sci. Eng. Appl., 8(4), p. 041003.

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