# Heat transfer through fins on a cylinder

• gfd43tg
In summary, the conversation revolves around a problem involving a copper tube with an aluminum sleeve and pin fins, and the calculation of heat transfer per meter length of the tube. The main focus is on determining the surface area of the fins and the heat transfer coefficients on both the inside and outside surfaces. There is also a discussion about finding the exposed area of the fins and determining the rate of heat loss from a single fin.
gfd43tg
Gold Member

## Homework Statement

A copper tube has a 2 cm inside diameter and a wall thickness of 1.5 mm. Over the tube is an aluminum sleeve of 1.5 mm thickness having 100 pin fins per centimeter length. The pin fins are 1.5 mm in diameter and are 4 cm long. The fluid inside the tube is at 100 ºC, and the inside heat transfer coefficient is 5000 W/m2 K. The fluid outside the tube is at 250 ºC, and the heat transfer coefficient on the outer surface is 7 W/m2 K. Calculate the heat transfer per meter length of tube. Take k = 204 W/m K for the aluminum and k =386 W/mK for the copper tube. You may ignore the heat loss from the fin tips.

## The Attempt at a Solution

This problem is pretty tough, but basically what I did was this. I tried to find the surface area of all the fins bases per unit length, and then subtract that from the total surface area per unit length. Then I said the convective heat resistance from the outside is the outside heat transfer coefficient times the exposed area plus the area of the fins that protrude from the cylinder. I added all of them in series with the multiple layers and inside convection to find total resistance and divided overall temperature difference by the total resistance. I am just unsure if I did the part about finding the exposed area correctly.

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What fraction of the outside area did you determine that the fins occupy?

The first step is to focus on a single fin. If T is the temperature at the base of the fin, do you know how to determine the rate of heat loss from the fin as a function of T and the outside temperature?

Chet

## What is "heat transfer through fins on a cylinder"?

Heat transfer through fins on a cylinder is the process by which heat is transferred from the surface of a cylinder to the surrounding medium through the use of fins attached to the cylinder.

## How do fins on a cylinder improve heat transfer?

Fins on a cylinder increase the surface area available for heat transfer, allowing for more efficient transfer of heat from the cylinder to the surrounding medium. They also disrupt the boundary layer, reducing the thermal resistance and enhancing heat transfer.

## What factors affect heat transfer through fins on a cylinder?

The heat transfer through fins on a cylinder is affected by the geometry and size of the fins, the material properties of the fins and the cylinder, the temperature difference between the surface of the cylinder and the surrounding medium, and the velocity of the surrounding medium.

## What is the formula for calculating heat transfer through fins on a cylinder?

The most commonly used formula for calculating heat transfer through fins on a cylinder is the Fin Efficiency Formula: Q = kAΔT/Δx, where Q is the heat transfer rate, k is the thermal conductivity, A is the surface area of the fins, ΔT is the temperature difference between the cylinder surface and the surrounding medium, and Δx is the thickness of the fin.

## What are some applications of heat transfer through fins on a cylinder?

Heat transfer through fins on a cylinder has many practical applications, such as in air conditioning and refrigeration systems, heat exchangers, and electronic cooling systems. It is also commonly used in the design of engines and other machinery to improve their efficiency and prevent overheating.

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