Pipeline Walking due to Temperature Transient: Enhanced Analytical Calculations

2020 ◽  
Author(s):  
Daniel Carneiro ◽  
Renata Carvalhal
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Transient Temperature ◽  
Temperature Profiles ◽  
Linear Temperature ◽  
Temperature Front ◽  
Non Linear ◽  
Closed Form Analytical Solution ◽  
Remarkable Agreement

Abstract Pipeline walking induced by transient temperature profiles as the pipeline heats up is assessed. Firstly, an integrated, closed-form solution is given for a problem for which only an ‘incremental’ solution was available [1]. This involves a short pipeline unrestrained at both ends subject to a linearly ramping temperature front. Secondly, the range of validity of this solution is significantly extended, whilst still presenting it in closed-form. Results are compared with previously published FEA results, presenting remarkable agreement. The closed-form analytical solution is then compared with FEA of more realistic transients (non-linear temperature front). Results show that the linear simplification can introduce excessive conservatism. The FEA results are then examined, and the reason for the excessive conservatism is found to be associated to early expansion of the cold end, which is not observed with the simplified linear front. A simplified incremental solution for non-linear transients is proposed. This is shown to be simple and effective in improving prediction for the range over which where the closed form solution is most conservative.

scholarly journals Analysis of hyperbolic Pennes bioheat equation in perfused homogeneous biological tissue subject to the instantaneous moving heat source

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Ali Kabiri ◽  
Mohammad Reza Talaee
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Method Comparison ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Profiles ◽  
Moving Heat Source ◽  
Bioheat Equation ◽  
Perfusion Rate

AbstractThe one-dimensional hyperbolic Pennes bioheat equation under instantaneous moving heat source is solved analytically based on the Eigenvalue method. Comparison with results of in vivo experiments performed earlier by other authors shows the excellent prediction of the presented closed-form solution. We present three examples for calculating the Arrhenius equation to predict the tissue thermal damage analysis with our solution, i.e., characteristics of skin, liver, and kidney are modeled by using their thermophysical properties. Furthermore, the effects of moving velocity and perfusion rate on temperature profiles and thermal tissue damage are investigated. Results illustrate that the perfusion rate plays the cooling role in the heating source moving path. Also, increasing the moving velocity leads to a decrease in absorbed heat and temperature profiles. The closed-form analytical solution could be applied to verify the numerical heating model and optimize surgery planning parameters.

A New Accurate Closed-Form Analytical Solution for Junction Temperature of High-Powered Devices

2014 ◽  
Vol 136 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Material Properties ◽  
Heat Dissipation ◽  
Field Effect Transistors ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Design Parameters ◽  
Closed Form Analytical Solution

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.

Closed-form and numerical solutions to the laser heating process

1998 ◽  
Vol 212 (2) ◽  
pp. 141-151 ◽  
Author(s):  
B S Yilbas ◽  
M Sami ◽  
A Al-Farayedhi
Keyword(s):  
Closed Form ◽  
Laser Heating ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heat Of Fusion ◽  
Heating Process ◽  
Temperature Profiles ◽  
Depth Analysis ◽  
Analytical Approaches

The laser processing of engineering materials requires an in-depth analysis of the applicable heating mechanism. The modelling of the laser heating process offers improved understanding of the machining mechanism. In the present study, a closed-form solution for a step input laser heating pulse is obtained and a numerical scheme solving a three-dimensional heat transfer equation is introduced. The numerical solution provides a comparison of temperature profiles with those obtained from the analytical approach. To validate the analytical and numerical solutions, an experiment is conducted to measure the surface temperature and evaporating front velocity during the Nd—YAG laser heating process. It is found that the temperature profiles resulting from both theory and experiment are in a good agreement. However, a small discrepancy in temperatures at the upper end of the profiles occurs. This may be due to the assumptions made in both the numerical and the analytical approaches. In addition, the equilibrium time, based on the energy balance among the internal energy gain, conduction losses and latent heat of fusion, is introduced.

Strain fields in cracked bodies under antiplane shear for a generalised non-hardening material law

2019 ◽  
Vol 24 (10) ◽  
pp. 3125-3135
Author(s):  
M Zappalorto
Keyword(s):  
Closed Form ◽  
Large Strain ◽  
Closed Form Solution ◽  
Form Solution ◽  
Antiplane Shear ◽  
Elastic Behaviour ◽  
Strain Fields ◽  
Hardening Material ◽  
Hardening Law ◽  
Non Linear

An exact, closed form, solution is derived for the non-linear stress distribution in a cracked body under antiplane shear deformation. A generalised, non work-hardening, law is introduced to describe the material behaviour, and the stress and strain fields are derived in closed form. Such a new generalised material law includes the effect of a new parameter, a, which allows the transition from the ideally elastic behaviour (low strain regime) to the pure non-linear behaviour (large strain regime) to be modulated. A discussion is carried out on the features of the new solution and on the behaviour of stresses and strains close to and far away from the crack tip.

scholarly journals A closed-form analytical solution for the valuation of convertible bonds with constant dividend yield

2006 ◽  
Vol 47 (4) ◽  
pp. 477-494 ◽  
Author(s):  
Song-Ping Zhu
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Analytical Formula ◽  
Solution Process ◽  
Closed Form Solution ◽  
Approximate Solutions ◽  
Convertible Bonds ◽  
Form Solution ◽  
Dividend Yield ◽  
Closed Form Analytical Solution

AbstractIn this paper, a closed-form analytical solution for pricing convertible bonds on a single underlying asset with constant dividend yield is presented. A closed-form analytical formula has apparently never been found for American-style convertible bonds (CBs) of finite maturity time although there have been quite a few approximate solutions and numerical approaches proposed. The solution presented here is written in the form of a Taylor's series expansion, which contains infinitely many terms, and thus is completely analytical and in a closed form. Although it is only for the simplest CBs without call or put features, it is nevertheless the first closed-form solution that can be utilised to discuss convertibility analytically. The solution is based on the homotopy analysis method, with which the optimal converting price has been elegantly and temporarily removed in the solution process of each order, and consequently, the solution of a linear problem can be analytically worked out at each order, resulting in a completely analytical solution for the optimal converting price and the CBs' price.

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