The above paper analyzed the effect of thermal radiation with a regular three-parameter perturbation in some free convection flows of Newtonian fluid saturated porous medium. The effects of the thermal radiation, permeability of the medium, pressure stress work and viscous dissipation on the flows and temperature fields have been included in the analysis. Four different vertical flows have been analyzed, those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source a vertical adiabatic surface. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The numerical results of the perturbation analysis for four conditions are solved numerically by the fourth-order Runge-Kutta integration scheme. Numerical values of the main physical quantities are the skin friction and heat transfer and total heat and mass convected downstream are presented in tabular with the parameters characterizing the radiation, permeability of the medium, pressure stress work and viscous dissipation. Many obtained results are compared and representative set is displayed graphically to illustrate the influences of the radiation, the radiation, permeability of the medium, pressure stress work and viscous dissipation on the velocity and the temperature profiles. However, the detailed responses to comments in Pantokratoras [2] will be presented below.
The first comment in [2] is essentially based on figures in the above paper titled above, see Rashad . The author mentioned that the profiles included in Fig. which correspond to R = 0 (solid line); that the profiles h 0 and h 3 are correct, because approach the horizontal axis asymptotically, but the contrast in the profiles h 1 and h 2 intersect the horizontal axis at g ¼ 4:0 and there are also many velocity and temperature profiles which intersect the horizontal axis in Rashad . The statements in this comment do not hold due to obvious misunderstanding of the results in the figures, which will be illustrated as follows. The author has missed the crucial importance of a direct mathematical interpretation of the relevant averaged profiles. It should be noted in figures that the plotted profiles h 1 in these figures represented the real results data multiplying by the value 5.0 zoomed in the region of the figures, whereas, the profiles h 0 shows the real of obtained results data. Then, if one looks carefully to the plotted profiles h 1 in figure corresponds to R = 0 (solid line), one will find that the data display of maximum temperature (maximum solid line) the exact data of temperature equals 0.307 at g ¼ 1:53 (i.e., the real value of h 1 ¼ 0:0614 at g ¼ 1:53), which means that temperature profile h 1 approach the ambient fluid conditions correctly (asymptotically) at g ¼ 4:0 as the profiles h 0 and h 3 , which the author has believed and be sure that these profiles were correct, and in a similar manner about the profilers h 2 . Moreover, it can be seen from other figures 3-7, For a given values of the various parameters of the problem the values of f 00 i ð0Þ and h 0 i ð0Þ, i = 1, 2, 3 were estimated and differential equations of the problem were integrated using Runge-Kutta method until the boundary conditions at infinity f 0 ð1Þ and hð1Þ decay exponentially to