Cooling and heating in multi-dimensional heat flow

5 Cooling and heating in multi-dimensional heat flow 

In geometric multi-dimensional heat flow the temperature fields that have to be calculated depend on two or three spatial coordinates and must satisfy the heat conduction equation 

Here the Laplace operator V2t has the form given in 2.1.2 for cartesian and cylindrical coordinate systems. We will once again consider the transient heat conduction problem solved for the plate, the infinitely long cylinder and the sphere in section 2.3.4 A body with a constant initial temperature is brought into contact with a fluid of constant temperature tfy so that heat transfer takes place between the fluid and the body, whereby the constant heat transfer coefficient a is decisive. 

In the following section we will consider two solution procedures  

The latter of the two methods offers a practical, simple applicable solution to transient heat conduction problems and should always be applied for sufficiently small Biot numbers. 

---