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Exact analytical solutions have been obtained for conduction heat transfer in a long rod or duct, having cross section of a semi-ellipse, using the “elliptic-cylindrical coordinate system”. Results are presented for two possible cross-sectional configurations of the rod: in one case, the cross section is bounded by a semi-ellipse with the straight edge aligned with the major axis, whereas, in other case, it is bounded by a semi-ellipse with the straight edge coincident with the minor axis. Expressions of temperature distribution, heat flux and heat line are determined for constant wall temperature as well as constant heat flux boundary conditions. The analytical results are illustrated graphically to highlight the salient physics associated with the problem. Apart from the analytical results, the “bivariate Chebyshev collocation spectral method” has been used to determine the numerical solution of the problem of heat conduction in the semi-elliptical geometries; numerical results are found to be consistent with the analytical expressions. The study opens up avenues for obtaining exponentially accurate numerical solution of energy equation in complex elliptic geometries using Chebyshev spectral method.

A linear model of the theory of thermoelasticity for an isotropic body in the cylindrical coordinate system is considered. The stationary temperature satisfies a three-dimensional Laplace equation. The general solution of the system of Navier’s differential equations, which describes the thermoelastic stress state of the body, is presented as a sum of homogeneous and partial solutions. The partial solution, which does not contain elastic displacements, is called the temperature solution. The theorem states that the sum of normal temperature stresses is zero. To solve the Navier’s equations, the temperature is presented as a Fourier-Bessel series, according to which properties the temperature solution of the Navier’s equations is constructed. Analytical formulas for the description of temperature displacements and stresses in explicit form are given. The general solution of the equations of the theory of thermoelasticity in terms of four harmonic functions is presented.

In this paper, we introduce a new definition of the general conformable fractional (GCF) Laplace transform with respect to the function Φ generated by the fractional conformable function ϕ. By the new definition, the usual Laplace transform and the ρ - Laplace transform are special cases of the GCF Laplace transform. We prove several important properties of these GCF Laplace transforms. In addition, we also define the GCF cylindrical coordinates system and derive the GCF Laplace operator on these coordinates. Furthermore, we study the approximate solution of the GCF position-dependent mass (PDM) Schrödinger equation for a symmetrical modified Pöschl-Teller potential in the GCF cylindrical coordinate system by using the GCF Laplace transform method. The GCF radial wave function and GCF energy eigenvalue are obtained from the approximate solution of the GCF Schrödinger equation. The behavior of the bound state conformable fractional energy levels was demonstrated and analyzed by using the computational method for various values of the order of conformable fractionality α , quantum number, and mass of the molecule. Moreover, the maximum conformable fractional energy-eigenvalue is obtained with respect to the influence of the order of conformable fractionality α and mass for diatomic molecules H 2 , LiH, and HCl.

Time-domain algorithms have significant performance advantages for missile-borne synthetic aperture radar (SAR) focusing with diving movement. However, due to the diving curve trajectory of the missile platform, the range and angular histories of the target become very sensitive to unknown tomography, which provides difficulties for SAR algorithm development. To address this problem, we have proposed a new fast factorized back-projection (FFBP) algorithm with reduced topography sensibility for missile-borne SAR focusing. The new algorithm was designed based on an orthogonal cylindrical coordinate (OCC) system, in which the cross section of a cylinder in the coordinate system is approximately orthogonal to the diving curve trajectory. Owing to the acquisition symmetry of the OCC system, the range and the angular histories of the grid in the OCC geometry become less dependent of the topography in every recursion of FFBP implementation, which can dramatically reduce the adverse effects of unknown topography and achieve high focusing performance. In the simulation, echo signal based on a set of typical parameters from a missile-borne SAR system is generated with unknown tomography. Promising results with 1 m resolution are finally achieved, which demonstrates the performance of the proposed algorithm. The limitation of the algorithm is also discussed in the final part, which will facilitate the development of raw data processes in practical application.

In this paper, we devise a new exact and partially explicit solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible azimuthal flow with a discontinuous density distribution that varies with both depth and latitude and subjected to forcing terms in terms of cylindrical coordinates. An analysis allows us to draw qualitative and quantitative results about the interface and the free surface of the azimuthal flow. Moreover, a particular example is considered to show that the interface can be determined explicitly. Finally, we obtain the expected monotonicity properties between the surface pressure and its distortion and derive an infinite regularity about the interface.

With the advances of material processing technology and miniaturization of mechanical devices and components, it is clear now that curvilinear coordinate systems in dealing with special configurations of elastic solids including cylinders are also naturally needed in the analytical process. By adopting the cylindrical coordinates, it is found that the Love wave in semi-infinite solids possess the same velocity as in the Cartesian coordinates, but the displacement is dependent on radius near the origin and decaying slowly with the radius by exhibiting a strong contrast of the uniform displacement in the Cartesian formulation. Numerical examples show that the asymptotic approximation is accurate in one wavelength away from the origin, implying that solutions will be different only in the vicinity of the point of excitation.

In this study, transient non-Fourier heat transfer in a solid cylinder is analytically solved based on dual-phase-lag for constant axial heat flux condition. Governing equations for the model are expressed in two-dimensional cylindrical coordinates; the equations are nondimensionalized and exact solution for the equations is presented by using the separation of variable method. Results showed that the dual-phase-lag model requires less time to meet the steady temperature compared with single-phase-lag model. On the contrary, thermal wave diffusion speed for the dual-phase-lag model is greater than the single-phase-lag model. Also the effect of relaxation time in dual-phase-lag model has been taken on consideration.

Fused filament fabrication (FFF) is an additive manufacturing (AM) process that is intended to build three-dimensional objects through selective deposition of melted material layer-by-layer along a pre-determined path. In the last few years, the utilization of the FFF technology has grown at a high pace and today its use has become widespread in several applications. In the light of the premises, this work emerges as a technology push effort to develop an innovative FFF machine where cylindrical coordinate-based print motion is combined with multiple print heads. The proposed FFF machine was conceived and designed guided by appropriate methodologies concerning product development, assembly, servicing, and design for AM. Furthermore, as a proof of concept, a physical prototype was produced gathering traditional manufacturing processes with AM. The physical prototype was validated with speed, temperature, and deposition tests. The presented FFF machine presents higher manufacturing versatility due to the possibility of processing different materials (in the same part and in all printing area) with an increased production rate, that enables printing up to three parts simultaneously.

This work formulates the simplified governing equations for granulation convection system in cylindrical coordinates by using the differential operator theory on Riemann manifold. We consider the case where the granulation convection system is under the influence of the control parameters R and E, Where R depends on the temperature difference and E is related to the magnetic field. Furthermore, we show that the simplified governing equations bifurcate from a trivial steady state solution, as the control parameters cross certain critical values. Notably, we are able to derive a RE-phase diagram in the case of two control parameters R and E, compared with the system without the influence of the control parameter E. In addition, our research shows that the difference of temperature and the magnetic field both accelerates the granulation convection.

— The paper considers the derivation of the basic differential equation of thermal conductivity of a stationary medium in a cylindrical coordinate system. The literature mainly considers versions of this equation for one- and two-dimensional axisymmetric temperature fields. In this paper, the most general form of this equation for a three-dimensional field is obtained and the identity of the two equations in different coordinate systems is shown, which confirms the fundamental reliability and applicability of the obtained equation. An example of a one-dimensional angular field and integral equations of thermal conductivity for three types of one-dimensional temperature fields in directions are also given. The applicability of the differential equation in cylindrical coordinates to describe the thermal conductivity of a flat wall is shown. The differential equation of convective heat transfer and the equation of continuity and continuity of the flow in cylindrical coordinates are also given.