• Title/Summary/Keyword: partial theta function

Search Result 12, Processing Time 0.019 seconds

Thermal diffusion and diffusion thermo effects on an unsteady heat and mass transfer magnetohydrodynamic natural convection Couette flow using FEM

  • Raju, R. Srinivasa;Reddy, G. Jithender;Rao, J. Anand;Rashidi, M.M.
    • Journal of Computational Design and Engineering
    • /
    • v.3 no.4
    • /
    • pp.349-362
    • /
    • 2016
  • The numerical solutions of unsteady hydromagnetic natural convection Couette flow of a viscous, incompressible and electrically conducting fluid between the two vertical parallel plates in the presence of thermal radiation, thermal diffusion and diffusion thermo are obtained here. The fundamental dimensionless governing coupled linear partial differential equations for impulsive movement and uniformly accelerated movement of the plate were solved by an efficient Finite Element Method. Computations were performed for a wide range of the governing flow parameters, viz., Thermal diffusion (Soret) and Diffusion thermo (Dufour) parameters, Magnetic field parameter, Prandtl number, Thermal radiation and Schmidt number. The effects of these flow parameters on the velocity (u), temperature (${\theta}$) and Concentration (${\phi}$) are shown graphically. Also the effects of these pertinent parameters on the skin-friction, the rate of heat and mass transfer are obtained and discussed numerically through tabular forms. These are in good agreement with earlier reported studies. Analysis indicates that the fluid velocity is an increasing function of Grashof numbers for heat and mass transfer, Soret and Dufour numbers whereas the Magnetic parameter, Thermal radiation parameter, Prandtl number and Schmidt number lead to reduction of the velocity profiles. Also, it is noticed that the rate of heat transfer coefficient and temperature profiles increase with decrease in the thermal radiation parameter and Prandtl number, whereas the reverse effect is observed with increase of Dufour number. Further, the concentration profiles increase with increase in the Soret number whereas reverse effect is seen by increasing the values of the Schmidt number.

Effect of TaB2 Addition on the Oxidation Behaviors of ZrB2-SiC Based Ultra-High Temperature Ceramics

  • Lee, Seung-Jun;Kim, Do-Kyung
    • Korean Journal of Materials Research
    • /
    • v.20 no.4
    • /
    • pp.217-222
    • /
    • 2010
  • Zirconium diboride (ZrB2) and mixed diboride of (Zr0.7Ta0.3)B2 containing 30 vol.% silicon carbide (SiC) composites were prepared by hot-pressing at $1800^{\circ}C$. XRD analysis identified the high crystalline metal diboride-SiC composites at $1800^{\circ}C$. The TaB2 addition to ZrB2-SiC showed a slight peak shift to a higher angle of 2-theta of ZrB2, which confirmed the presence of a homogeneous solid solution. Elastic modulus, hardness and fracture toughness were slightly increased by addition of TaB2. A volatility diagram was calculated to understand the oxidation behavior. Oxidation behavior was investigated at $1500^{\circ}C$ under ambient and low oxygen partial pressure (pO2~10-8 Pa). In an ambient environment, the TaB2 addition to the ZrB2-SiC improved the oxidation resistance over entire range of evaluated temperatures by formation of a less porous oxide layer beneath the surface SiO2. Exposure of metal boride-SiC at low pO2 resulted in active oxidation of SiC due to the high vapor pressure of SiO (g), and, as a result, it produced a porous surface layer. The depth variations of the oxidized layer were measured by SEM. In the ZrB2-SiC composite, the thickness of the reaction layer linearly increased as a function of time and showed active oxidation kinetics. The TaB2 addition to the ZrB2-SiC composite showed improved oxidation resistance with slight deviation from the linearity in depth variation.