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Please Upload the MATLAB script. Thank you in advance. 1. (5 points) In heat treatment processes it is important to know the distribution of temperature
Please Upload the MATLAB script.
Thank you in advance.
1. (5 points) In heat treatment processes it is important to know the distribution of temperature in an object. In a thermodynamics or heat transfer course the temperature distribution of a flat metal plate is given by: T(x,y) = (T2 - T)w(x,y) + T1 where: . Ti is the temperature on three sides of the plate (held constant @ T1) T2 is the temperature on the fourth side T(x,y) is the temperature in the center of the plate w(x,y) is described by . . 250 2 w(x,y) = nux sinh(nay/L) sin (474) 'n oddn sinh(W /L) TT T2 W T(x,y) TE T1 Use the following data: T1 = 70C, T2 = 200C, and W = L = 2 meters 0 0 a. The terms in the series become smaller in magnitude as n increases. Write a MATLAB script to verify this fact for n=1 19 for the center of the plate (x = y = 1). b. Using x = y = 1 add additional code to the script to determine the number of terms required to produce a temperature calculation for the temperature in the middle of the plate, T(x,y), that is accurate to within 1%, i.e., what value of n would the addition of the next term produce a change of I less than 1 %?) HINT: Consider using the while command. Answer: Part a) 3.9854e-01, 5.9884e-03, 1.5528e-04, 4.7931e-06, 1.6110e-07, 5.69608-09, 2.0828e-10, 7.8004e-12, 2.9743e-13, 1.1500e-14 (getting smaller) Part b) T_middle = 102.5 C and n = 9 1. (5 points) In heat treatment processes it is important to know the distribution of temperature in an object. In a thermodynamics or heat transfer course the temperature distribution of a flat metal plate is given by: T(x,y) = (T2 - T)w(x,y) + T1 where: . Ti is the temperature on three sides of the plate (held constant @ T1) T2 is the temperature on the fourth side T(x,y) is the temperature in the center of the plate w(x,y) is described by . . 250 2 w(x,y) = nux sinh(nay/L) sin (474) 'n oddn sinh(W /L) TT T2 W T(x,y) TE T1 Use the following data: T1 = 70C, T2 = 200C, and W = L = 2 meters 0 0 a. The terms in the series become smaller in magnitude as n increases. Write a MATLAB script to verify this fact for n=1 19 for the center of the plate (x = y = 1). b. Using x = y = 1 add additional code to the script to determine the number of terms required to produce a temperature calculation for the temperature in the middle of the plate, T(x,y), that is accurate to within 1%, i.e., what value of n would the addition of the next term produce a change of I less than 1 %?) HINT: Consider using the while command. Answer: Part a) 3.9854e-01, 5.9884e-03, 1.5528e-04, 4.7931e-06, 1.6110e-07, 5.69608-09, 2.0828e-10, 7.8004e-12, 2.9743e-13, 1.1500e-14 (getting smaller) Part b) T_middle = 102.5 C and n = 9Step by Step Solution
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