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Consider the following partial differential equation and boundary conditions ay- D %D Ox C = C, y = 0 C =C,,y= L,x= 0 Consider the situation of short time when L is essentially infinitely far away from the bottom plate at y=0, i.e. solve the equation for the region close to the bottom plate. a) Define a dimensionless concentration, 0, such that 0=0 at x=0 and 0=1 at y=0. VWrite the equation and boundary conditions for 0

Consider the following partial differential equation and boundary conditions ay- D %D Ox C = C, y = 0 C =C,,y= L,x= 0 Consider the situation of short time when L is essentially infinitely far away from the bottom plate at y=0, i.e. solve the equation for the region close to the bottom plate. a) Define a dimensionless concentration, 0, such that 0=0 at x=0 and 0=1 at y=0. VWrite the equation and boundary conditions for 0

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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Consider the following partial differential equation and boundary conditions ô²C ay- C = C,,y=0 C=C,,y= L,x=0 Consider the situation of short time when L is essentially infinitely far away from the bottom plate at y=0, i.e. solve the equation for the region close to the bottom plate. a) Define a dimensionless concentration, 0, such that 0=0 at x=0 and 0=1 at y=0. Write the equation and boundary conditions for 0 b) Assume a solution of the form 0=f(n)=f(y/g(x)) and determine g(x) c) Solve the resulting equation for 0 which can be written in the form of an integral (do not try to integrate the integral)
Transcribed Image Text:Consider the following partial differential equation and boundary conditions ô²C ay- C = C,,y=0 C=C,,y= L,x=0 Consider the situation of short time when L is essentially infinitely far away from the bottom plate at y=0, i.e. solve the equation for the region close to the bottom plate. a) Define a dimensionless concentration, 0, such that 0=0 at x=0 and 0=1 at y=0. Write the equation and boundary conditions for 0 b) Assume a solution of the form 0=f(n)=f(y/g(x)) and determine g(x) c) Solve the resulting equation for 0 which can be written in the form of an integral (do not try to integrate the integral)
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