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Gwar
16 days ago
14

A liquid food with 12% total solids is being heated by steam injection using steam at a pressure of 232.1 kPa (Fig. E3.3). The p

roduct enters the heating system at 508C at a rate of 100 kg/min and is being heated to 1208C. The product specific heat is a function of composition as follows: cp 5 cpwðmass fraction H2OÞ 1 cpsðmass fraction solidÞ and the specific heat of product at 12% total solids is 3.936 kJ/(kg 8C). Determine the quantity and minimum quality of steam to ensure that the product leaving the heating system has 10% total solids.
Engineering
1 answer:
iogann1982 [279]16 days ago
3 0

Answer:

m_{s}=20kg/min

H_{s}=1914kJ/kg

Explanation:

A liquid food containing 12% total solids is heated via steam injection at a pressure of 232.1 kPa (see Fig. E3.3). The product starts at a temperature of 50°C and has a flow rate of 100 kg/min, being elevated to a temperature of 120°C. The specific heat of the product varies with its composition as follows:

c_{p}=c_{pw}(mass fraction H_{2}0)+c_{ps}(mass fraction solid) and the

specific heat of the product at 12% total solids is 3.936 kJ/(kg°C). The goal is to calculate the quantity and minimum quality of steam required to ensure that the leaving product has 10% total solids.

Given

Product total solids in (X_{A}) = 0.12

Product mass flow rate (m_{A}) = 100 kg/min

Product total solids out (X_{B}) = 0.1

Product temperature in (T_{A}) = 50°C

Product temperature out (T_{B}) = 120°C

Steam pressure = 232.1 kPa at (T_{S}) = 125°C

Product specific heat in (C_{PA}) = 3.936 kJ/(kg°C)

The mass equation is:

m_{A}X_{A}=m_{B}X_{B}

100(0.12)=m_{B}(0.1)\\m_{B}=\frac{100(0.12)}{0.1} =120

Also m_{a}+m_{s}=m_{b}\\

Therefore: 100}+m_{s}=120\\\\m_{s}=120-100=20

The energy balance equation is:

m_{A}C_{PA}(T_{A}-0)+m_{s}H_{s}=m_{B}C_{PB}(T_{B}-0)

3.936 = (4.178)(0.88) +C_{PS}(0.12)\\C_{PS}=\frac{3.936-3.677}{0.12} =2.161

C_{PB}= 4.232*0.9+0.1C_{PS}= 4.232*0.9+0.1*2.161=4.025  kJ/(kg°C)

By substituting values into the energy equation:

100(3.936)(50-0)+20H_{s}=120(4.025)}(120-0)

19680+20H_{s}=57960\\20H_{s}=57960-19680 \\20H_{s}=38280\\H_{s}=\frac{38280}{20} =1914

H_{s}=1914kJ/kg

From the properties of saturated steam at 232.1 kPa,

H_{c} = 524.99 kJ/kg

H_{v} = 2713.5 kJ/kg

% quality = \frac{1914-524.99}{2713.5-524.99} =63.5%

Any steam quality above 63.5% will result in higher total solids in the heated product.

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