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## Lesson 30. HEAT AND MASS BALANCE OF CONTINUOUS DRYERS

Module 3. Food dehydration

**Lesson 30**

**HEAT AND MASS BALANCE OF CONTINUOUS DRYERS**

**30.1 Dehydration System Design**

The design of dehydration systems involves several considerations. The parameters that have a direct influence on capacity of a system include the quality and characteristics of air available for drying along with the drying time required for individual pieces of the product being dried.

**Mass and Energy Balance **

By application of mass and energy balance analysis to an entire dehydration system several parameters influencing design are accounted for.

Moisture balance on the system gives:

m_{a} W_{1} + m_{p} w_{1} = m_{a} W_{2} + m_{p }w_{2}

Where,

m_{a} = Air flow rate (kg dry air / h), m_{p} = Product flow rate (kg dry solids / h) , W = Absolute humidity (kg water / kg dry air) and w = Product moisture content (kg water / kg solid) T_{a}= Temperature of air ( ⁰ C) T_{p} = Temperature of product ( ⁰ C ) and 1 is inlet condition; and 2 is the outlet condition.

__Energy balance__ for the system gives:

_{a}H

_{a1}+ m

_{p }H

_{p1}= m

_{a}H

_{a2}+ m

_{p}H

_{p2 }+ Q

_{l}

Where, Q_{l} = Heat losses from dehydration system, H_{a} = Heat content of air (kJ / kg dry air) and H_{p} = Heat content of product (kJ / kg dry solids).

Considering 0 ⁰ C as the reference temperature the expressions for heat content of air and product are :

H_{a} = 1.005 T_{a }+ W (2500.5+ 1.884 T_{a)}

H_{p} = C_{pp} T_{p} + w C_{pw} T_{p}

Where,

C_{pp} – Specific heat of product solids (kJ /kg K)

C_{pw} – Specific heat of water (kJ /kg K),

T_{p} – Product temperature.

Using these equations, the quality of air required for drying an established amount of product over known moisture content range can be determined. In addition, for known inlet conditions of air, the moisture characteristics of air at the system outlet can be established.

The overall coefficient is from 1160 to 2100 W/ m^{2} K under optimum condition, although it may be only 1/10 of these values when conditions are adversed. Since the thickness of drum wall is small compared to the diameter of the drum, the area A can be regarded simply as the outer surface area of the drum. The U depends on h_{s} , k and h_{p} and other coefficients.

The factor having the greatest effect on U is the condition of the liquid film and the drum speed. Drying rates for drum dryers can be extremely high when thin film of low viscosity is evaporated, and it is thus permissible to use high temperature. In addition to assuring the adequate heat transfer the drying system must provide for removal of water vapour. If the speed of a particular drum is measured, then the U value and the moisture content of the product will be increased, if the conditions are unchanged. The overall thermal efficiency of drum dryer is 35 – 80%. The moisture content x of a milk product containing m_{w} amount of water and m_{s} amount of dry matter including fat is given by:

During the evaporation of a product from the original moisture content x_{0} containing amount of water m_{w0} to a final moisture content x containing an amount of water m_{w}, the following amount of water is removed.