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A lumped mass of m 35 kg with the initial temperature of To 2000 K radiates and convects heat from its surface of A = 1.5 m² to a medium at the temperature of T₁ = 100 K. The lumped transient temperature response T that varies with time t is determined from the ordinary differential equation dT dt εσ Α + (TT) + hA (T-Ta) = 0 mc mC (1) where = 0.7 is the surface emissivity, σ = 5.67×10-8 J/sec-m²-K4 is the Stefan- Boltzmann constant, and c= 445 J/kg-K is the specific heat of the lumped mass, and h= 50 W/m²-K is the convective heat transfer coefficient. (a) Use the Euler, modified Euler, and Heun's methods to calculate the transient temperature T(t) from t = 0 to 100 sec. Plot the results from all three methods on the same graph. (b) Apply finite difference (backward, forward, and central) to the solution obtained in part (a). Compare the finite difference results with the original ODE by plotting both sets of data. Present three separate graphs to compare the solutions from Euler, modified Euler, and Heun's methods.

A lumped mass of m 35 kg with the initial temperature of To 2000 K radiates and convects heat from its surface of A = 1.5 m² to a medium at the temperature of T₁ = 100 K. The lumped transient temperature response T that varies with time t is determined from the ordinary differential equation dT dt εσ Α + (TT) + hA (T-Ta) = 0 mc mC (1) where = 0.7 is the surface emissivity, σ = 5.67×10-8 J/sec-m²-K4 is the Stefan- Boltzmann constant, and c= 445 J/kg-K is the specific heat of the lumped mass, and h= 50 W/m²-K is the convective heat transfer coefficient. (a) Use the Euler, modified Euler, and Heun's methods to calculate the transient temperature T(t) from t = 0 to 100 sec. Plot the results from all three methods on the same graph. (b) Apply finite difference (backward, forward, and central) to the solution obtained in part (a). Compare the finite difference results with the original ODE by plotting both sets of data. Present three separate graphs to compare the solutions from Euler, modified Euler, and Heun's methods.

Elements Of Electromagnetics
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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This question is over numerical methods using the following three methods shown in the problem to estimate the curve of the ODE given. I have most of the code figured out, but I'm not quite sure what to do with the ODE, and how to apply it to my Python code for parts a and b. If you could show me how to do that I would really appreciate it. This is a review question my teacher posted today for an upcoming final.
A lumped mass of m 35 kg with the initial temperature of To 2000 K radiates and convects heat from its surface of A = 1.5 m² to a medium at the temperature of T₁ = 100 K. The lumped transient temperature response T that varies with time t is determined from the ordinary differential equation dT dt εσ Α + (TT) + hA (T-Ta) = 0 mc mC (1) where = 0.7 is the surface emissivity, σ = 5.67×10-8 J/sec-m²-K4 is the Stefan- Boltzmann constant, and c= 445 J/kg-K is the specific heat of the lumped mass, and h= 50 W/m²-K is the convective heat transfer coefficient. (a) Use the Euler, modified Euler, and Heun's methods to calculate the transient temperature T(t) from t = 0 to 100 sec. Plot the results from all three methods on the same graph. (b) Apply finite difference (backward, forward, and central) to the solution obtained in part (a). Compare the finite difference results with the original ODE by plotting both sets of data. Present three separate graphs to compare the solutions from Euler, modified Euler, and Heun's methods.
Transcribed Image Text:A lumped mass of m 35 kg with the initial temperature of To 2000 K radiates and convects heat from its surface of A = 1.5 m² to a medium at the temperature of T₁ = 100 K. The lumped transient temperature response T that varies with time t is determined from the ordinary differential equation dT dt εσ Α + (TT) + hA (T-Ta) = 0 mc mC (1) where = 0.7 is the surface emissivity, σ = 5.67×10-8 J/sec-m²-K4 is the Stefan- Boltzmann constant, and c= 445 J/kg-K is the specific heat of the lumped mass, and h= 50 W/m²-K is the convective heat transfer coefficient. (a) Use the Euler, modified Euler, and Heun's methods to calculate the transient temperature T(t) from t = 0 to 100 sec. Plot the results from all three methods on the same graph. (b) Apply finite difference (backward, forward, and central) to the solution obtained in part (a). Compare the finite difference results with the original ODE by plotting both sets of data. Present three separate graphs to compare the solutions from Euler, modified Euler, and Heun's methods.
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