Answered: A plastics plant manufactures larges…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A plastics plant manufactures larges pieces of plastic by continuously extruding thin sheets.
As the sheets flow out of the extruder, they are cooled via forced convection and radiation.
The plastic sheets are 1 mm thick, 1 m wide, and leave the extruder at a rate of 9 m/min.
A fan blows air over the top and bottom surface of the sheet during the first meter after the
sheet leaves the extruder. The fan accelerates the air to 3 m/s and the air is known to be at
27°C at the fan outlet. At the exit of the extruder, the plastic is at 90°C. The plastic is
estimated to have an emissivity of ? = 0.9 and the general surroundings are at 20°C.

A) Determine the rate of heat transfer via convection and radiation from the 1-m-long
section of the plastic sheet that is being force cooled. take the surface temperature to be 90°C over
the entire section of interest.

B) The density-specific heat product of the plastic is ?? = 1920 kJ m3– K⁄ . What is the
temperature of the plastic at the end of the cooling section

**Diagram Explanation on Heat Transfer During Plastic Sheet Cooling Process**

This diagram illustrates the setup for cooling a plastic sheet using air.

- **Plastic Sheet**: The plastic sheet is depicted in pink. It measures 1 m in length on each side and has a thickness of 1 mm. During the process, the sheet's surface temperature is maintained at 90°C.

- **Roller Movement**: The sheet moves over rollers at a speed of 9 meters per minute.

- **Air Cooling**: Air at a temperature of 27°C is blown over the surface of the plastic sheet at a velocity of 3 m/s. The air flows at an angle towards the sheet, aiding in the cooling process.

This setup is typically used to study the heat transfer rate from the plastic sheet to the surrounding air, an essential consideration in materials engineering and manufacturing processes.

Expert Solution

Step 1: Write the given data and what is to find

Given:

$table row t equals cell 1 space m m end cell row w equals cell 1 space m end cell row cell q with dot on top end cell equals cell 9 space m divided by m i n end cell row V equals cell 3 space m divided by s end cell row cell T subscript f end cell equals cell 27 to the power of o C end cell row cell T subscript p end cell equals cell 90 to the power of o C end cell row epsilon equals cell 0.9 end cell row cell T subscript infinity end cell equals cell 20 to the power of o C end cell row L equals cell 1 space m end cell row cell rho C subscript p end cell equals cell 1920 space k J divided by m cubed minus K end cell end table$

To find:

(a) Rate of heat transfer via convection and radiation.

(b) Temperature of the plastic at the end of the cooling.

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