Heat and Mass Transfer Problem

In summary, the rate of heat transfer per unit length in a plastic pipe with inner and outer radii of 1 and 1.25 cm, respectively, and inner and outer surface temperatures of 60 °C and 30 °C, is approximately 78 W/m. This is calculated using the heat transfer equation and assuming a length of 1 meter.
  • #1
dzj633

Homework Statement


A plastic pipe (k=0.092 W/m.K) of inner and outer radius of 1 and 1.25 cm, respectively. If the inner and outer surfaces are at 60 °C and 30 °C, respectively. The rate of heat transfer per unit length is close to:
a) 98 W/m b) 89 W/m c) 78 W/m d) 168 W/m e) 112 W/m

Homework Equations


Qk = ( Ti - To )/( ln| ro / ri | / 2π * k * l )

The Attempt at a Solution


I set up all of my given values into the heat transfer equation above but i am not given a length of the pipe.. Am i missing key information to finish this problem, or do i not need the length to solve? Also, I converted temps to Kelvin and the radii to meters.[/B]
 
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  • #2
The key phrase here is heat transfer per unit length. You do not need the total length of pipe because you are not looking for the total heat transferred.
 
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  • #3
I see.. Would it be a safe assumption to assume L = 1 meter? Per "1" unit length?
 
  • #4
dzj633 said:
I see.. Would it be a safe assumption to assume L = 1 meter? Per "1" unit length?
What do the units W/m mean to you?
 
  • #5
W/m means Amount of heat transfer per unit length to me and a watt is the rate at which work is done. [J/s]
 
  • #6
dzj633 said:
W/m means Amount of heat transfer per unit length to me and a watt is the rate at which work is done. [J/s]
With that being said, my thought of "a unit" would be 1 unit of length.
 
  • #7
Yes, it's Watts per meter.
 
  • #8
Correct, after my calculations I got 78 W/m.
 

1. What is the difference between heat transfer and mass transfer?

Heat transfer is the movement of thermal energy from one system to another, while mass transfer is the movement of a substance from one location to another. Heat transfer can occur through three main mechanisms: conduction, convection, and radiation. Mass transfer can occur through diffusion, convection, or advection.

2. What is the importance of heat and mass transfer in engineering applications?

Heat and mass transfer play a crucial role in various engineering applications, such as chemical and process industries, power generation, refrigeration and air conditioning, and environmental engineering. Proper understanding and control of heat and mass transfer are essential for the design, operation, and optimization of these systems.

3. How do you calculate heat and mass transfer coefficients?

The heat transfer coefficient is a measure of how easily heat can be transferred from one system to another. It can be calculated using the heat transfer rate, temperature difference, and surface area. The mass transfer coefficient is a measure of how easily mass can be transferred from one system to another and can be calculated using the mass transfer rate, concentration difference, and area.

4. What are some common applications of heat and mass transfer in everyday life?

Heat and mass transfer are present in many everyday activities, such as boiling water on a stovetop, using a refrigerator to cool food, and sweating to regulate body temperature. They are also essential in natural processes, such as evaporation, condensation, and air circulation in the atmosphere.

5. How does the geometry of a system affect heat and mass transfer?

The geometry of a system plays a significant role in heat and mass transfer. For example, a larger surface area can lead to more efficient heat transfer, while a smaller area can cause a higher temperature gradient. The shape and size of the system also affect factors such as boundary layer thickness and flow patterns, which can impact mass transfer rates.

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