A method for minimizing the number of states for a restricted class of incompletely specified sequential machines

Summary In this paper are considered incompletely specified sequential machines for which the only unspecified entries are those which occur because of a restriction on the input states which can directly follow each possible input state.For these machines the minimum number of states is equal to the chromatic number of the graph of all pairs of incompatible states. A new method for determining a minimum-class partition of the set of states which is formed from compatible classes is given.     

Analysis of first and second laws of thermodynamics between two isothermal cylinders with relative rotation in the presence of MHD flow

In this paper, an analysis of the first and second laws of thermodynamics is presented to show the effects of MHD flow on the distributions of velocity, temperature and entropy generation between two concentric rotating cylinders. The flow inside the gap is assumed to be steady state and laminar for an incompressible, viscous, and Newtonian fluid. The walls of the cylinders are kept at different constant temperatures. Governing equations in cylindrical coordinates are simplified and analytically solved to obtain the local and average (overall) entropy generation rate. Due to the nature of the problem, the velocity distribution in the annulus becomes as the modified Bessel functions I₁(MR) and K₁(MR). Therefore, to obtain the temperature field, the expansions of the modified Bessel functions I₁(MR) and K₁(MR), with 3 terms, are employed in the energy equation. The results are presented for various values of Hartmann number (M), radius ratio (Π), group parameter (Ω/Br), and Brinkman number (Br).     

Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet

The unsteady boundary layer flow of a nanofluid over a permeable stretching/shrinking sheet is theoretically studied. The governing partial differential equations are transformed into ordinary ones using a similarity transformation, before being solved numerically. The results are obtained for the skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and the nanoparticle fraction profiles for some values of the governing parameters, namely, the unsteadiness parameter, the mass suction parameter, the Brownian motion parameter, the thermophoresis parameter, Prandtl number, Lewis number and the stretching/shrinking parameter. It is found that dual solutions exist for both stretching and shrinking cases. The results also indicate that both unsteadiness and mass suction widen the range of the stretching/shrinking parameter for which the solution exists.     

Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet

The effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated. The self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method. The analysis reveals that for the steady flow of micropolar fluid, the wall mass suction needs to be increased. Dual solutions of velocity and temperature are obtained for several values of the each parameter involved. For increasing values of the material parameter K, the velocity decreases for first solution, whereas, for second solution it increases. Due to increase of thermal radiation, the temperature and thermal boundary layer thickness reduce in both solutions and also the heat transfer from the sheet enhances with thermal radiation.     

Effects of moving lid direction on MHD mixed convection in a linearly heated cavity

Effects of moving lid-direction on MHD mixed convection in a cavity with the bottom wall being linearly heated are analyzed using a numerical technique. Vertical walls of the enclosure are adiabatic and the sliding wall at the top has constant temperature. The lid moves in the negative and positive x-direction. Finite volume method has been used to solve the governing equations. Results are presented for different values of Hartmann number (0 ? Ha ? 30), Reynolds number (100 ? Re ? 1000) and Grashof number (10⁴ ? Gr ? 10⁶). It is found that direction of lid is more effective on heat transfer and fluid flow in the case of mixed convection than it is the case in forced convection. Heat transfer is also decreased with increasing of magnetic field for all studied parameters.