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An environmentally toxic radioactive chemical is continually released at a constant rate of 1 (mg per vol per time) at the midpoint of a canal of length L. As it diffuses through the canal with diffusion constant D = 1, it decays at rate A (per unit time). The ends of the canal are connected to large bodies of toxic-free water. Set up the model equations and the boundary conditions. Find the steady-state concentration and sketch its spatial profile for different values of L and A. (Hint: Break the problem up into two parts, on each side of the source. At the source the concentration must be continuous, and in a small interval about the source, the "flux in" minus the "flux out" equals one).

An environmentally toxic radioactive chemical is continually released at a constant rate of 1 (mg per vol per time) at the midpoint of a canal of length L. As it diffuses through the canal with diffusion constant D = 1, it decays at rate A (per unit time). The ends of the canal are connected to large bodies of toxic-free water. Set up the model equations and the boundary conditions. Find the steady-state concentration and sketch its spatial profile for different values of L and A. (Hint: Break the problem up into two parts, on each side of the source. At the source the concentration must be continuous, and in a small interval about the source, the "flux in" minus the "flux out" equals one).

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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An environmentally toxic radioactive chemical is continually released at a constant rate of 1 (mg per vol per time) at the midpoint of a canal of length L. As it diffuses through the canal with diffusion constant D = 1, it decays at rate A (per unit time). The ends of the canal are connected to large bodies of toxic-free water. Set up the model equations and the boundary conditions. Find the steady-state concentration and sketch its spatial profile for different values of L and A. (Hint: Break the problem up into two parts, on each side of the source. At the source the concentration must be continuous, and in a small interval about the source, the "flux in" minus the "flux out" equals one).
Transcribed Image Text:An environmentally toxic radioactive chemical is continually released at a constant rate of 1 (mg per vol per time) at the midpoint of a canal of length L. As it diffuses through the canal with diffusion constant D = 1, it decays at rate A (per unit time). The ends of the canal are connected to large bodies of toxic-free water. Set up the model equations and the boundary conditions. Find the steady-state concentration and sketch its spatial profile for different values of L and A. (Hint: Break the problem up into two parts, on each side of the source. At the source the concentration must be continuous, and in a small interval about the source, the "flux in" minus the "flux out" equals one).
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