Steam in a heating system flows through tubes whose outer...

Steam in a heating system flows through tubes whose outer diameter is $3 \mathrm{~cm}$ and whose walls are maintained at a temperature of $120^{\circ} \mathrm{C}$. Circular aluminum alloy fins $(k=$ $180 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$ of outer diameter $6 \mathrm{~cm}$ and constant thickness $t=$ $2 \mathrm{~mm}$ are attached to the tube, as shown in Fig. P3-189. The space between the fins is $3 \mathrm{~mm}$, and thus there are 200 fins per meter length of the tube. Heat is transferred to the surrounding air at $25^{\circ} \mathrm{C}$, with a combined heat transfer coefficient of $60 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. Determine the increase in heat transfer from the tube per meter of its length as a result of adding fins.

Key Concepts

Extended Surfaces (Fins)

Extended surfaces, commonly known as fins, are added to objects to increase their effective surface area, thereby enhancing the rate of heat transfer to or from the object. By augmenting the available area for convective heat transfer, fins help in dissipating heat more effectively in applications like heat exchangers and cooling systems.

Fin Efficiency

Fin efficiency quantifies how effectively a fin transfers heat compared to an ideal fin of the same geometry. It accounts for the temperature gradient along the fin, recognizing that not all parts of the fin achieve the same temperature as its base, which impacts the net heat transfer from the fin surface.

Thermal Conductivity

Thermal conductivity is a material property that measures the ability of a material to conduct heat. In the context of fins, high thermal conductivity ensures that heat is rapidly distributed along the fin, reducing temperature gradients and improving the overall effectiveness of the fin in transferring heat.

Convection Heat Transfer

Convection heat transfer involves the transfer of heat between a surface and a fluid (such as air) moving past it. The heat transfer coefficient in convection indicates how efficiently heat is removed or supplied by the fluid, playing a crucial role in determining the overall heat transfer rate from surfaces, including fins.

Surface Area Enhancement

Surface area enhancement refers to the increase in effective heat transfer area provided by adding features such as fins to a base surface. This concept is vital in heat exchanger design where maximizing the contact area between the solid surface and the fluid can lead to significantly improved thermal performance.

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