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Some mass of material is released at the point z = 0. At t> 0 the material density evolves according to the formula p=t-1/² exp 4kt 1. Sketchp and against z (direct axis z to the right) at some moment t> 0 (no accuracy is required, just show general trends). 2. Verify that p satisfies the diffusion equation др Ət k əx² 3. Find the flux of material as a function of r and t and show that at x = 1 the material is tranferred to the right and at x = -1 the material is tranferred to the left.

Some mass of material is released at the point z = 0. At t> 0 the material density evolves according to the formula p=t-1/² exp 4kt 1. Sketchp and against z (direct axis z to the right) at some moment t> 0 (no accuracy is required, just show general trends). 2. Verify that p satisfies the diffusion equation др Ət k əx² 3. Find the flux of material as a function of r and t and show that at x = 1 the material is tranferred to the right and at x = -1 the material is tranferred to the left.

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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Some mass of material is released at the point z = 0. At t > 0 the material density evolves according to the formula p=t-1/² exp(-4-1) - 1. Sketch p and against a (direct axis x to the right) at some moment t> 0 (no accuracy is required, just show general trends). 2. Verify that p satisfies the diffusion equation 8² p dx² Əp Ət = k 3. Find the flux of material as a function of a and t and show that at x = 1 the material is tranferred to the right and at x = -1 the material is tranferred to the left.
Transcribed Image Text:Some mass of material is released at the point z = 0. At t > 0 the material density evolves according to the formula p=t-1/² exp(-4-1) - 1. Sketch p and against a (direct axis x to the right) at some moment t> 0 (no accuracy is required, just show general trends). 2. Verify that p satisfies the diffusion equation 8² p dx² Əp Ət = k 3. Find the flux of material as a function of a and t and show that at x = 1 the material is tranferred to the right and at x = -1 the material is tranferred to the left.
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