Question

Consider a short cylinder whose top and bottom surfaces are insulated. The cylinder is initially at a uniform temperature \(T_{i}\) and is subjected to convection from its side surface to a medium at temperature \(T_{\infty e}\), with a heat transfer coefficient of \(h\). Is the heat transfer in this short cylinder one-or twodimensional? Explain.

Short answer

Explain your reasoning.

Step-by-step solution

Understand the given information

The short cylinder is initially at a uniform temperature \(T_{i}\) and its top and bottom surfaces are insulated. Therefore, no heat transfer occurs at these surfaces. The side surface is in contact with a medium at a temperature \(T_{\infty e}\), with a heat transfer coefficient of \(h\). We need to determine whether the heat transfer is one- or two-dimensional.

Analyze the heat transfer through the side surface

Since the top and bottom surfaces are insulated, the heat transfer occurs only through the side surface via convection. This means that the heat transfer will be primarily in the radial direction, from the inside of the cylinder to the outer surface which is in contact with the medium.

Determine the dimensionality of heat transfer

Due to the insulation of the top and bottom surfaces, there is no heat transfer in the axial direction (along the height) of the cylinder. The main heat transfer is in the radial direction (from the inside to the outside). This implies that the heat transfer within the short cylinder is one-dimensional. In summary, the heat transfer in the short cylinder is one-dimensional due to the insulation of the top and bottom surfaces and the convection from the side surface to the surrounding medium.