Water is heated by submerging 50-mm diameter, thinwalled copper tubes in a tank and psssing hot

step 1 In this problem, k is already given, h is given, outer diameter is given. So, inner diameter is

Water is heated by submerging 50-mm diameter, thinwalled...

Water is heated by submerging $50-\mathrm{mm}$ diameter, thinwalled copper tubes in a tank and psssing hot combustion gases $\left(T_{t}=750 \mathrm{~K}\right)$ through the tubes, To enhance heat transfer to the water, four straight fins of uniform cross section, which form a cross, are inserted in each tube. The fins are 5 mm thick and are also made of copper $(k=400 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$. If the tube surface temperature is $T_{2}=350 \mathrm{~K}$ and the gas-side convection coefficient is $h_{2}=30 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. what is the rate of heat transfer to the water per meter of pipe Iength?

Key Concepts

Composite Heat Transfer Analysis

This concept involves combining various mechanisms of heat transfer, such as conduction through the tube and fins, along with convection from the external surfaces, to analyze the overall thermal performance of a composite system. It requires a careful balance of all contributing resistances to accurately predict the rate of heat transfer in practical applications.

Thermal Resistance Networks

Thermal resistance networks are an analytical tool used to model the different modes of heat transfer—such as conduction through solids and convection from surfaces—by representing them as resistances in series or parallel. This approach simplifies the calculation of the total heat transfer in systems where multiple resistances control the process.

Fin Efficiency

Fin efficiency is a measure of how effectively a fin transfers heat relative to an ideal fin that would transfer heat uniformly along its entire length. It takes into account the conduction resistance within the fin itself and quantifies the actual performance compared to the theoretical maximum performance, thereby influencing the overall heat transfer calculation.

Convection Heat Transfer

This concept deals with the transfer of heat between a solid surface and a fluid moving over the surface. It involves the convection coefficient (h), which quantifies the effectiveness of this process, and is used in the equation Q = hA(T_surface - T_fluid) to determine the rate of heat transfer from the surface to the fluid or vice versa.

Extended Surfaces (Fins)

Extended surfaces, commonly known as fins, are added to increase the effective surface area available for heat transfer. They are particularly useful when the natural surface area is insufficient for achieving the desired thermal performance. The analysis of fins involves calculating the additional heat transfer provided by these extra surfaces.

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