Letter to the editor

Citation

Pantokratoras, A. (2015), "Letter to the editor", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 7. https://doi.org/10.1108/HFF-12-2014-0377

Letter to the editor

Article Type: Letter to the editor From: International Journal of Numerical Methods for Heat & Fluid Flow, Volume 25, Issue 7.

Comment on “‘Joule heating effect on magnetohydrodynamic mixed convection boundary layer flow with variable electrical conductivity’ by Md Anwar Hossain and Rama Subba Reddy Gorla, International Journal of Numerical Methods for Heat & Fluid Flow, 2013, 23(2):275-288”

In the above paper the mixed convection flow of an electrically conducting and viscous incompressible fluid past an isothermal vertical surface with Joule heating in the presence of a uniform transverse magnetic field is investigated. It was assumed that the electrical conductivity of the fluid varies linearly with the transverse velocity component. The governing boundary layer equations were solved numerically.

The energy equation used by the authors is the following (equation (4) in Hossain and Gorla, 2013):

where u and v are the velocities along the x and y axes, T is the fluid temperature, α is the thermal diffusivity, σ0 is the fluid electrical conductivity, B is the strength of the magnetic field, ρ is the fluid density, Cp is the specific heat and U∞ is the ambient fluid velocity.

On page 278 it is mentioned that “In energy equation, effects of Joule heating and viscous dissipation are also considered”. However, the viscous dissipation term is missing from the energy Equation (1). On the same page it is mentioned that “Further, we neglected viscous dissipation term in the energy equation”.

On page 283 the following transformed energy equation appears (equation (30c) in Hossain and Gorla, 2013):

In the above Equation (2) the last term is a viscous dissipation term. Therefore a complete confusion exists in the paper concerning the viscous dissipation term. It is not clear if this term has been taken into account or not.

On page 277 the local magnetic parameter is defined as:

However, the above parameter is not correct. A possible correct form would be:

In equation (10) of Hossain and Gorla (2013) a magnetic parameter is defined as:

In Equation (5) we used the symbol M to avoid confusion with symbol m which will be used later. Let us calculate the units of the above magnetic parameter M2. The units of the electrical conductivity are (Davidson, 2001, p. 417):

The unit of the magnetic field is Tesla. The definition of Tesla is:

Eliminating ampere from the units we have:

and:

The units of dynamic viscosity are:

The units of velocity are:

Using the units of the above parameters the units of the magnetic parameter M2 are:

Therefore the magnetic parameter is dimensional and not dimensionless as the authors claim. A possible correct form of the magnetic parameter would be:

On page 280 the mixed convection parameter is defined as:

Taking into account that the Grashof number Gr L and the Reynolds number ReL are dimensionless and the magnetic parameter M2 is dimensional the mixed convection parameter λ is also dimensional and not dimensionless as the authors claim.

On pages 286-287 it is mentioned that “Figure 2 shows the numerical values of τ and q obtained from the perturbation solutions for smaller values of ξ as well as the solutions obtained in the region of ξ in the interval [0,2] from the direct finite difference equations (32) of the PVF given in equations (30). In this figure solutions are presented for values of the mixed convection parameter λ=1,2,3,4 and 5 for fluid having Pr=6.5” whereas the corresponding data in figure 2 are λ=0.5 and Pr=0.1.

On page 287 it is mentioned that “Figure 3 shows results for the shear-stress and heat transfer for fluid of different Prandtl numbers in presence of buoyancy force, Joule heating and viscous dissipation effects. Prandtl number Pr was varied from 1 to 50” whereas the corresponding Pr numbers in figure 3 are Pr=0.054, 0.01 and 0.005.

Taking into account all the above the credibility of the results presented by Hossain and Gorla (2013) is doubtful.

Asterios Pantokratoras - School of Engineering, Democritus University of Thrace, Xanthi, Greece

References

Hossain, M.A. and Gorla, R.S.R. (2013), “Joule heating effect on magnetohydrodynamic mixed convection boundary layer flow with variable electrical conductivity”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 2, pp. 275-288

Davidson, P.A. (2001), An Introduction to Magnetohydrodynamics, 1st ed., Cambridge University Press, Cambridge