Question

What is a semi-infinite medium? Give examples of solid bodies that can be treated as semi-infinite media for heat transfer purposes.

Short answer

Answer: A semi-infinite medium is a material that extends to infinity in one direction, while the other dimensions are finite. This simplification is often used in heat transfer problems to make calculations more manageable. Examples of solid bodies that can be treated as semi-infinite media for heat transfer purposes include the surface of a large solid (e.g. ground or large structure), a very thin slab, thick insulation layers, and pipes with a long length and small diameter. These examples assume temperature changes occur primarily in one direction, making the other dimensions negligible for calculations.

Step-by-step solution

Definition of a Semi-infinite Medium

A semi-infinite medium refers to a material that extends to infinity in one direction, while the other dimensions are finite. This is a simplification often used in heat transfer problems to make calculations more manageable, assuming that any heat transfer in the infinite direction has negligible effects on the overall process.

Example 1: Surface of a Large Solid

A common example of a semi-infinite medium in heat transfer is the surface of a large solid, such as the ground or a large structure. During heat transfer, the temperature at the surface interacts with the surrounding fluid, causing conduction within the solid. For modeling purposes, the solid can be treated as a semi-infinite medium since the heat transfer occurs primarily near the surface, with negligible effects deep within the solid.

Example 2: Thin Slab

Another example of a semi-infinite medium is a very thin slab, where the thickness is small compared to the other dimensions. In this case, heat transfer can be assumed to occur only in the thickness direction, and the slab can be treated as a semi-infinite medium to simplify calculations.

Example 3: Thick Insulation Layers

Large structures, such as buildings or industrial equipment, often have thick insulation layers that can also be considered a semi-infinite medium. Since the insulation layers are much thicker than their width and height dimensions, heat transfer occurs primarily in the depth direction of the insulation, and the insulation can be treated as a semi-infinite medium.

Example 4: Pipes

Pipes with a long length and relatively small diameter can also be treated as semi-infinite media for heat transfer purposes. The assumption is that temperature changes occur predominantly along the axial length of the pipe while the heat transfer in the radial direction is considered negligible. This simplification can be applied to model heat losses or gains in the pipe flow.