Finite element implementation of the eigenfunction series solution for transient heat conduction problems with low Biot number

Abstract Analytical solutions to transient heat conduction problems are often obtained by superposition of a particular solution (often the steady-state solution) and an eigenfunction series, representing terms that decay exponentially with time. Here, we present a finite element realization of this method in which conventional finite element discretization is used for the spatial distribution of temperature and analytical methods for the time dependence. This leads to a linear eigenvalue problem whose solution then enables a general numerical model of the transient system to be created. The method is an attractive alternative to conventional time-marching schemes, particularly in cases where it is desired to explore the effect of a wide range of operating parameters. The method can be applied to any transient heat conduction problem, but we pay particular attention to the case where the Biot number is small compared with unity and where the evolution of the system is very close to that with zero heat loss from the exposed surfaces. This situation arises commonly in machines such as brakes and clutches which experience occasional short periods of intense heating. Numerical examples show that with typical parameter values the simpler zero heat loss solution provides very good accuracy. We also show that good approximations can be achieved using a relatively small subset of the eigenvectors of the problem

Thermal Performance of a Single Slope Solar Water Still with Enhanced Solar Heating System

Abstract. This paper investigates experimentally the thermal performance of conventional solar water still with enhanced solar heating system. A number of variables have been considered including the water depth inside the still and the inlet saline water temperature to the solar still from the preheater solar collector system and the still basin geometry. The still is modified to include preheating solar system, to preheat saline water before entering the solar still, in order to enhance its hourly or daily yield of pure water. A single slope conventional solar still with solar preheating unit was constructed and experimentally tested under different weather conditions. Different quantities of water in the solar still basin were tested to find the effect of water quantity on the hourly yield and still's thermal efficiency. It was found that 1 cm depth and finned still basin gives the best performance in terms of fresh water yield and thermal efficiency. The addition of the solar water preheater to the system has significantly increases the inlet basin saline water temperature to almost saturated temperature and saline water in the basin needed only small heat to be vaporized and hence increases the production of fresh water and enhances the solar still thermal efficiency

EXPLORING THE IMPACTS OF COVID-19 PANDEMIC ON OMAN'S ELECTRICITY SECTOR

This article reviews the recent trends of Oman's electricity sector before the COVID-19 pandemic outbreak. The impacts of the pandemic on the Main Interconnected System (MIS) of Oman were analyzed using hourly load data. The analysis shows that the MIS demand declined as a result of the decrease in economic activities during the lockdown. In addition, the MIS demand experienced temporal and geographical variations: the former is demonstrated by a shift in peak demand hours, while the latter is represented by a reduction in Muscat's urban areas' load compared with those of other areas

An experimental investigation of the effect of defect shape and orientation on the burst pressure of pressurised pipes

The burst pressure of commonly used ductile steel pipes in oil and gas industries, i.e. X52 and X60, is measured under internal pressure loading. The pipes were machined with circular and boxed defects at different orientations to simulate actual metal loss defects. Defect shapes and orientations were investigated in detail to study how they affect the failure behaviour of interacting defects. The experimental burst pressure results were compared with those obtained using existing analytical methods from Design Codes. Comparison of the results showed conservatism in the existing analytical methods which may potentially lead to unnecessary plant shutdowns and pipe repairs. The outcome of the experimental tests revealed that the shapes of the defects have very small influence on the defect interaction behaviour. The burst tests interestingly showed that the defect orientation has an important effect on defect interaction. Defects oriented in the hoop and diagonal directions showed no defect interaction even when spaced by a distance of one wall thickness, while defects oriented in the longitudinal directions showed that defects interact even when the spacing is up to six wall thickness but the interaction fades away for defects spaced at longer distances

Transient solution of a thermoelastic instability problem using a reduced order model.

Above a certain critical speed, sliding systems with frictional heating such as brakes and clutches can exhibit thermoelastic instability (TEI) in which non-uniform perturbations develop in the pressure and temperature fields. A method is described in which the transient thermomechanical behavior of such systems is approximated by a reduced order model, describing few dominating perturbations or eigenfunctions. The goal is to construct a mathematical model of the system with modest number of degrees of freedom. If a single dominant perturbation is used, an integral expression can be written for the evolution of the perturbation with time. A more accurate description involving several terms requires that the transient behavior be generated by a sequence of operations in which the sliding speed is piecewise constant. Both models are evaluated by comparison with direct numerical simulation and prove to give good accuracy with a dramatic reduction in computation time. A method is also described for solving the unperturbed thermoelastic contact problem with frictional heating, which involves non-homogenous equations. A solution method is explored based on the concept of superimposing a steady state solution to an eigenfunction expansion of an equivalent homogenous problem. The difference between the initial temperature field and the steady state distribution acts as an initial disturbance that can grow yielding a non-uniform distribution in the temperature and contact pressure. This method was evaluated by comparison with direct numerical simulation and provides an excellent computational efficiency. A reduced order model, in which few dominating eigenfunctions are retained in the expansion series, gives an excellent approximation especially during the growth phase of a clutch or brake engagement when the sliding speed is above the critical speed. The contact area may shift or change in size causing the thermoelastic contact problem to be non-linear. An approximate transient solution is described in which the contact area is treated as a piecewise constant in time. This is investigated in the context of a typical clutch problem for the maximum temperature reached by the system. A typical clutch system operates above the critical speed, causing reduction in the contact area and, therefore, high local contact. A parametric study is conducted for better clutch performance. Short stopping time is shown to result in higher temperature caused by the high rate of heat generation. The effect of a multiple clutch engagement cycles is explored, in which the temperature is found to decay to a uniform state between the engagements. Finally, the cooling fluid, found in wet clutch systems, plays an important role in preventing temperature accumulation between engagement cycles.Ph.D.Applied SciencesMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129078/2/3042036.pd

Stresses and deformations analysis of a dry friction clutch system

The friction clutch is considered the essential element in the torque transmission process. In this paper, the finite element method is used to study the stresses and deformations for clutch system (pressure plate, clutch disc and flywheel) due to the contact pressure of diaphragm spring and the centrifugal force during the full engagement of clutch disc (assuming no slipping between contact surfaces). The investigation covers the effect of the contact stiffness factor FKN on the pressure distribution between contact surfaces, stresses and deformations. The penalty and Augmented Lagrangian algorithms have been used to obtain the pressure distribution between contact surfaces. ANSYS13 software has been used to perform the numerical calculation in this paper. © 2013 Published by Faculty of Engineering

Investigation of thermoelastic problem of multiple-disc friction clutches applying different thermal loads

The designers of friction clutch systems in vehicular applications should always take into account a number of essential criteria. The friction clutch should be able to transfer the torque from the driving shaft to the driven one within a short time and minimum amount of shocks and vibrations to make the engagement (disengagement) as gentle as possible. Furthermore, it is well known that high surface temperatures were noticed during the beginning of engagement period due to slipping between the contacting elements of the friction clutch system with ensuing heat generation. The transient thermoelastic problem of multi-disc systems has been deeply investigated by many scientists and researchers using numerical techniques such as finite element method. In this analysis, the influence of the sliding speed on the thermoelastic behavior when the initial heat generated is constant was studied. For this purpose an axisymmetric finite element models were developed and used in the simulation shown in the paper