Assignment on Design the hydro cooling unit that can cool fruits and vegetable from

Given data

How long the items need to remain in channel

temperature of vegetables=  T_( 1)  →  〖T 〗_2   

initial temperature  =T_( i)   =  T_1  =    30 C=   303 K

final temperature  =T_( f)   =  T_( f)  =    5 C  =   278 K

mass flow rate =  20,000 ( kg)/( h)  

Mass flow rate (m)=20000Kg/h=5.56Kg/s

width =   3 cm 

 height =  90 cm 

temperature of coils  inside  =   - 2^0  C

  how long it should remain =   t  

(〖T 〗_(f )  -〖 T〗_( ∞) \ )/(〖T 〗_(i )  - T_( ∞) )   =   〖 e〗^( - (( A h)/(ρ C_p  v))  t)

t =   (ρ C_p  v)/(- A h)  Ln⁡〖 [(〖T 〗_(f )  -T_( ∞) \ )/(〖T 〗_(i )  -T_( ∞) )]〗

Substituting the values gives 

I assumed that Cp of fruits is 41.8 ( as an average of Cp of fruits and vegetables) then

The value of the ρ C_p is assumed form the steam table because temperature is given  

http://thermopedia.com/content/1150/

t   =   ( 600 ×41.80 )/(   A × 3000)  〖 ln 〗⁡[( 30 -  3\ )/(5 - 3)]

t   =   (2,50,800 V )/(   A × 3000)  Ln⁡[( 27\ )/2]

t =  836 [( V)/( A)]  Ln⁡〖 ( 12.5 )〗

t =   2175 [( V)/( A)]s

Now calculating the slope with the values of V/A we get 

( V)/( A)   =     (3 ×  3  ×  10)/( 10  (3 ×  4)  +   2 (3 × 3) )

( V)/( A)   =   ( 90)/( 120 +   18)   =   ( 90)/( 138)

( V)/( A)  =  0.6521  cm  =    6.5×10^( -3)  m

Substituting the values back gives 

t =  2175 ( 6.5 × 10^( -3)  )  s

t =   14.18 sec 

The value of time required to cool the vegetables or fruits becomes 14.18 seconds. 

( V)/( A)   =   ( R)/( 3)    =   ( 5)/( 3)    =  1.6  ×  10^( -2)   m

Substituting the value of V/A back in the equation gives 

t =   2175 [( V)/( A)  ]  s

t =  2175  ×  1.6  ×  〖 10〗^( -2)  =  34.8  Sec⁡   

According to calculations, the value of time for cooling the items in the cooling pool is 34.8 second. 

B. Length of channel 

E =   ( rT)/( r L)

here rL = longitudinal radius  =   90 

rT  =  transversal radius  =  3

E =   (r T)/(r L)   =     ( 90)/( 3)   =   30 cm 

C. Water velocity through the channel 

h_( i)  +   1/2 m g h   =  h_( f)  +   1/2 m v^( 2)

h_( i)  +   m g h   =  h_( f)  +   m v^( 2)

Here mass is 5.56 

g  = 9.81  ( m)/( s^( 2) )

initial enthalpy =  h_( i)  =    104.75 ( KJ)/( Kg)

final enthalpy  =  〖h 〗_(f  )  =  21.02  ( KJ)/( Kg )

Using the enthalpy equation, we calculate the velocity of channel 

104.75  ( KJ)/( Kg)  +   (5.56 ×  9.81  ×  90 )   =  21.02  +  ( 5.56 )  〖 v〗^( 2)

 v =  29.96 

D. Velocity of conveyer 

The refrigeration process is the system of keeping the temperature of items below than the room temperature. The system depends on the cooling temperature and velocity of conveyer in the system. The velocity of conveyer depends on the type of refrigerator system such as mechanical compression refrigeration system and the most common type as absorption refrigeration system etc. In the present condition the velocity of conveyer is comparable to the velocity of water in the channel. Therefore, velocity of conveyer becomes 29.92 meter / second.

E. Refrigeration capacity 

initial temperature  = T_( i)   =     30 C =   303 K

final temperature  = T_( f)   =    5 C  =    278 K

Here we use properties from steam table for the enthalpy based on temperature, 

From the properties table (steam table)

initial enthalpy = h_( i)  =    125.75 ( KJ)/( Kg)

final enthalpy  =  〖h 〗_(f  )  =  21.41  ( KJ)/( Kg )

Mass flow rate (m)=20000Kg/h=5.56Kg/s

 P  =    m (h_( 1)  -   h_( 2) )  =   5.56 ( 125.75  -  21.41 )

P  =    m  (h_( 1)  -   h_( 2) )  =   581.04 KW

The power capacity of the system is 581.04 KW.

F. Type of heat exchanger 

The simple method to identify the type of heat exchanger is to check the enthalpy flow. Below is the method to measure the inflow and outflow of heat in the system,

q =   (h_( out)   -   h_( in) )  × m

where m is mass flow rate,that is 20000  ( kg)/( h)   =  20000  ( kg)/( h ×  36,000)

    q =   ( 21.02  -   104.75 )  × 20000  (  kg)/(  h ×  36,000)

q  =  - 465.16

The negative sign with the heat flow shows that the heat is released.

heat flow  =   465.167  ( kg)/( s)

The type of the heat exchanger is Shell and tube.