5.2 Three-Dimensional Heat Equation

5.2 Three-Dimensional Heat Equation

• We are going to derive the three-dimensional heat equation using a different method.

• The next job is to quantify the statement.
• The inflow is negative because this quantity is positive.

• The term "rate of generation inside" is meant to indicate the rate of conversion of energy from other forms to thermal.

• This is how the argument goes.
• The integral over that sub region would be either positive or negative.

• The minus sign makes the heat flow "downhill" from hotter to colder regions.

A given function is 1

• The given function is 2.

• The three-dimensional problem for a solid in the form of a rectangular parallelepiped was set up.

• The top and bottom surfaces should be insulated.

• They transfer heat from one place to another.

• A full, three-dimensional problem is difficult to solve, so we often look for ways to reduce it to two or even one dimensions.

• The averaging process was applied to Eqs.