Determine the necessary shell temperature
Course:- MATLAB Programming
Reference No.:- EM13396

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In a shell-and-tube heat exchanger, one fluid passes through a central tube while another fluid flows through an outer shell in the opposite direction. The purpose is to heat the fluid passing through the central tube.  It is possible to maintain a constant temperature TS of the outer shell fluid by continually condensing a vapor (for example, steam) along the length of the shell.

By integrating a heat balance equation along the tube, it is possible to relate the length L and diameter D of the heat exchanger to the input temperature T1  and output temperature T2 :

693_determine the necessary shell temperature.png

549_determine the necessary shell temperature1.png

and where

P  = viscosity of the fluid (depends on T)

k  = thermal conductivity of the fluid (depends on T)

cp  = specific heat of the fluid (depends on T)

m  = flow rate of the fluid through the tube

D  = diameter of the tube

The temperature dependence of the specific heat, viscosity, and thermal conductivity depend on the working fluid and, therefore, upon temperature,  T.  For this assignment use:

2023_determine the necessary shell temperature2.png

The thermal conductivity data, k(T), has been evaluated, experimentally, at only a few data (temperature) points.  We have decided, therefore, to use a polynomial approximation and we do so with the full knowledge that our experimental data may contain errors.

559_determine the necessary shell temperature3.png

where T is measured in degrees Fahrenheit ( F) throughout.

The Problem:

Given the values of D, m, T1, T2, L, determine the necessary shell temperature, TS. In particular, given that D =1.95 inches (convert to ft), m = 25 lb/hr, 170o TF, and the heat exchanger length is L = 5 ft, find the shell temperature Ts needed to heat the output gas to T2  =  360oF.

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