Modified Differential Transform Method (DTM) Simulation of Hydromagnetic Multi-Physical Flow Phenomena from a Rotating Disk ()

Mohammad Mehdi Rashidi, Esmael Erfani, Osman Anwar Bég, Swapan Kumar Ghosh

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**DOI: **10.4236/wjm.2011.15028
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A similarity solution for the steady hydromagnetic convective heat and mass transfer with slip flow from a spinning disk with viscous dissipation and Ohmic heating yields a system of non-linear, coupled, ordinary differential equations. These equations are analytically solved by applying a newly developed method namely the **DTM-Padé** technique which is a combination of the **D**ifferential **T**ransform **M**ethod (**DTM**) and the Padé approximation. A full analytical solution is presented, as a benchmark for alternative numerical solutions. **DTM-Padé** is implemented without requiring linearization, discretization, or perturbation, and holds significant potential for solving strongly nonlinear differential equations which arise frequently in fluid dynamics. The regime studied is shown to be controlled by the slip parameter (*γ*), magnetohydrodynamic body force parameter (*M*), Eckert (viscous heating) number (*Ec*), Schmidt number (Sc), Soret number (Sr), Dufour number (*Du*) and Prandtl number (*Pr*). The influence of selected parameters on the evolution of dimensionless velocity, temperature and concentration distributions is studied graphically. Increasing magnetic field (*M*) is found to significantly inhibit the radial (*f*) and tangential (*g*) velocities, but to accentuate the axial velocity field (*h*); furthermore temperature (*θ*) and concentration (*φ*) are both enhanced with increasing *M*. Increasing Soret number (*Sr*) acts to boost the dimensionless concentration (*φ*). Temperatures are significantly elevated in the boundary layer regime with a rise in Eckert number (*Ec*). Excellent correlation between the **DTM-Padé** technique and numerical (shooting) solutions is achieved. The model has important applications in industrial energy systems, process mechanical engineering, electromagnetic materials processing and electro-conductive chemical transport processes.

Keywords

Differential Transform Method, Padé Approximants, Thermal-Diffusion, Heat Transfer, Soret Effect, Boundary-Layers, Hydromagnetics, Slip, Dissipation, Electromagnetic Processing of Materials

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M. Rashidi, E. Erfani, O. Bég and S. Ghosh, "Modified Differential Transform Method (DTM) Simulation of Hydromagnetic Multi-Physical Flow Phenomena from a Rotating Disk," *World Journal of Mechanics*, Vol. 1 No. 5, 2011, pp. 217-230. doi: 10.4236/wjm.2011.15028.

Conflicts of Interest

The authors declare no conflicts of interest.

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