Analytical solution for transient flow of energy in a one-dimensional radiating fin.

AIAA Journal ◽  
1968 ◽  
Vol 6 (1) ◽  
pp. 90-93 ◽  
Author(s):  
LYNN D. RUSSELL ◽  
ALAN J. CHAPMAN
Keyword(s):  
Analytical Solution ◽  
Transient Flow ◽  
One Dimensional

A new analytical solution for one dimensional transient flow in unsaturated soils

2010 ◽  
pp. 1029-1034
Author(s):  
H Aghjani ◽  
A Soroush
Keyword(s):  
Analytical Solution ◽  
Unsaturated Soils ◽  
Transient Flow ◽  
One Dimensional

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

Analytical Solution and Numerical Simulation for One-Dimensional Steady Nonlinear Heat Conduction in a Longitudinal Radial Fin with Various Profiles

2013 ◽  
Vol 44 (1) ◽  
pp. 20-38 ◽  
Author(s):  
R.J. Moitsheki ◽  
M.M. Rashidi ◽  
A. Basiriparsa ◽  
A. Mortezaei
Keyword(s):  
Numerical Simulation ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Nonlinear Heat Conduction ◽  
One Dimensional

Building Vertical Walls by Deposition of Molten Metal Droplets

2005 ◽  
Author(s):  
M. Fang ◽  
S. Chandra ◽  
C. B. Park
Keyword(s):  
Surface Layer ◽  
Analytical Solution ◽  
Substrate Temperature ◽  
Layer By Layer ◽  
Droplet Temperature ◽  
Droplet Generator ◽  
One Dimensional ◽  
Metallurgical Bonding ◽  
Experimental Parameters ◽  
Vertical Walls

Experiments were conducted to determine conditions under which good metallurgical bonding was achieved in vertical walls composed of multiple layers of droplets that were fabricated by depositing tin droplets layer by layer. Molten tin droplets (0.75 mm diameter) were deposited using a pneumatic droplet generator on an aluminum substrate. The primary parameters varied in experiments were those found to most affect bonding between droplets on different layers: droplet temperature (varied from 250°C to 325°C) and substrate temperature (varied from 100°C to 190°C). Considering the cooling rate of droplet is much faster than the deposition rate previous deposition layer cooled down too much that impinging droplets could only remelt a thin surface layer after impact. Assuming that remelting between impacting droplets and the previous deposition layer is a one-dimensional Stefan problem with phase change an analytical solution can be found and applied to predict the minimum droplet temperature and substrate temperature required for local remelting. It was experimentally confirmed that good bonding at the interface of two adjacent layers could be achieved when the experimental parameters were such that the model predicted remelting.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

Semi-analytical solution for the one-dimensional consolidation of multi-layered unsaturated soils with semi-permeable boundary

2021 ◽  
Vol 130 (1) ◽  
Author(s):  
Linzhong Li ◽  
Aifang Qin ◽  
Lianghua Jiang
Keyword(s):  
Analytical Solution ◽  
Unsaturated Soils ◽  
One Dimensional ◽  
The One

scholarly journals ANALYTICAL SOLUTION OF THE PROBLEM OF A CONVERGENT SHOCK IN GAS FOR ONE-DIMENSIONAL CASE

2017 ◽  
Vol 9 (4) ◽  
pp. 52-58 ◽  
Author(s):  
V.F. Kuropatenko ◽  
◽  
F.G. Magazov ◽  
E.S. Shestakovskaya ◽  
◽  
...  
Keyword(s):  
Analytical Solution ◽  
Dimensional Case ◽  
One Dimensional

Analytical Solution to the Transient-Flow Problems for a Well Located near a Finite-Conductivity Fault in Composite Reservoirs

2003 ◽  
Author(s):  
N.M. Anisur Rahman ◽  
Michael D. Miller ◽  
Louis Mattar
Keyword(s):  
Analytical Solution ◽  
Transient Flow ◽  
Finite Conductivity ◽  
Flow Problems
Sign in / Sign up

Export Citation Format

Share Document