Final answer:
The heat transfer area (A) for a cylinder in a 1-D heat conduction problem is expressed as 2πrl, while for a sphere, it is expressed as 4πr². These areas are not constants; they vary based on the cylinder's or sphere's dimensions. The rate of heat transfer changes proportionally with the change in area and distance.
Step-by-step explanation:
The expression for A (the heat transfer area) for a cylinder in a 1-D heat conduction problem is 2πrl (where r is the radius and l is the length of the cylinder) and for a sphere, it is 4πr² (where r is the radius of the sphere).
When analyzing heat transfer through conduction, understanding the role of the surface area is crucial. Given the formula Q/t = kA(T₂ - T₁)/d, where Q/t is the rate of heat transfer, k is the thermal conductivity, A is the surface area, d is the thickness, and (T₂ - T₁) is the temperature difference, we can see that for a cylinder and a sphere, A is not a constant but rather depends on their geometric dimensions.
For a cylinder, increasing spatial dimensions alter the heat transfer rate. If the radius and length are doubled, the area increases by a factor of four but the distance only doubles. This means that the rate of heat transfer by conduction would increase by a factor of two.