Question

Under what conditions is the thermal resistance of the tube in a heat exchanger negligible?

Short answer

Answer: The thermal resistance of a tube in a heat exchanger is negligible when the material of the tube has a very high thermal conductivity (k), the tube's length (L) is very short, and the surface area (A) of the tube in contact with the heat transfer fluids is very large.

Step-by-step solution

Understand thermal resistance

Thermal resistance is a measure of the resistance that a material or system offers to the flow of heat. It depends on the material's thermal conductivity (k), length (L), and area (A) of the material or system. The thermal resistance (R) can be calculated using the following formula: R = L / (k * A)

Negligible thermal resistance

For the thermal resistance of a tube in a heat exchanger to be negligible, the value of R should be very small. This can happen when the material's thermal conductivity (k) is very high, the length (L) of the tube is very short, or the area (A) of the tube is very large.

Thermal conductivity (k)

Thermal conductivity is a property of a material that determines its ability to conduct heat. A material with higher thermal conductivity will have a lower thermal resistance. A tube in a heat exchanger will have negligible thermal resistance when the material used for the tube has a very high thermal conductivity.

Length (L) of the tube

The length of the tube in a heat exchanger also plays a role in thermal resistance. A shorter tube will have a lower thermal resistance as there is less distance for the heat to travel. Therefore, a tube will have negligible thermal resistance when its length is extremely short.

Area (A) of the tube

The surface area of the tube in contact with the heat transfer fluids also affects the thermal resistance. A larger surface area will allow more heat transfer and thus result in a lower thermal resistance. A tube can have negligible thermal resistance when its surface area is very large, allowing for efficient heat transfer. In conclusion, the thermal resistance of a tube in a heat exchanger is negligible under the following conditions: 1. The material of the tube has a very high thermal conductivity (k). 2. The tube's length (L) is very short. 3. The surface area (A) of the tube in contact with the heat transfer fluids is very large.

Key concepts

Thermal Conductivity

Thermal conductivity is an intrinsic property of materials that indicates their ability to conduct heat. In the context of heat exchangers, materials with high thermal conductivity are preferred because they facilitate the transfer of thermal energy between fluids at different temperatures.

Consider the metals used in many heat exchanger tubes; copper, for instance, has a thermal conductivity of approximately 401 W/mK, which is significantly higher than that of stainless steel, with a conductivity around 15 W/mK. Consequently, copper tubes can transfer heat more effectively, reducing the resistance to heat flow. In designing a heat exchanger, selecting materials with high thermal conductivity is crucial to minimize thermal resistance and maximize the system's efficiency.

For a practical understanding, think of a kitchen pot: a copper-bottomed pot heats up more quickly and evenly than a pot made of a less conductive material. Similarly, in heat exchangers, materials with higher thermal conductivity ensure that heat is swiftly transferred through the tube walls from the hot to the cold fluid.

Heat Exchanger Design

Heat exchanger design is a complex discipline that involves various physical and engineering principles to maximize efficiency and satisfy specific operational requirements. Designers must consider not only thermal conductivity but also factors such as tube length, diameter, surface area, and flow configuration.

In terms of thermal resistance, it's preferable to design a heat exchanger with short tubes of large diameter, increasing the overall surface area for heat transfer. Another design aspect is the arrangement of the tubes; for example, counterflow heat exchangers can achieve higher heat transfer rates compared to parallel-flow designs, due to the temperature gradient being maintained along the length of the exchanger.

Furthermore, the design must facilitate maintenance and withstand environmental factors like pressure and corrosion. Therefore, the choice of material, tube design, and overall configuration are all critical in minimizing thermal resistance and ensuring the heat exchanger operates effectively and reliably under various conditions.

Heat Transfer Efficiency

Heat transfer efficiency is the effectiveness with which heat is transferred from one medium to another in a heat exchanger. Thermal resistance directly affects this efficiency; the lower the thermal resistance, the higher the heat transfer efficiency.

Efficiency can be quantified using the heat transfer coefficient, which is inversely related to thermal resistance. In an efficient heat exchanger, the temperature differences between the hot and cold fluids are harnessed at their maximum potential, with minimal energy losses.

To improve heat transfer efficiency, besides using materials of high thermal conductivity, designers may increase the heat transfer area with fins or corrugations or optimize the flow rates and turbulence of the fluids to enhance convective heat transfer. All these factors, when carefully considered and balanced, lead to a more efficient heat exchanger design, ensuring that the process needs are met while consuming the least amount of energy.