Ethylene glycol flows at 0.01 kg/s through a 3-mm diameter, thin-walled tube. The tube is coiled and submerged in well-stirred water bath maintained at 25°C. If the fluid enters the tube at 85°C, what heat rate and tube length are required for the fluid to leave at 35°C?

heat rate= 1281W

length = 15.8m

Explanation:

we have this data to answer this question with

Tmi = 85 degrees

Tmo = 35 degrees

Ts = 25 dgrees

flow rate = 25 degrees

using engine oil property from table a-5

Tm = Tmo - TMi/2 = 333k

u =0.522x10⁻²

k = 0.26

pr = 51.3

cp = 2562 J/kg.k

mcp(Tmo-Tmi) =

0.01 x 2562(35-85)

= 1281 W

we find the change in Tim

= [(35-25)-(85-25)]/ln[(35-25)/(85-25)]

= -50/ln0.167

= -50/-1.78976

= 27.9°c

we finf the required reynold number

4x0.01/πx0.003x0.522x10⁻²

= 0.04/0.00004921

= 812.8

= 813

we find approximate correlation

NuD = hd/k

NuD = 3.66

3.66 = 0.003D/0.26

cross multiply

0.003D = 3.66x0.26

D = 3.66x0.26/0.003

= 317.2

As = 1281/317x27.9

= 0.145

As = πDL

L = As/πD

= 0.145/π0.003

= 0.145/0.009429

L = 15.378

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