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For an endoreversible heat engine operates steadily between two fixed temperatures, Bejan found the engine's best performance can be obtained if the total thermal conductance is evenly divided for hot-end and cold-end heat exchangers. In this study, a heat by-pass model is used to represent the losses due to internal irreversibilities, and the more general formulations are derived for both the optimal area allocation and the maximum thermal efficiency. The results calculated from the present formulations when there is no internal irreversibility(a special case) are consistant with that obtained by Bejan.
The solutions for flow and heat transfer in a steady laminar boundary layer flow are presented analytically for an electrically conducting viscoelastic fluid, subject to a transverse uniform magnetic field, past a semi-infinite stretching sheet. The temperature profiles and thermal characteristics at the wall are drawn and tabulated for selected parameters with prescribed surface temperature (PST) and prescribed surface heat flux (PHF) conditions. We also give the asymptotic solutions for temperature when the Prandtl number is very large. It is found that the inclusion of Joule heating has a significant influence on the thermal characteristics at the wall and the wall heat transfer strongly depends on the Prandtl number Pr as well as the Eckert number Ec. The heat flow may transfer from the fluid to the wall when Ec is large rather than from wall to the fluid when Ec is small. A physical argument about the thermal characteristics at the wall is proposed.
As an essential foundation for the associated thermoelasticity analysis in the boundary element method (BEM), this article proposes an expedient, yet powerful, approach to analyze the heat conduction in multiply jointed anisotropic media with bonding defects/interface cracks. The direct domain mapping technique (DDM) is applied to treat a domain consisting of dissimilar anisotropic sub-regions in the potential theory of BEM. The heat transfer across a crack is modeled with a gap conductance equation specially formulated for the BEM analysis. Two numerical examples are provided as illustrations of the validity and the applicability of this proposed scheme.
This paper describes the applications of the method of fundamental solutions (MFS) as a mesh-free numerical method for the Stokes' first and second problems which prevail in the semi-infinite domain with constant and oscillatory velocity at the boundary in the fluid-mechanics benchmark problems. The time-dependent fundamental solutions for the semi-infinite problems are used directly to obtain the solution as a linear combination of the unsteady fundamental solution of the diffusion operator. The proposed numerical scheme is free from the conventional Laplace transform or the finite difference scheme to deal with the time derivative term of the governing equation. By properly placing the field points and the source points at a given time level, the solution is advanced in time until steady state solutions are reached. It is not necessary to locate and specify the condition at the infinite domain such as other numerical methods. Since the present method does not need mesh discretization and nodal connectivity, the computational effort and memory storage required are minimal as compared to the domain-oriented numerical schemes. Test results obtained for the Stokes' first and second problems show good comparisons with the analytical solutions. Thus the present numerical scheme has provided a promising mesh-free numerical tool to solve the unsteady semi-infinite problems with the space-time unification for the time-dependent fundamental solution.
The purpose of this work is to study the dynamic mechanical response of silicon wafer subjected to low-velocity impact loading. Transient finite element analysis was utilized to obtain the numerical simulated result and was used to check against the experimental findings. Good relationship between each other was observed. A pair of polysilicon microsensors manufactured by the micro-fabrication technique was directly fabricated on the surface of silicon wafer so as to detect the impact induced dynamic strain. A series of low-velocity impact tests utilizing the home-made drop-weight mini-tower tester was conducted. These test results were used to examine the accuracy and adequacy of the current micro strain sensors for stress wave propagation measurements. It is concluded that the difference between the present measured wave speed and the one-dimensional longitudinal wave speed under conditions of plane strain were determined to be within 5.6% for the present low-speed impact problem. A maximum of 10.9% deviation between the test determined elastic modulus and a reference value (16) of 130 GPa was found based on a series of impact test results. In addition, a difference of 2% error was reported when we compared the test detected peak stress value after impact initiated (before wave is reflected from the boundary) and the corresponding numerical simulated response.
Stair locomotion has been used in the rehabilitation of the lower extremity as a motor performance test and multi-joint exercise. Controversies exist regarding joint loads during stair locomotion. The purposes of the study were to investigate the three-dimensional kinetics of the lower limb joints during stair locomotion, and to compare them with those during level walking. Ten normal young adults walked, and ascended and descended stairs in a gait laboratory while kinematic and kinetic data were collected and analyzed. The results showed that the intersegmental resultant forces at the joints during the activities were generally similar in pattern but the force magnitudes, moments and angular impulses were significantly different. The general impression that the loads in the lower limb were larger during stair descent than stair ascent only holds for certain kinetic variables. Most of the peak joint moments and angular impulses over the entire stance phase were bigger during stair ascent than descent. The study provides a complete knowledge of the three-dimensional loading patterns at and dynamic functions of the lower limb joints during level walking and stair locomotion. It will be helpful for the planning and evaluation of treatment programs for patients with neuromusculoskeletal pathologies in the lower extremities.
Reusable launch vehicles (RLV) currently envisioned incorporate a wide variety of propulsion types. Various propulsion devices have been designed, or are being designed. The Integral-Rocket-Ramjet (IRR) propulsion mainly applies to a tactical missile boost system and few have mentioned this system in RLV design. According to the technological ability of Taiwan and a feasibility study, it shows that the present reusable launch system can exploit the potential benefit of IRR propulsion for the RLV system. A conceptual study of an unmanned two-stage-to-orbit (TSTO) launch vehicle is designed in this paper. The first stage of the vehicle is reusable with IRR engines. The second stage is expendable and rocket powered. The assumed mission is designed to insert a 100kg payload into a low earth circular orbit at various inclination angles. The calculations are made for the case where the TSTO system is used in Taiwan. The fundamentals of launch vehicle design are examined using simplified two-stage performance equations. Launch vehicle design is optimized when the performance and programmatic drivers are balanced. There is an acceptable set of launch and landing sites on islands off the coast of Taiwan.
An analysis is performed to the study of the momentum, heat and mass transfer of a viscous fluid-saturated porous medium past an impermeable, non-isothermal stretching sheet with internal heat generation or absorption and chemical reaction. The governing partial differential equations are converted into ordinary differential equations by means of a similarity transformation. Exact solutions of velocity components together with the pressure distribution, which can not be found in the boundary layer theory, are obtained analytically; in addition, the temperature and concentration functions are given in terms of confluent hypergeometric functions. The velocity, temperature (concentration) profiles and thermal characteristics at the sheet for relevant parameters are plotted, tabulated and discussed.