A unified approach to closed-form solutions of moving heat-source problems

1998 ◽  
Vol 33 (5-6) ◽  
pp. 415-424 ◽  
Author(s):  
S. M. Zubair ◽  
M. Aslam Chaudhry
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Moving Heat Source ◽  
Unified Approach ◽  
Closed Form Solutions

Closed-Form Expression for Temperature in a Semi-Infinite Solid Due to a Fast Moving Surface Heat Source

1991 ◽  
Vol 113 (4) ◽  
pp. 828-831 ◽  
Author(s):  
J. A. Tichy
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Frictional Contact ◽  
Closed Form Expression ◽  
Moving Heat Source ◽  
Convolution Integral ◽  
Form Expression ◽  
Exponential Integral ◽  
Surface Conditions ◽  
Closed Form Solutions

In the thermal analysis of an asperity on a sliding surface in frictional contact with an opposing surface, conditions are often idealized as a moving heat source. The solution to this problem at arbitrary Pe´cle´t number in terms of a singular integral is well known. In this study, closed-form solutions are found in terms of the exponential integral for high Pe´cle´t number. Fortunately, the closed-form solutions are accurate at Pe´cle´t number of order one. While several restrictions are necessary, the closed-form expressions offer considerable numerical savings relative to evaluations of the convolution integral.

Melting Solid Plug Between Two Coaxial Pipes by a Moving Heat Source in the Inner Pipe

1994 ◽  
Vol 116 (4) ◽  
pp. 1028-1033 ◽  
Author(s):  
S. A. Fomin ◽  
P. S. Wei ◽  
V. A. Chugunov
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Surrounding Medium ◽  
Scale Analysis ◽  
Moving Heat Source ◽  
Closed Form Solutions ◽  
Entire Process ◽  
Annular Gap ◽  
Independent Parameters ◽  
Molten Region

Melting of a solid plug in the gap between two coaxial pipes by inserting a moving heat source in the inner pipe is investigated. Using a scale analysis, closed-form solutions for temperatures of liquid in the inner pipe, solid plug and liquid in the annular gap, and the surrounding medium around the outer pipe are determined. It is shown that eight independent dimensionless parameters are required to specify the entire process. The effects of independent parameters on the shapes of the molten region in the gap are found. The analysis and results provided are useful for the design of oil pipes.

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.

Closed-Form Solutions of the Elastic Half Space due to a Line Heat Source

2014 ◽  
Vol 638-640 ◽  
pp. 2082-2091
Author(s):  
John C.C. Lu ◽  
Feng Tsai Lin
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Line Heat Source ◽  
Closed Form Solutions ◽  
Line Sink ◽  
Vertical Displacements ◽  
Thermoelastic Response

Thermoelastic response due to a line heat source is analog to poroelastic reaction caused by a fluid line sink. In this study, the strata are modeled as a thermoelastic or poroelastic half space bounded by horizontal surface in the mathematical model. Thermomechanics and poromechanics are applied on the formulation of basic governing equations, and an analogy is drawn to show the similarity. Using Hankel transform technique and approaching symbolic integral through Mathematica, the closed-form solutions of the horizontal and vertical displacements due to a fluid line sink are obtained. The displacements produced by the line heat source are described through analog quantities between thermoelasticity and poroelasticity. The solutions can be applied to dewater operations and build waste repository.

IT'S YOUR CHOICE: A UNIFIED APPROACH TO CHOOSER OPTIONS

2010 ◽  
Vol 13 (01) ◽  
pp. 139-161 ◽  
Author(s):  
KLAUS SANDMANN ◽  
MANUEL WITTKE
Keyword(s):  
Interest Rates ◽  
Closed Form ◽  
International Economy ◽  
Multidimensional Model ◽  
Unified Approach ◽  
Unified Framework ◽  
Stochastic Interest Rates ◽  
Closed Form Solutions ◽  
Inflation Rates ◽  
Stochastic Interest

We propose a unified framework for the pricing and hedging of chooser options on lognormal assets. This includes e.g. exchange or inflation rates under stochastic interest rates or equities under stochastic interest rates and dividend yields. This extends and includes chooser options under deterministic interest rates by a multidimensional model of an international economy with correlated stochastic processes. In this framework we derive closed form solutions of the arbitrage price for different specifications of chooser options. Also different hedge strategies are derived and their properties compared.

The Nonlinear Bending of Thin Rods

1959 ◽  
Vol 26 (1) ◽  
pp. 40-43 ◽  
Author(s):  
T. P. Mitchell
Keyword(s):  
Closed Form ◽  
Normal Load ◽  
Unified Approach ◽  
Nonlinear Bending ◽  
Circular Arc ◽  
Closed Form Solutions

Abstract The nonlinear bending of straight and circular-arc cantilevers under vertical and horizontal point loads is analyzed from a unified approach. Formulas for determining the deflected shape of the cantilevers are presented. Closed-form solutions are obtained for bending under two types of distributed loads. In particular, the problem of bending under a uniformly distributed normal load is solved.

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