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[en] This article theoretically analyzes the cutting depth and material removal rate of an atomic force microscope (AFM) cantilever during nanomachining. An analytical expression for the vibration frequency and displacement of the cantilever has been obtained by using the modified couple stress theory. The theory includes one additional material length scale parameter revealing the micro-scale effect. According to the analysis, the results show that the effect of size-dependent on the vibration behavior of the AFM cantilever is obvious. The maximum displacement of nanomachining with the AFM cantilever represents the cutting depth. The area under the displacement-time curve is related to the material removal rate. When the excitation frequency is closer to the nature frequency of the cantilever, a larger material removal rate is obtained
[en] In this study, a conjugate gradient method based on an inverse algorithm is applied to estimate the unknown space and time dependent forced convection heat transfer rate of two in line cylinders placed in a cross stream. While knowing the temperature history at the measuring positions near the surfaces of the cylinders, the heat transfer rate on the surfaces of both cylinders can be successfully computed. No prior information is needed on the functional form of the unknown heat transfer rate. A particular feature in this study is that the considered Reynolds number is high enough to result in an unsteady flow around the cylinders. In addition to the transient temperature field, this makes the flow field itself time dependent as well, thus adding more complexity to the numerical analysis. The accuracy of the inverse analysis is examined by using the simulated temperature measurement. Results show that an excellent estimation on the heat transfer rate and temperature distributions can be obtained for the case considered in this study
[en] Highlights: • A parametric study on a low-temperature-differential Stirling engine has been conducted by using CFD. • The effects of three geometric and two operational parameters on engine performance have been investigated. • It is found that each parameter produces different effects except power piston stroke and power piston radius. • The results are useful for guiding the design of new low-temperature-differential Stirling engines. - Abstract: An in-house CFD code has been applied to a low-temperature-differential (LTD) γ-type Stirling engine to understand the effects posed by several geometrical and operational parameters on engine performance. The results include variations of pressure, temperature, and heat transfer rates within an engine cycle as well as variations of engine’s power and efficiency versus these parameters. It is found that power piston stroke and radius influence engine performance very similarly, and power and efficiency both increase as these two parameters increase. In fact, the effects of the two parameters can be assimilated into those by the parameter of compression ratio. The stroke of displacer is observed to affect strongly on heat input but weakly on power, thus causing the efficiency to decrease as it increases. As expected, both power and efficiency increase as temperature difference between the hot and cold ends increases. Lastly, engine speed is observed to pose strong positive effects on power but exert weak effects on efficiency. This study reveals the effects produced by several important parameters on engine performance, and such information is very useful for the design of new LTD Stirling engines.
[en] Highlights: ► Time-dependent base heat flux of a functionally graded fin is inversely estimated. ► An inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied. ► The distributions of temperature in the fin are determined as well. ► The influence of measurement error and measurement location upon the precision of the estimated results is also investigated. - Abstract: In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent base heat flux of a functionally graded fin from the knowledge of temperature measurements taken within the fin. Subsequently, the distributions of temperature in the fin can be determined as well. It is assumed that no prior information is available on the functional form of the unknown base heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors and measurement location upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent base heat flux and temperature distributions can be obtained for the test case considered in this study.
[en] In this study, a conjugate gradient method based on an inverse algorithm is applied to estimate the unknown space and time dependent convection heat transfer coefficient of an annular fin. While knowing the temperature or strain history at the measuring positions of the fin, the convection heat transfer coefficient between the fin and the ambient fluid can be successfully computed. No prior information is needed on the functional form of the unknown convection heat transfer coefficient; and thus, the present study is classified as the function estimation inverse calculation. A particular feature in this study is that the thermal and strain fields are coupled, which makes solving the inverse problem a highly challenging task. The accuracy of the inverse analysis is examined by using the simulated temperature or strain measurements. Results show that excellent estimations of the convection heat transfer coefficient, temperature distributions and thermal stress distributions can be obtained for all the cases considered in this study