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Oxigen diffuses radially into a cylinder of tissue with a radius r 50 μm and is consumed at a constant rate RA-0.11 umol.cm-3 s-1. The concentration of oxygen at rp is constant and equal to CA-0.1 umolcm-3. The diffusion coefficient of oxygen in the tissue is DAB 2x 10-5 cm 2 s^-1. (a) Simplify the diffusion equation in cylindrical coordinates (see below) by eliminating negligible or null terms. Additionally, indicate tw appropriate boundary conditions. Admit steady state. 1 0² CA + A + RA -D (1) + (b) Solve the differential equation obtained in (a) and obtain the concentration profile of oxygen in the cylinder. (c) Are there hypoxic regions (i.e. zones with zero oxygen concentration) in the cylinder?

Oxigen diffuses radially into a cylinder of tissue with a radius r 50 μm and is consumed at a constant rate RA-0.11 umol.cm-3 s-1. The concentration of oxygen at rp is constant and equal to CA-0.1 umolcm-3. The diffusion coefficient of oxygen in the tissue is DAB 2x 10-5 cm 2 s^-1. (a) Simplify the diffusion equation in cylindrical coordinates (see below) by eliminating negligible or null terms. Additionally, indicate tw appropriate boundary conditions. Admit steady state. 1 0² CA + A + RA -D (1) + (b) Solve the differential equation obtained in (a) and obtain the concentration profile of oxygen in the cylinder. (c) Are there hypoxic regions (i.e. zones with zero oxygen concentration) in the cylinder?

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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Oxigen diffuses radially into a cylinder of tissue with a radius r= 50 um and is consumed at a constant rate RA= 0.11 umol.cm^-3 s-1. The concentration of oxygen at r=r is constant and equal to CA = 0.1 umolem"-3. The diffusion coefficient of oxygen in the tissue is DAR = 2 x 10-5 cm 2 s-1. (a) Simplify the diffusion equation in cylindrical coordinates (see below) by eliminating negligible or null terms. Additionally, indicate two appropriate boundary conditions. Admit steady state. + +RA at (b) Solve the differential equation obtained in (a) and obtain the concentration profile of oxygen in the cylinder. (e) Are there hypoxic regions (i.e. zones with zero oxygen concentration) in the cylinder?
Transcribed Image Text:Oxigen diffuses radially into a cylinder of tissue with a radius r= 50 um and is consumed at a constant rate RA= 0.11 umol.cm^-3 s-1. The concentration of oxygen at r=r is constant and equal to CA = 0.1 umolem"-3. The diffusion coefficient of oxygen in the tissue is DAR = 2 x 10-5 cm 2 s-1. (a) Simplify the diffusion equation in cylindrical coordinates (see below) by eliminating negligible or null terms. Additionally, indicate two appropriate boundary conditions. Admit steady state. + +RA at (b) Solve the differential equation obtained in (a) and obtain the concentration profile of oxygen in the cylinder. (e) Are there hypoxic regions (i.e. zones with zero oxygen concentration) in the cylinder?
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