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A 50-cm metal rod initially at 20°C has its left end maintained at 50°C and its right end at 100°C. Use the forward difference method to discretize the temperature distribution along the rod. Use the following data: Ax = 10 cm, At = 30 s, a = 17 x 10-2 cm² a) Solve for the stability b) Provide a matrix/table for the discretized temperature distribution up to time = 120 seconds. c) What is the temperature distribution at the end of 120 seconds?

A 50-cm metal rod initially at 20°C has its left end maintained at 50°C and its right end at 100°C. Use the forward difference method to discretize the temperature distribution along the rod. Use the following data: Ax = 10 cm, At = 30 s, a = 17 x 10-2 cm² a) Solve for the stability b) Provide a matrix/table for the discretized temperature distribution up to time = 120 seconds. c) What is the temperature distribution at the end of 120 seconds?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A 50-cm metal rod initially at 20°C has its left end maintained at 50°C and its right end at 100°C. Use the forward difference method to discretize the temperature distribution along the rod. Use the following data: Δæ = 10 cm, Δt = 30 s, a = 17 × 10 =2 cm . a) Solve for the stability b) Provide a matrix/table for the discretized temperature distribution up to time = 120 seconds. c) What is the temperature distribution at the end of 120 seconds?
Transcribed Image Text:A 50-cm metal rod initially at 20°C has its left end maintained at 50°C and its right end at 100°C. Use the forward difference method to discretize the temperature distribution along the rod. Use the following data: Δæ = 10 cm, Δt = 30 s, a = 17 × 10 =2 cm . a) Solve for the stability b) Provide a matrix/table for the discretized temperature distribution up to time = 120 seconds. c) What is the temperature distribution at the end of 120 seconds?
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