“Heat Conduction Equation--Disk”的概念、定义、习题解题方法及翻译-数学辞典

　

单词

Heat Conduction Equation--Disk

释义

Heat Conduction Equation--Disk

To solve the Heat Conduction Equation on a 2-D disk of radius , try to separate the equation using

(1)

Writing the

and

terms of the Laplacian in Spherical Coordinates gives

(2)

so the Heat Conduction Equation becomes

(3)

Multiplying through by

gives

(4)

The

term can be separated.

(5)

which has a solution

(6)

The remaining portion becomes

(7)

Dividing by

gives

(8)

where a Negative separation constant has been chosen so that the

portion remains finite

(9)

The radial portion then becomes

(10)

(11)

which is the Spherical Bessel Differential Equation. If the initial temperature is

and the boundarycondition is

, the solution is

(12)

where

is the

th Positive zero of the Bessel Function of the First Kind

.

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更新时间：2025/4/5 8:31:25