Comments on the paper “A study of induced magnetic field with chemically reacting and radiating fluid past a vertical permeable plate” by S. Ahmed

Abstract

In the paper "A study of induced magnetic field with chemically reacting and radiating fluid past a vertical permeable plate" by S. Ahmed published in Journal of Engineering Physics and Thermophysics [1], the influence of thermal radiation and chemical reaction on the steady MHD heat and mass transfer by a mixed convective flow of a viscous, incompressible, electrically conducting Newtonian fluid past a vertical permeable plate with account for an induced magnetic field was investigated. The similarity solutions of the transformed nondimensional governing equations were obtained by the series expansion technique. All the results were presented for air and water at 20C with the Prandtl numbers equal to 0.71 and 7, respectively. The above work is of interest, but it has serious disadvantages, which will be analyzed below: 1. On p. 1363, the Eckert number Ec as a parameter is used. However, this parameter was not defined anywhere in the paper. Usually, this number is used when the viscous dissipation term is included into the energy equation. However, in the present problem no viscous dissipation term exists. 2. The assumption that, except for the applied external uniform magnetic field, a new magnetic field appears, which is induced by the electrically conducting fluid and which interacts with the external field, gives a fresh approach to the problem. However, the importance of the induced magnetic field depends on the magnetic Reynolds number defined [2] as Rm = μσul, where μ is the magnetic permeability, σ is the fluid electrical conductivity, u is the characteristic flow velocity, and l is the characteristic length scale. When the magnetic Reynolds number is much smaller than unity, the induced magnetic field is negligible, and the imposed external magnetic field is unaffected by the moving conducting fluid [2]. In most laboratory experiments or industrial processes, Rm is very low, being usually less than 10 [3]. In contrast, when the magnetic Reynolds number is equal to or greater than unity, the induced magnetic field is of importance and should be taken into account. Indeed, certain applications, such as advanced schemes for controlling magnetogasdynamic flows around hypersonic vehicles, involve the values of Rm in the range 1–10 [3]. In the discussed work [1], the author took into account the induced magnetic field without any reference to the magnetic Reynolds number that is the characteristic criterion. We can calculate Rm for air at 20 C. According to [4], at this temperature the electrical conductivity of air varies from 3⋅10 to 8⋅10 Ω⋅m, whereas the magnetic permeability is equal to 1.257⋅10 H/m [5]. For a typical velocity u = 1 m/ s and a typical length scale l = 0.1 m, the magnetic Reynolds number is Rm 3.8⋅10 . For water at 20C, σ = 10 Ω⋅m [6] and μ = 1.257⋅10 H/m [5]. Here, for typical velocity and length scale Rm = 1.257⋅10 . Instead of using the above-mentioned magnetic Reynolds number, the author of [1] used the parameter Pm, called the magnetic Prandtl number: Pm = σνμ, where ν is the fluid kinematic viscosity. In [1], all the results were obtained for air and water, which corresponds, in the author’s opinion, to Pm changing from 0.1 to 1. Let us calculate Pm for air at 20C. Here, ν = 1.827⋅10 m/s [7], so that we have Pm 6.9⋅10. For water ν = 9.8⋅10 m/s [7], and we obtain Pm = 1.23⋅10. Journal of Engineering Physics and Thermophysics, Vol. 86, No. 1, January, 2013