Heat Conduction in a Functionally Graded Plate Subjected to Finite Cooling/Heating Rates: An Asymptotic Solution.
ABSTRACT: This work investigates transient heat conduction in a functionally graded plate (FGM plate) subjected to gradual cooling/heating at its boundaries. The thermal properties of the FGM are assumed to be continuous and piecewise differentiable functions of the coordinate in the plate thickness direction. A linear ramp function describes the cooling/heating rates at the plate boundaries. A multi-layered material model and Laplace transform are employed to obtain the transformed temperatures at the interfaces between the layers. An asymptotic analysis and an integration technique are then used to obtain a closed form asymptotic solution of the temperature field in the FGM plate for short times. The thermal stress intensity factor (TSIF) for an edge crack in the FGM plate calculated based on the asymptotic temperature solution shows that the asymptotic solution can capture the peak TSIFs under the finite cooling rate conditions.
Project description:For plate tectonics to operate on a planet, mantle convective forces must be capable of forming weak, localized shear zones in the lithosphere that act as plate boundaries. Otherwise, a planet's mantle will convect in a stagnant lid regime, where subduction and plate motions are absent. Thus, when and how plate tectonics initiated on the Earth is intrinsically tied to the ability of mantle convection to form plate boundaries; however, the physics behind this process are still uncertain. Most mantle convection models have employed a simple pseudoplastic model of the lithosphere, where the lithosphere 'fails' and develops a mobile lid when stresses in the lithosphere reach the prescribed yield stress. With pseudoplasticity high mantle temperatures and high rates of internal heating, conditions relevant for the early Earth, impede plate boundary formation by decreasing lithospheric stresses, and hence favour a stagnant lid for the early Earth. However, when a model for shear zone formation based on grain size reduction is used, early Earth thermal conditions do not favour a stagnant lid. While lithosphere stress drops with increasing mantle temperature or heat production rate, the deformational work, which drives grain size reduction, increases. Thus, the ability of convection to form weak plate boundaries is not impeded by early Earth thermal conditions. However, mantle thermal state does change the style of subduction and lithosphere mobility; high mantle temperatures lead to a more sluggish, drip-like style of subduction. This 'sluggish lid' convection may be able to explain many of the key observations of early Earth crust formation processes preserved in the geologic record. Moreover, this work highlights the importance of understanding the microphysics of plate boundary formation for assessing early Earth tectonics, as different plate boundary formation mechanisms are influenced by mantle thermal state in fundamentally different ways.This article is part of a discussion meeting issue 'Earth dynamics and the development of plate tectonics'.
Project description:The initiation mechanism of Earth's plate tectonic cooling system remains uncertain. A growing consensus suggests that multi-plate tectonics was preceded by cooling through a single-plate lithosphere, but models for how this lithosphere was first broken into plates have not converged on a mechanism or a typical early plate scale. A commonality among prior efforts is the use of continuum mechanics approximations to evaluate this solid mechanics problem. Here we use 3D spherical shell models to demonstrate a self-organized fracture mechanism analogous to thermal expansion-driven lithospheric uplift, in which globe-spanning rifting occurs as a consequence of horizontal extension. Resultant fracture spacing is a function of lithospheric thickness and rheology, wherein geometrically-regular, polygonal-shaped tessellation is an energetically favored solution because it minimizes total crack length. Therefore, warming of the early lithosphere itself-as anticipated by previous studies-should lead to failure, propagating fractures, and the conditions necessary for the onset of multi-plate tectonics.
Project description:Convection in an isolated planet is characterized by narrow downwellings and broad updrafts--consequences of Archimedes' principle, the cooling required by the second law of thermodynamics, and the effect of compression on material properties. A mature cooling planet with a conductive low-viscosity core develops a thick insulating surface boundary layer with a thermal maximum, a subadiabatic interior, and a cooling highly conductive but thin boundary layer above the core. Parts of the surface layer sink into the interior, displacing older, colder material, which is entrained by spreading ridges. Magma characteristics of intraplate volcanoes are derived from within the upper boundary layer. Upper mantle features revealed by seismic tomography and that are apparently related to surface volcanoes are intrinsically broad and are not due to unresolved narrow jets. Their morphology, aspect ratio, inferred ascent rate, and temperature show that they are passively responding to downward fluxes, as appropriate for a cooling planet that is losing more heat through its surface than is being provided from its core or from radioactive heating. Response to doward flux is the inverse of the heat-pipe/mantle-plume mode of planetary cooling. Shear-driven melt extraction from the surface boundary layer explains volcanic provinces such as Yellowstone, Hawaii, and Samoa. Passive upwellings from deeper in the upper mantle feed ridges and near-ridge hotspots, and others interact with the sheared and metasomatized surface layer. Normal plate tectonic processes are responsible both for plate boundary and intraplate swells and volcanism.
Project description:A peridynamic (PD) model of functionally graded materials (FGMs) is presented to simulate transient heat conduction in the FGM plate with insulated cracks. The surface correction is considered in the model to reduce the surface effect near the domain boundary and insulated cracks. In order to verify the proposed model, a numerical example for the FGM plate is carried out. The results show good agreement with the analytical solution. The convergence of the model with the surface correction for FGMs without cracks is then investigated. The results reveal that our model converges to the classical solutions in the limit of the horizon going to zero. The effects of two material points discretization schemes on the accuracy of numerical results are investigated. For transient heat conduction of FGMs with a static crack, the results obtained from the proposed PD model agree well with that from the finite element method. Finally, transient heat conduction of the FGM plate with a dynamic horizontal crack and intersecting cracks is simulated and discussed.
Project description:The division of the earth's surface into continents and oceans is a consequence of plate tectonics but a geological paradox exists at continent-ocean boundaries. Continental plate is thicker and lighter than oceanic plate, floating higher on the mantle asthenosphere, but it can rift apart by thinning and heating to form new oceans. In theory, continental plate subsides in proportion to the amount it is thinned and subsequently by the rate it cools down. However, seismic and borehole data from continental margins like the Atlantic show that the upper surface of many plates remains close to sea-level during rifting, inconsistent with its thickness, and subsides after breakup more rapidly than cooling predicts. Here we use numerical models to investigate the origin and nature of this puzzling behaviour with data from the Kwanza Basin, offshore Angola. We explore an idea where the continental plate is made increasingly buoyant during rifting by melt produced and trapped in the asthenosphere. Using finite element simulation, we demonstrate that partially molten asthenosphere combined with other mantle processes can counteract the subsidence effect of thinning plate, keeping it elevated by 2-3?km until breakup. Rapid subsidence occurs after breakup when melt is lost to the embryonic ocean ridge.
Project description:Thermal nanoimprint lithography is playing a vital role in fabricating micro/nanostructures on polymer materials by the advantages of low cost, high throughput, and high resolution. However, a typical thermal nanoimprint process usually takes tens of minutes due to the relatively low heating and cooling rate in the thermal imprint cycle. In this study, we developed an induction heating apparatus for the thermal imprint with a mold made of ferromagnetic material, nickel. By applying an external high-frequency alternating magnetic field, heat was generated by the eddy currents and magnetic hysteresis losses of the ferromagnetic nickel mold at high speed. Once the external alternating magnetic field was cut off, the system would cool down fast owe to the small thermal capacity of the nickel mold; thus, providing a high heating and cooling rate for the thermal nanoimprint process. In this paper, nanostructures were successfully replicated onto polymer sheets with the scale of 4-inch diameter within 5 min.
Project description:We study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at t = σ. Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.
Project description:To understand the effects of thermal shock on microcrack propagation and permeability in coal, thermal shock tests were conducted on coal specimens by using a constant temperature drying oven (105 °C) and a SLX program controlled cryogenic tank. The growth and propagation of microcracks were measured with computer tomography (CT) scanning and scanning electron microscope (SEM) tests. Results showed that thermal shocks improved the permeability of coal significantly. Notably, the permeability of coal after thermal shocks increased from 211.31% to 368.99% and was positively correlated with temperature difference. CT scanning images revealed that thermal shocks increased the crack number, crack volume and crack width as well as smoothened and widened the gas flow paths, thereby enhancing coal permeability. Moreover, SEM images showed that heating-cooling shocks created more new microcracks, forming more complex crack propagation paths and better connectivity among microcracks in coal compared to cooling shocks. We proposed a crack propagation criterion for coal to explain the mechanism of crack failure and propagation during thermal shocks. Our experiment results and theoretical analysis indicate that the heating-cooling shock is more effective in damaging and breaking coal than the cooling shock. Thus, it can be used as an alternative approach to enhance coal permeability in the production of coalbed methane (CBM).
Project description:Maintaining human body temperature is one of the most basic needs for living, which often consumes a huge amount of energy to keep the ambient temperature constant. To expand the ambient temperature range while maintaining human thermal comfort, the concept of personal thermal management has been recently demonstrated in heating and cooling textiles separately through human body infrared radiation control. Realizing these two opposite functions within the same textile would represent an exciting scientific challenge and a significant technological advancement. We demonstrate a dual-mode textile that can perform both passive radiative heating and cooling using the same piece of textile without any energy input. The dual-mode textile is composed of a bilayer emitter embedded inside an infrared-transparent nanoporous polyethylene (nanoPE) layer. We demonstrate that the asymmetrical characteristics of both emissivity and nanoPE thickness can result in two different heat transfer coefficients and achieve heating when the low-emissivity layer is facing outside and cooling by wearing the textile inside out when the high-emissivity layer is facing outside. This can expand the thermal comfort zone by 6.5°C. Numerical fitting of the data further predicts 14.7°C of comfort zone expansion for dual-mode textiles with large emissivity contrast.
Project description:Polymerase chain reaction (PCR) is a technique for nucleic acid amplification, which has been widely used in molecular biology. Owing to the limitations such as large size, high power consumption, and complicated operation, PCR is only used in hospitals or research institutions. To meet the requirements of portable applications, we developed a fast, battery-powered, portable device for PCR amplification and end-point detection. The device consisted of a PCR thermal control system, PCR reaction chip, and fluorescence detection system. The PCR thermal control system was formed by a thermal control chip and external drive circuits. Thin-film heaters and resistance temperature detectors (RTDs) were fabricated on the thermal control chip and were regulated with external drive circuits. The average heating rate was 32 °C/s and the average cooling rate was 7.5 °C/s. The disposable reaction chips were fabricated using a silicon substrate, silicone rubber, and quartz plate. The fluorescence detection system consisted a complementary metal-oxide-semiconductor (CMOS) camera, an LED, and mirror units. The device was driven by a 24 V Li-ion battery. We amplified HPV16E6 genomic DNA using our device and achieved satisfactory results.