Formulation of surface temperature for laser evaporative pulse heating: The time exponentially decaying pulse case

2002 ◽  
Vol 216 (3) ◽  
pp. 289-299 ◽  
Author(s):  
B S Yilbas ◽  
M Kalyon
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Solid Substrate ◽  
Form Solution ◽  
Solution Temperature ◽  
Heating Process ◽  
Pulse Parameter ◽  
Pulse Profile ◽  
Transform Method

Modelling of the laser heating process is fruitful, since it enhances the understanding of the physical processes involved and minimizes the experimental cost. In the present study, an analytical solution for the temperature distribution inside the solid substrate is obtained using a Laplace transform method. A time exponentially decaying laser pulse profile is introduced in the analysis. The phase change process and recession velocity are accommodated to account for the evaporation at the surface. The closed-form solution obtained is compared with the analytical solution obtained previously for a conduction limited heating case. It is found that the closed-form solution obtained from the present study reduces to a previously obtained analytical solution when the pulse parameter, β∗, is set to zero in the closed-form solution. Temperature predictions from simulations agree well with the results obtained from the closed-form solution.

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.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

On the Analytical Solution of Externally Pressurized Porous Gas Journal Bearings

1978 ◽  
Vol 100 (3) ◽  
pp. 442-444 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Journal Bearings ◽  
Form Solution ◽  
Performance Characteristics ◽  
Gas Bearing ◽  
Good Agreement

A closed form solution of pressure distribution which leads to the determination of bearing performance characteristics of an externally pressurized porous gas bearing without journal rotation is obtained. A good agreement with a similar available solution confirms the validity of the method.

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.

Exact solution for time exponentially varying pulsed laser heating: Convective boundary condition case

2001 ◽  
Vol 215 (5) ◽  
pp. 591-606 ◽  
Author(s):  
M Kalyon ◽  
B S Yilbas
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Closed Form ◽  
Temperature Rise ◽  
Laser Heating ◽  
Closed Form Solution ◽  
Convective Boundary Condition ◽  
Form Solution ◽  
Heating Process ◽  
Convective Boundary

Laser heating offers considerable advantages over conventional methods. The closed-form solution for the temperature rise in the substrate during the laser heating process gives insight into the physical phenomena involving during the heating process and the material response to a laser heating pulse. In the present study, the exact solution for the temperature rise due to a time exponentially varying pulse and convective boundary condition at the surface is obtained. The closed-form solution to the solutions available in the literature for a step input intensity pulse with a convective boundary condition at the surface as well as a time exponentially varying pulse with a non-convective boundary condition at the surface is deduced. A Laplace transformation method is used in the analysis. In order to account for a pulse resembling a typical laser pulse, an intensity function resulting in exponentially increasing and decaying intensity distribution is employed in the source term in the governing transport equation. The effects of the pulse parameters β′, β′/γ′ and Biot number Bi on the resulting temperature profiles are presented and the material response to a pulse profile resembling a typical actual laser pulse is discussed. It is found that the closed-form solution obtained in the present study becomes identical with those presented in the previous studies for different pulse and boundary conditions. Moreover, the coupling effect of pulse parameter β and Bi is significant for the temperature rise at the surface.

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.

An analytical solution for jointed tunnel linings in elastic soil or rock

2008 ◽  
Vol 45 (11) ◽  
pp. 1572-1593 ◽  
Author(s):  
Hany El Naggar ◽  
Sean D. Hinchberger
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Segmental Lining ◽  
Sophisticated Method ◽  
Walled Cylinder ◽  
Elastic Soil

This paper presents a closed-form solution for tunnel linings that can be idealized as an inner jointed segmental lining and an outer thick-walled cylinder embedded in a homogeneous infinite elastic soil or rock. Solutions for moment and thrust have been derived for cases involving slip and no slip at the lining–ground and lining–lining interfaces. In addition, the closed-form solution is verified by comparing it with finite element results where it is shown to agree well with this more sophisticated method of analysis.

scholarly journals INFLUENCE OF BEACH LENGTH ON THE DEVELOPMENT OF ESTUARINE DELTAS

2018 ◽  
pp. 12
Author(s):  
Duy Dinh Van ◽  
Hitoshi Tanaka ◽  
Magnus Larson ◽  
Yuta Mitobe ◽  
Viet Nguyen Trung
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
River Mouth ◽  
Form Solution ◽  
River Delta ◽  
Sediment Supply ◽  
Infinite Extent

Larson et al. (1987) proposed a closed-form solution to describe the development of river delta coastlines owing to sediment supply from the river. This solution is for a beach of infinite extent adjacent to the river mouth. However, in reality, the beach length is always finite due to the existence of man-made structures or headlands. It is, therefore, useful to derive a new analytical solution to gain a better understanding of beach behavior under the effect of boundaries.

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