Approximate Solutions for the Flow and Heat Transfer ...

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E-mail: mostafabdelhameed@yahoo.com. [email protected]. The authors numerically studied the problem of the boundary layer flow and.
Comments on " Approximate Solutions for the Flow and Heat Transfer due to a Stretching Sheet Embedded in a Porous Medium with Variable Thickness, Variable Thermal Conductivity and Thermal Radiation using Laguerre Collocation Method" by Mohamed M. Khader, and Ahmed M. Megahed , Applications and Applied Mathematics, Vol. 10, Issue 2 (December 2015), pp. 817 – 834

By Mostafa A. A. Mahmoud Department of Mathematics, Faculty of Science, Benha University (13518), Benha , Egypt E-mail: [email protected] [email protected]

The authors numerically studied the problem of the boundary layer flow and heat transfer of a Newtonian fluid over a non-linear stretching sheet embedded in a porous medium with variable thickness and thermal radiation using Laguerre collocation method in the above paper [1] .There are many fundamental errors: 1. To obtain the similarity solutions in the above paper , the authors assumed that the permeability of the porous medium k (x) is in the form :

k ( x) = k 0 ( x + b )1− m

(1) ,

where k 0 is the permeability parameter. This definition is wrong . 2. The authors defined the porous parameter D as : D=

2υ k 0 C (m + 1)

(2) .

From Eqs.(1) and (2) it is easy to see that D is in dimensional form and is a function of x . From the above one can conclude that : (i)

The problem does not admit the similarity solutions as the authors assumed .

(ii)

Eqs.(13) and (17) are in dimensional form not as the authors reported that they are in dimensionless form .

3. b and F are not defined through the paper (this comment exists also in refs. [2-4] ) . From the above comments it is clear that the problem [1] is wrong . References [1] M. M. Khader and Ahmed M. Megahed , " Approximate Solutions for the Flow and Heat Transfer due to a Stretching Sheet Embedded in a Porous Medium with Variable Thickness, Variable Thermal Conductivity and Thermal Radiation using Laguerre Collocation Method ," Applications and Applied Mathematics , 2015, 10, 817 – 834 . [2] M. M. Khader, M. M. Babatin, A. Eid, A. M. Megahed, "Numerical Study for Simulation the MHD Flow and Heat-Transfer Due to a Stretching Sheet on Variable Thickness and Thermal Conductivity with Thermal Radiation ," Applied Mathematics, 2015, 6, 2045-2056 . [3] M. M. Khader, " Shifted LegendreCollocation Method for the Flow and Heat Transfer due to a Stretching Sheet Embedded in a Porous Medium with Variable Thickness, Variable Thermal Conductivity and Thermal Radiation," Mediterr. J. Math. DOI 10.1007/s00009-015-0594-3 . [4] Mostafa A.A. Mahmud , “Comments on the two published papers By M.M.Khader and Ahmed M. Megahed In 1. Numerical solution for boundary layer flow due to a nonlinearly stretching sheet with variable thickness and slip velocity [Eur. Phys. J. Plus (2013) 128: 100].2. Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity, and thermal radiation [Appl. Math. Mech.Engl. Ed., 35(11), 1387–1400 (2014)] ,” researchgate.net DOI: 10.13140/2.1.5026.1283 . . .