The average effective thermal conductivity Keff is measured for forty-eight multilayered needle-punched nonwoven samples. Samples are produced using glass and ceramic fibers layered in several different constructions and punched with needles with varying numbers of barbs. The thermal conductivities are determined at steady state, using a Holometrix guard hot plate at an average applied temperature of 455°C. Statistical results show an ability to predict effective thermal conductivity with greater than 88% accuracy. Important parameters of the model include fabric weight, thickness, porosity, and structure, along with the applied temperature. Results also show that the nine-barbed structure with the highest ceramic content has the greatest potential for thermal insulation at elevated temperatures.

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A theoretical equation of the combined thermal conductive, convective, and radiative heat flow through heterogeneous multilayer fibrous materials is presented. Samples whose properties are analyzed by this equation were constructed from glass and ceramic webs and used in an earlier work to experimentally determine their thermal conductivities. In that experimental work, overall effective thermal conductivities were determined using a guarded hot plate instrument with temperatures ranging from 430 to 480°C. In the theoretical equation presented here, thermal convective heat flow is ignored because of fabric structural conditions, and the conduction component of the overall conductivity is determined by Fricke's equation. Furthermore, the results of Fricke's equation and the overall effective thermal conductivity are used to estimate the radiative thermal conductivity of the samples.Heat transfer through porous materials can be attributed to the simultaneous operation of three mechanisms: solid-to-solid conduction, gas conduction, and radiation [3, 10, 13, 17]. Viskanta [ 18] stated that due to interactions, these three mechanisms, strictly speaking, are not separable. In some special instances, however, treating total, heat transfer as the sum of the three independent contributions can be a reasonable approximation. As a general principle, separation of conduction and radiation is not valid. If the distance between the two surfaces is small and if they are separated by a transparent medium, only then is it a tolerably good approximation to ignore the interaction of conduction and radiation [18]. Radiation leaving a surface and passing through the material may pass through the voids in the porous materials, be transmitted through the particles, be absorbed by the particles and subsequently re-emitted, or be scattered by the particles [ 18].Heat transfer by simultaneous conduction and radiation in thermal radiation absorbing, emitting, and scattering materials was investigated theoretically by Viskanta [18]. He considered a one-dimensional system consisting of two diffuse, nonblack, isothermal, parallel plates separated by a finite distance. The space between the two plates was filled with an isotropically scattering material, and the problem was formulated exactly in terms of integro-differential and integral equations. The results both defined and illustrated several mechanisms of radiant energy transfer and showed how one mode of heat transfer influenced the other.The &dquo;state of the art&dquo; for heat transfer in materials of this type was reported by Wechsler and Glaser [20]. When radiation is coupled with the other modes of heat transfer, the energy equation, which is normally a differential equation, becomes a nonlinear integro-differential equation. This comes about because the radiative contribution to the total energy flux is due, in part, to the geometric configuration of the system and reflection [ 19]. There are no general solutions available for integrodifferential equations, but a few attempts ...

This article presents a simple mathematical model for predicting the running attitude of warped planing boats fixed in a heel angle and free to trim and sinkage. The proposed model is based on asymmetric 2D + T theory utilizing a pressure equation which is previously introduced in the literature to compute the hydrodynamic force acting on a heeled planing hull. Integration of pressure distribution on the asymmetric wedge sections enables the suggested model to compute trim angle, center of gravity rise, resistance, and heeling moment acting on the heeled planing boat in calm water. The hydrostatic force in addition to two drag forces acting on the pressure area and spray area are also taken into account. Finally, a computational algorithm is introduced to find the running attitude of the heeled planing boats. The validity of the proposed model is examined by comparing the obtained running attitudes for two planing hulls series with zero heel angle and computed lift force and heeling moment of a heeled planing boat against available experimental data. Based on the comparisons, favorable accuracy is observed for both symmetrical and asymmetrical conditions. Moreover, it is shown that existence of a heel angle can lead to a decrease in trim angle and resistance, while it intensifies the center of gravity rise of planing boats. It is also observed that as the beam Froude number increases, the heeling moment of the heeled boat reduces.

Water impact is one of the most critical phenomena from the viewpoint of the structural design of ships and offshore structures. The impact force can impose a large load with high local pressure on the body surface. On the other hand, determination of the maximum impact force during impact and acting point itself is very important in the design of floats. In this paper, the water entry of a two-dimensional wedge section is considered. This study is carried out in the framework of a potential-flow assumption. In particular, water impact on a dropping wedge with a constant velocity is pursued analytically by using the Schwartz–Christoffel conformal mapping. In order to determine a position of the wedge where the instantaneous effective force is largest during the impact, a particular equation is introduced here for the first time. The pressure distribution and maximum impact force are also calculated. The obtained results are compared against other numerical and experimental works and favorable agreement is displayed.