In this paper condensation heat transfer inside horizontal Elliptical tubes is investigated for a stratified; concurrent two-phase flow of vapor and liquid. The analysis takes into account the effects of interfacial shear, axial pressure gradient, saturation temperature level and the development of the stratified angle associated with the accumulated condensate layer at the bottom of the tube. The governing equations are solved numerically with finite difference method. The results are presented for two cases; i.e. with and without fins. Also different values of ellipticity (b/a) are considered and discussed. At first, the results for special case of circle (b/a=l) are compared with available data in the literature that shows good agreement. Also, comparing of obtained results for different values of ellipticity shows that for ellipticity values of less than one, condensation heat transfer is greater than circular tubes; both above case's show greater transfer than those corresponding to ellipticity values bigger than one

In this study, heat transfer and pressure drop through the four-row fin tube bundle with annular Elliptical fins in a triangular layout were investigated. Five different geometries in three fin densities for four different Reynolds numbers were simulated. For circular fins, results are in good agreement with empirical equations in predicting pressure drop and heat transfer. In this regard, the Elliptical fins were also examined. It was found that the Nusselt numbers in horizontal Elliptical fins are the least and in vertical are the highest. It was also found that pressure drop in the circular fins is higher than in horizontal or vertical Elliptical fins and the vertical Elliptical fins in comparison with circular fins with the same vertical diameter, exert less pressure drop. Furthermore, although the heat transfer coefficient in horizontal Elliptical fins is slightly less than in circular fins, the pressure drop can be as much as 70%. The performance evaluation criterion shows that the circular fin performance is much lower compared with the Elliptical fin. Finally, equations are proposed to predict the pressure drop and heat transfer coefficient for Elliptical fins relative to circular fins.

One of the most common used heat exchangers is the shell & tube heat exchanger. It has many usages in the oil and gas, petrochemical and pharmaceutical industries. The heat exchanger is the best which has the highest heat transfer rate with the lowest energy consumption. In this research, we want to increase heat transfer and reduce pressure drop by changing the cross section of tubes. We used tubes with different cross section,circular, ellipse with 0°,attack angle and ellipse with 90°, attack angle. We study pressure drop and heat transfer coefficient for Re between 3000 to 15000. Then two combined models are examined. Case 1: Circular tubes in the center of the shell and Elliptical tubes with 90°,attack angle around the shell, case 2: Elliptical tubes with 90°,attack angle in the center of the shell and circular tubes around the shell. Which indicates an increase in heat transfer in Elliptical tubes, especially Elliptical tubes with 90°,attack angle compared to the circular, while circular tubes have the lowest pressure drop. However the heat transfer in the case 1 (STHE-CT&ET90°, ) and the case 2 (STHE-ET90°, &CT) increase by 10% and 3% compared to the STHE-CT respectively, it caused increasing the pressure drop.

Shell and tube heat exchangers are used in various industrial processes, and are one of the most commonly used heat exchangers. A shell and tube heat exchanger with a 25% baffle cut was used in this study. tubes of different cross-sections (circular, Elliptical with an attack angle of 90° and Elliptical with an attack angle of 0° ) were studied. A combined model of a shell and tube heat exchanger with Elliptical tubes with an attack angle of 90° and circular tubes was introduced. A heat exchanger with ellipsoidal tubes near the shell with an attack angle of 90° and circular tubes in the center of the shell showed the highest heat transfer compared with the shell and tube heat exchangers with circular tubes and Elliptical tubes with an attack angle of 90° and 0° . The pressure drop in the tube and shell side was also investigated for all five cases in this study. The effect of the location of tubes on heat transfer was investigated. It was shown that tubes located near the shell have a greater impact on heat transfer compared with tubes located in the center of the shell.

The multilinear normal distribution is a widely used tool in the tensor analysis of magnetic resonance imaging (MRI). Diffusion tensor MRI provides a statistical estimate of a symmetric 2nd-order diffusion tensor for each voxel within an imaging volume. In this article, tensor Elliptical (TE) distribution is introduced as an extension to the multilinear normal (MLN) distribution. Some properties, including the characteristic function and distribution of affine transformations are given. An integral representation connecting densities of TE and MLN distributions is exhibited that is used in deriving the expectation of any measurable function of a TE variate.

In this paper, novel types of antenna arrays constructed from combination of linear and Elliptical antenna arrays, are presented. These types are called EA, CEA, ECA, ECCA, HA, CHA, HCA, HCCA, HCCA, ECOA, ECCOA, HCOA and HCCOA where only the array factors are considered. The effect of the element factor can be considered separately and combined to the array factor. The expressions for all array factors have been obtained. HA is treated as consisting of two concentric N-element Elliptical arrays of different semi-major and semi-minor axes and ECOA is treated as EA's that are placed one above another, so that the semi-major and semi-minor axes of each EA decrease linearly. The directivities and side lobe levels of them are simulated and compared for various ellipse eccentricity, element spacing and number of elements. Simulations show that CHA has the best directivity and ECOA has the lowest SLL.

In the restricted Elliptical linear model, an approximation for the risk of a general shrinkage estimator of the regression vector-parameter is given. Superiority condition of the shrinkage estimator over the restricted estimator is investigated under the Elliptical assumption. It is evident from numerical results that the shrinkage esti-mator performs better than the unrestricted one in the multivariate t-regression model.

Orbital transfer has a significant role in any space mission. This transfers generally categorized in impulsive and continuous maneuvers. An important challenge is fuel consumption in the maneuver. This problem is considered as a required Dn problem.Hence, minimization of Dn means minimization of fuel consumption orbital transfer. In simple cases, the problem has closed form solution for example transfer between coplanar circular orbits or transfer between coplanar coaxial Elliptical orbits. The conventional methods cannot solve complex cases of initial and target orbits. In this paper the impulsive optimal transfer between two coplanar- noncoaxial Elliptical orbits is considered. The numerical solution of optimality nonlinear equations is necessary to obtain the solutions of complex problems. According to nonlinearity of equations two issues arise, firstly numerical solution is sensitive to initial guess, secondly the local minimum solutions only may be find. In this paper some equations have been derived that using them behavior of required Dn function can be investigate based on various values of independent variables and can be find the boundary of global solution. In this way one can be determined a reasonable and proper initial guess for nonlinear solver. The proposed methodology is applied to an example and the results are provided. The results include the local and global solutions and they show a good ability of the proposed method.