An analysis is performed on non-Darcy mixed convective flow of non-Newtonian fluid past a vertical surface in the presence of volumetric heat source originated by some electromechanical or other devices. Further, the vertical bounding surface is subjected to power law variation of wall temperature, but the numerical solution is obtained for isothermal case. In the present non-Darcy flow model, effects of high flow rate give rise to inertia force. The inertia force in conjunction with volumetric heat source/sink is considered in the present analysis. The Runge-Kutta method of fourth order with shooting technique has been applied to obtain the numerical solution. To avoid mathematical impasse for applying R-K method we have considered isothermal wall condition. The results of major interest include velocity as well as temperature profiles and the local Nusselt number for some representative values of power-law indices. Most importantly, introduction of the coordinate and parametric transformation applied to governing equations, rarely reported in the existing literature, add to the knowledge front. Some important findings of the study are: Ergun number reduces the pseudoplastic fluid velocity boundary layer, a desirable outcome, but enhances the thermal boundary layer whereas, in case of Newtonian and dilatant fluid, the effect is not so significant. An increase in all the flow and heat transfer parameters leads to decelerate the surface cooling from pseudoplasticity to dilatancy through Newtonian; thus the present model slows down the surface cooling and decreases the skin friction in the presence of heat source for dilatant fluid.
A study on heat and mass transfer of a steady laminar boundary layer flow of an electrically conducting fluid of second grade in a porous medium subject to a uniform magnetic field past a semi-infinite stretching sheet with power law surface temperature or power law surface heat flux. The variations in fluid velocity, fluid temperature and species concentration are displayed graphically whereas the numerical values of skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of the pertinent flow parameters. The asymptotic expansions of the solutions for large Prandtl number are also given for the two heating conditions. The temperature distribution decreases with the increase in thermal radiation parameter in case of PST and PHF. The rate of mass transfer at the solid surface increases in the presence of magnetic field and decreases with heavier diffusing species.
A mathematical discussion of two different classes of nanofluids, such as Copper (Cu)-Kerosene and Aluminum oxide (Al2O3)-Kerosene, over a stretching/shrinking surface, has been discussed in this manuscript. Here Kerosene based nanofluids carry Copper and Aluminum oxide as nanoparticles. The ODEs are obtained from basic equations by introducing the similarity approach. The respective coupled nonlinear ODEs are solved with the help of a suitable numerical technique named as Runge-Kutta fourth-order method. It is found that Al2O3-Kerosene possesses a slightly greater velocity than Cu-Kerosene, but a reverse effect is found in the case of temperature and nanofluids. The presence of volume concentration is important due to the presence of nanoparticles as nanofluids property depends on the physical properties of nanoparticles.
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