$\"\"$

\

Radius of the sphere is $\"\"$ and its temaparature is $\"\"$ .

\

Radius of the concentric sphere is $\"\"$ and its temaparature is $\"\"$ .

\

The differential equation is $\"\"$ .

\

First-order differential equation is $\"\"$ .

\

$\"\"$

\

Second-order differential equation is $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

Apply integration on each side.

\

$\"\"$

\

Apply exponent on each side.

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in the above equation.

\

$\"\"$

\

Apply integration on each side.

\

$\"\"$

\

Let $\"\"$ .

\

Substitute $\"\"$ in the above equation.

\

$\"\"$

\

Substitute $\"\"$ in the above equation.

\

$\"\"$

\

Let $\"\"$ .

\

Substitute $\"\"$ in the above equation.

\

$\"\"$

\

Substitute $\"\"$ in the above equation.

\

$\"\"$

\

$\"\"$

\

Subtract equation (1) equation (2).

\

$\"\"$

\

From equation (1) : $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

The equation of temparature is $\"\"$ .

\

$\"\"$

\

The equation of temparature is $\"\"$ .