Periodic Array Of Strips Research Articles

Heat transfer enhancement of a periodic array of isothermal pipes

We address the problem of two-dimensional heat conduction in a solid slab whose upper and lower surfaces are subjected to uniform convection. In the midsection of the slab there is a periodic array of isothermal pipes of general cross section. The main objective of this work is to find the optimum shapes of the pipes that maximize the Shape Factor (heat transport rate). The Shape Factor is obtained by transforming the periodic array of pipes into a periodic array of strips, using the generalized Schwarz–Christoffel transformation, and applying the collocation boundary element method on the transformed domain. Subsequently we pose the inverse problem, i.e. finding the shape that maximizes the Shape factor given the perimeter of the pipes. For large Biot number the optimum shapes are in agreement with the isothermal case, i.e. circular for sufficiently small perimeters/heat transfer, and elongated towards the surfaces of the slab for larger perimeters/heat transfer. Furthermore, for the isothermal case, we were able to discover a new family of optimum shapes for large thickness of the slab and large perimeters, which do not have their maximum width on the horizontal axis of symmetry. For small Biot number the optimum pipes are flatter than the isothermal ones for a given perimeter. The flatness becomes more apparent for larger perimeters. Most important, for large perimeters there exists a critical thickness which is characterized by maximum heat transfer rate. This is further investigated using the finite element method to obtain the critical thickness of a slab and the critical depth of the periodic array of circular pipes.

Shape factor and shape optimization for a periodic array of isothermal pipes

We address the problem of two-dimensional heat conduction in a solid slab embedded with a periodic array of isothermal pipes of general cross-section. The objective of this work is two-fold: to develop a numerical procedure through which we can obtain the shape factor associated with a given configuration and, to develop a numerical shape optimization algorithm through which we can compute shapes that extremize the transport rate. The shape factor is obtained by first transforming the periodic array of pipes into a periodic array of strips using the generalized Schwarz–Christoffel transformation and, subsequently, by developing an integral equation of the first kind for the temperature gradient using the boundary element method. The integral equation is solved both numerically and analytically/asymptotically with excellent agreement between the results. The shape optimization problems, which are formulated with respect to the parameters of the generalized Schwarz–Christoffel transformation, are solved numerically to compute the shape that maximizes the cross-sectional area and the shape that minimizes the perimeter of the cross-section, given the shape factor and the distance between two consecutive pipes. It is inferred that the problems are adjoint to the transport rate minimization and transport rate maximization problems, respectively. The optimal shapes are computed numerically and validated with available analytical and numerical results for a single pipe. Furthermore, motivated by the analytical result, we propose a parametric set of equations that describe well the optimal shapes. The versatility of the Laplace equation suggests that similar formulations have applications in continuum mechanics, electricity, hydraulics and drug reduction.

Isotropic “Islands” in a Cholesteric “Sea”: Patterned Thermal Expansion for Responsive Surface Topologies

Finite-element simulations were performed to model and understand the basic phenomena of a periodic array of strips of the cholesteric and isotropic materials, bonded to a nominally rigid substrate. Different thermal-expansion coefficients were used in the chiral nematic and isotropic states in order to fabricate a patterned film with different thermal-expansion properties. A photosensitized mixture of the nematic and the chiral monomers was placed between two glass plates coated with a polyimide alignment layer which was further rubbed with a velvet cloth to create orienting grooves for the liquid crystal. A white-light interference microscope was used to characterize the change in the surface of the film during heating. The results show that these thermally sensitive active surface topologies have potential applications in the areas of controllable face-relief structures, nanoactuators, and sensors.

Analytical expressions for reflection coefficients of artificially soft and hard surfaces: dielectric slab loaded with a periodic array of strips over a ground plane

Simple and closed form expressions for plane wave reflection coefficients of a dielectric slab loaded with a periodic array of strips over a ground plane are presented for use in antenna applications. In the analysis, a set of integral equations for the fields between the strips and dielectric slab are derived from the three-dimensional boundary value problem. Using the low frequency approximation, closed form expressions were obtained for the reflection coefficients. Numerical comparison with the point matching method shows that the accuracy is excellent in practical uses. The frequency bandwidth of the surfaces at the artificially soft and hard boundaries is discussed.

Excitation of Guided Modes of a Slab Waveguide Using a Finite Strip Grating

An accurate numerical solution is presented for the excitation problem of guided modes of a slab waveguide at a plane wave incidence, where a finite periodic array of strips is used for excitation. This system is one of the typical models of grating couplers. The problem is two-dimensional and only the TE mode is treated. We derive a set of singular integral equations and solve it by the moment method, where the Chebyshev polynomials are successfully used as the basis and the testing functions. Numerical calculations are carried out under the condition that the error on the optical theorem is less than 0.1%. It is shown that the frequency which yields maximum excitation efficiency is somewhat different from one predicted by the Bragg condition. We also confirm that too many strips lead to deterioration of the efficiency. The calculations predict that the efficiency of the first even mode at its maximum is 37%.

Electromagnetic scattering by a dielectric slab loaded with a periodic array of strips over a ground plane

Scattering of electromagnetic waves from a dielectric slab loaded with a periodic array of perfectly conducting strips is analyzed by a mode-matching technique. The variation of energy of significant scattered modes with various structure parameters is presented for both principal polarizations of the incident wave. The convergence and accuracy of the numerical method is evaluated. Further numerical results are obtained to show the effects of various parameters on the distribution of power in various propagating modes. The results show the usefulness of these structures as reflection-type gratings, polarizers, and filters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

AN ANALYSIS OF THE SPECTRAL ITERATIVE TECHNIQUE FOR ELECTROMAGNETIC SCATTERING FROM INDIVIDUAL AND PERIODIC STRUCTURES

ABSTRACT It is shown that the disctete system solved by the Spectral Iterative Technique (SIT) is of Toeplitz or block Toeplitz form, and thus may be more amenable to direct solution in certain cases. In addition, the discrete system associated with the SIT is shown to be equivalent to a moment method matrix equation, with basis and testing functions chosen implicitly in the process. Thus, there is no additional generality in the SIT type of approach compared to the conventional method of moments. These statements concern the discretization procedure used within the SIT, and apply whether the SIT is implemented in its original form or in connection with the conjugate gradient method. Simple examples of scattering from a single strip and from a periodic array of strips are used to illustrate the concepts.