Summer 2018
Homework 4
Due date: July 6, Friday 5:00 pm in PILOT dropbox
1. Consider that you are using an extrusion based ABS printer. Calculate the required heater
power, total pressure drop in liquefier, and motor power for extrusion at steady state
condition for deposition speed of 0.5, 1, 1.5, 3, 5, 10, and 50 mm/s and plot them on three
separate graphs. Use the following data:
m = 2.16
 = 7.4 x 10-5 (kPa)-m s-1
 = 900 kg/m3
cp = 1500 J/kg-K
D1 = 1.8 mm
L1 = 10 mm
Some required data is missing that can be found from literature.
2. The generalized heat equation for laser melting is given by
𝜌𝑐 𝜕𝑇
𝜕𝑡 =
𝜕
𝜕𝑥 [𝑘𝑥
𝜕𝑇
𝜕𝑥 ] +
𝜕
𝜕𝑦 [𝑘𝑦
𝜕𝑇
𝜕𝑦 ] +
𝜕
𝜕𝑧 [𝑘𝑧
𝜕𝑇
𝜕𝑧 ] + 𝜌𝑐 (𝑉𝑥
𝜕𝑇
𝜕𝑦 + 𝑉𝑦
𝜕𝑇
𝜕𝑦 + 𝑉𝑧
𝜕𝑇
𝜕𝑧 ) + 𝑄
where
Reduce the above equation for steady-state thermal analysis of a system having a stationary heat
flux and no-heat generation. Then solve the following problem:
Consider a case where the surface of a metal plate is irradiated by a stationary laser so that the
steady-state temperature near the laser-irradiated region of the top surface is defined by an
exponential function given in the figure below. The remaining boundaries are maintained room
temperature (23oC). Consider kx = 50 W/m 2-K, ky = 60 W/m
2-K, and grid sizes x = 0.6 mm, y
= 0.5 mm.
1. Derive finite difference equations for all the interior nodes.
2. Develop a MATLAB code, and determine temperatures at all interior nodes.

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