The temperature in a process unit is controlled by passing cooling water at a me

Question

The temperature in a process unit is controlled by passing cooling water at a measured rate through a jacket that encloses the unit. The exact relationship between the unit temperature T(C) and the cooling flow water flow rate (L/s) is extremely complex, and it is desired to derive a simple empirical formula to approximate this relationship over a limited range of flow rates and temperatures. Data are taken for T versus . Plots of T versus on rectangular and semi log coordinates are distinctly curved (ruling out T = a + b and T = aeb as possible empirical (functions), but a log plot appears as follows: A line drawn through the data goes through the points (1 = 25, T1 = 210) and (2 = 40. T2 = 120) (a) What is the empirical relationship between and T? (b) Using your derived equation, estimate the cooling water flow rates needed to maintain the process unit temperature at 85oC, 175oC, and 290oC.

Explanation / Answer

Let the relation between cooling water flow rate and temperature T

log =a logT+b

where a and b are constants

1=25 at T= 210 deg.c and 2= 40 and T= 120

hence log 25= alog210+b , 1.39794= a*2.3222+b (1) and log 40 = alog 120+b , 1.60206= a*2.079181+b (2)

Eq.1- Eq.2 gives 1.39794-1.60206= a*(2.3222-2.079181), a = -0.83987

from Eq.1, 1.39794 = -0.83987*2.3222+b or b= 3.348

The equation becomes log = -0.83987*logT+3.348

Temperatuee      (L/s)

85                      53.4

175               29.11

290                   19.05

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