Two-fluid model and hydrodynamic constitutive relations
Two-fluid formulation for two-phase flow analyses is presented. A fully three-dimensional model is obtained from the time averaging, whereas the one-dimensional model is developed from the area averaging. The constitutive equations for the interfacial terms are the weakest link in a two-fluid model because of considerable difficulties in terms of experimentation and modeling. However, these are of supreme importance in determining phase interactions. In view of this, the interfacial transfer terms have been studied in great detail both for the three- and one-dimensional models. New interfacial area, drag, virtual mass, droplet size and entrainment correlations are presented. In the one-dimensional model, a number of serious shortcomings of the conventional model have been pointed out and new formulations to eliminate them are presented. These shortcomings mainly arose due to the improper consideration of phase distributions in the transverse direction. 
Application of Computational Fluid Dynamics in building services engineering
Application of Computational Fluid Dynamics to building services design is illustrated and reviewed. Principal areas of application are designs requiring an understanding of the air flow pattern, such as design of smoke control systems and air distribution in a heating, ventilation and air-conditioning system. In such an approach, the indoor air motion is described by a set of partial differential equations describing conservation of mass, momentum, enthalpy and chemical species concentration, if any. The air flow pattern, temperature contour, and chemical species concentration distribution induced by thermal sources are predicted by solving that system of equations using the finite difference method. Assessment of the longitudinal ventilation in a tunnel, smoke filling in an atrium, and the interaction between the airflow induced by a fire and a sprinkler water spray are illustrated in the area of fire engineering. Simulation of the combustion process is briefly reviewed. Calculation of the macroscopic flow parameters in an air-conditioned gymnasium and an office is demonstrated. 
Computational methods in engineering and science, with applications to fluid dynamics and nuclear systems
Comprehensive coverage of computational methods for differential equations in engineering and science is provided. Three categories of computational methods, the finite difference method, the finite element method, and the statistical (Monte Carlo) method, provide numerical solutions of eigenvalue problems of ordinary differential equations, elliptic partial differential equations, and parabolic and hyperbolic partial differential equations. Comprehension of materials rather than mathematical rigor is emphasized. The fundamentals of the necessary numerical methods are reviewed and the following are described: Finite difference methods for Sturm-Liouville eigenvalue problems; elliptic and parabolic partial differential equations; finite difference methods for fluid flow; weighted residual methods and their application to computational techniques; the principle of the finite element method and its application to partial differential equations; the coarse mesh rebalancing method as a technique to accelerate the convergence rate of iterative schemes; and the Monte Carlo method for neutron transport and heat transfer, as a statistical approach to the numerical calculation. 
Application of the Laplace Decomposition Method for Motion of Spherical/Non-Spherical Particles within a Highly Viscous Fluid
Downward movement of solid particles within a fluid in the presence of a gravitational field occurs in many industrial and engineering processes, e.g. particulate processing and two phase solid-liquid applications. Three highly viscous liquids including water, glycerin and ethylene-glycol were selected to study the motion of spherical/non-spherical solid particles for a wide range of Reynolds numbers employing a drag coefficient as defined by Chien . The governing equation of the motion is strongly nonlinear due to the nonlinear nature of the drag force exerted on the solid body during falling. In this paper, a numerical technique, namely the Laplace Decomposition Method (LDM), is applied to solve the governing equation. This method applies the Laplace transform to the differential equation whereas the nonlinear term is decomposed in terms of Adomian polynomials. A good agreement was achieved when compared with a famous numerical method, then the effects of solid sphericity were tested for the different liquids. This study demonstrates the effectiveness of the present mathematical technique and illustrates a simple application for this type of problem which may be used for a large class of nonlinear differential equations. 
Hall Current Effects on Unsteady Mhd Fluid Flow with Radiative Heatflux and Heat Source over a Porous Medium
In this paper the study of unsteady hydromagnectic free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium was conducted. The temperature is assumed to be oscillating with time, also the effects of hall-current is taken in to account. The solution of velocity, temperature and concentration profiles have been obtained. The effects of various parameters on temperature, concentration primary and secondary velocity profiles were presented graphically. 
 Ishii, M. and Mishima, K., 1984. Two-fluid model and hydrodynamic constitutive relations. Nuclear Engineering and design, 82(2-3), pp.107-126.
 Chow, W.K., 1996. Application of computational fluid dynamics in building services engineering. Building and Environment, 31(5), pp.425-436.
 Nakamura, S., 1977. Computational methods in engineering and science, with applications to fluid dynamics and nuclear systems.
 Sojoudi, R., Salehi Tabrizi, M. and Sojoudi, A. (2014) “Application of the Laplace Decomposition Method for Motion of Spherical/Non-Spherical Particles within a Highly Viscous Fluid”, Journal of Advances in Mathematics and Computer Science, 5(6), pp. 748-762. doi: 10.9734/BJMCS/2015/14019.
 Ahmed, A., Uwanta, I. J. and Sarki, M. N. (2015) “Hall Current Effects on Unsteady Mhd Fluid Flow with Radiative Heatflux and Heat Source over a Porous Medium”, Journal of Advances in Mathematics and Computer Science, 6(3), pp. 233-246. doi: 10.9734/BJMCS/2015/13849.