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

Steam in a heating system flows through tubes whose outer diameter is $5 \mathrm{~cm}$ and whose walls are maintained at a temperature of $180^{\circ} \mathrm{C}$. Circular aluminum alloy 2024-T6 fins $(k=186 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$ of outer diameter $6 \mathrm{~cm}$ and constant thickness $1 \mathrm{~mm}$ are attached to the tube. The space between the fins is $3 \mathrm{~mm}$, and thus there are 250 fins per meter length of the tube. Heat is transferred to the surrounding air at $T_{\infty}=25^{\circ} \mathrm{C}$, with a heat transfer coefficient of $40 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. Determine the increase in heat transfer from the tube per meter of its length as a result of adding fins.

Key Concepts

Convection Heat Transfer

Convection heat transfer involves the movement of heat between a solid surface and a fluid (such as air or water) in motion. Governed by Newton’s law of cooling, this process is characterized by a convective heat transfer coefficient that quantifies how effectively heat is carried away (or supplied) from the surface, making it a key factor in the thermal performance of systems such as heating and cooling devices.

Extended Surfaces (Fins)

Extended surfaces, or fins, are added to bodies to increase the effective area available for heat transfer. By augmenting the surface area without significantly increasing the overall size of the device, fins facilitate improved heat dissipation or absorption, which is particularly beneficial when the base surface does not offer enough area for the desired thermal performance.

Fin Efficiency and Effectiveness

Fin efficiency measures the ratio between the actual heat transfer from a fin and the ideal heat transfer that would occur if the entire fin were at the base temperature. Effectiveness extends this idea by comparing the additional heat transfer achieved with fins to that from the same area of bare surface. Both concepts help in evaluating and optimizing fin design by accounting for the loss of performance due to temperature gradients along the fin.

Thermal Conduction in Solids

Thermal conduction in solids is the process by which heat is transferred within a material due to a temperature gradient, and it is described by the material’s thermal conductivity. In the context of fins, conduction is responsible for transporting heat from the base (where the temperature is highest) throughout the fin, thereby influencing the temperature distribution and ultimately affecting the convective heat transfer from the fin surface.

Transcript

Please give Ace some feedback