Estimate the maximum melt temperature in the pumping zone of a 45mm diameter single screw extruder with a channel depth

Post by **answerhappygod** » Fri Jul 08, 2022 5:48 am

Estimate the maximum melt temperature in the pumping zone of a45mm diameter single screw extruder with a channel depth of 3 mm asa function of rotational speed. The polymer melt is PE-HD with adensity of 960 kg/m3, a specific heat of 2,300 kJ/kg/K, a thermalconductivity of 0.63 W/m/K and a viscosity of 200 Pa-s. Assume aheater temperature, Tb, of 190 °C and a melting temperature, Tm, of130 °C. The screw is not heated or cooled, which means it can betreated as an insulated surface. ` Hint: Because of the highthermal conductivity of steel, the screw will reach thermalequilibrium rapidly and have a constant temperature Ts. Also,please define Θ=𝑇−𝑇𝑚/𝑇𝑏−𝑇𝑚.

: Estimate The Maximum Melt Temperature In The Pumping Zone Of A 45mm Diameter Single Screw Extruder With A Channel Depth 1 (7.25 KiB) Viewed 32 times

a. Determine the Brinkman number, Br, as a function of screwspeed.
b. Derive 𝜃=−(𝐵𝑟/2)𝑦̂2+𝐵𝑟/2+1 from the Energy Balance, Equation9.421.
c. Derive the equation describing the temperature of the polymeras a function of screw speed, n, in revolutions per second.
d. Plot the equation found in part c from 0 to 360 rpm (0 to 6revolutions per second).
e. If the polymer has a temperature of 240 °C, what is the screwspeed?
f. From the screw speed found in part e, what is the Brinkmannumber for that screw speed?

: Estimate The Maximum Melt Temperature In The Pumping Zone Of A 45mm Diameter Single Screw Extruder With A Channel Depth 2 (58.69 KiB) Viewed 32 times

y h T₂ Melt T₁ U₂ → up-
Start off with writing down Equation 8.42 for the polymer. DT (0²T 8²T 0²T) = k ▪ • I Now you have to simplify Equation 8.42. What is Q? Is there an arbitrary heat source Q in the polymer? What is Qviscous heating? How is it defined? Keep reading the chapter and have a look at Equation 8.47. I I DT I How is defined? Write down all terms associated with Hint: Have a look at Table 8.5 • What terms/derivatives are assumed to be zero? And why? I Assume this problem to be stationary. In this case, what happens to time derivatives? Assume this problem to be 2D simple shear. In this case, what happens to the velocity components? For example, is there a z-velocity component? No, it is 2D. What happens to the temperature derivatives? (Hint: Think about the hint on the HW assignment) 1 After you simplified Equation 8.42 you have to make your simplified Equation dimensionless. ▪ You will then end up with an Equation that has the form: I I I pCp Dt I ax² + y² +z²+Q+ Qviscous heating I 8²0 =ay2 + Br əū 2 əy an Assume to be 1. Then solve the differential equation. DT Once you have the solved the differential equation you have to solve for the boundary conditions to get your integration constants (C₁ and C₂) Your final equation should have the form: 8=-- Br Br -29² +2+1 At what y-location will the maximum temperature occur? With the correct y-location, Tmax=240 C, the definition of theta, 8 and the above equation, you can solve for Br for the maximum melt temperature of 240 C. In order to find the rotational speed for that temperature, go back to the original definition of the Brinkmann number. How is the Brinkmann number defined? You will see there is a velocity component, u. Hint: d U₂ = 2n= (rpm)