051407-132a-hw 4

051407-132a-hw 4 - insulating no heat can ow o oF them....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
C HEMICAL E NGINEERING 132A Professor Todd Squires Spring Quarter, 2007 Homework 4 Due Friday, May 18 Problem 1. A bar is located between x = 0 and x = 2, and has an inital temperature profle T 0 ( x ) = 0 , 0 x < 1 / 2 (1) T 0 ( x ) = 100 , 1 / 2 x 3 / 2 (2) T 0 ( x ) = 0 , 3 / 2 x 2 (3) At t = 0, the rod is placed between two ice blocks to maintain T = 0 at both ends ( x = 0 and x = 2), For all time. Solve the heat equation ∂T ∂t = k 2 T ∂x 2 (4) to fnd the evolution oF the temperature. Show all steps – the separable solution, ±ourier Sine Series, etc. As t → ∞ , what happens to the temperature in the bar? Problem 2. Consider the same problem as above, except now the ends are
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: insulating no heat can ow o oF them. Remember this means T/x = 0 For all times at x = 0 and x = 2. As t , what happens to the temperature in the bar? How is this dierent than in Problem 1, and why? Problems 3a-d. p503, probs 1, 2, 5, 8 Problems 4a-d. p503, probs. 10, 16, 21, 27 (these analyze your solutions above; not so involved) Problem 5a-c. p504, probs 32, 33, 36. Comment on what these boundary conditions correspond to physically....
View Full Document

Ask a homework question - tutors are online