[aadicfd]

Hello everyone,
(This is an urgent problem so please have a look at it and suggest me if you have a solution as soon as possible)

I am having a trouble calculating the final temperatures of fluid in a heat exchanger. The problem is as follows:


I have a heat exchanger with effectiveness of 0.67
The fluid inside the tube is water with following properties:
inlet temperature: 303 K
Specific heat capacity (water) = 4184 J/kg K
flow rate (water)= 0.00002 m^3/sec
density = 1000 kg/m³


The fluid outside is air with following properties

inlet temperature: 298 K
Specific heat capacity (air) = 1006.3 J/kg K
flow rate (water)= 0.10372 m^3/sec
density = 1.1845 kg/m^3

My approach:


Cp_water = 4184 * 1000 * 0.00002 = 83.68

Cp_air = 1006.3 * 1.1845 * 0.10372 = 123.63



Q_max = Cp_min * (T_water_inlet - T_air_inlet) =83.68 * 5


Q_max = 418.4 W


Actual heat flow = Q_act = Q_max * Effectiveness = 418.4* 0.67 = 280.328 W


For both the fluids the difference in outlet and inlet temperatures is referred below as T_diff with _a and _w as suffix for air and water respectively


T_diff = T_inlet - T_outlet


Q_act = Cp_water * T_diff


Thus,

T_diff_w = Q_act / Cp_water = 280.328 / 83.68 = 3.35 K


T_diff_a = Q_act / Cp_air = 280.328 / 123.63 = 2.267


Here as you can see the final temperature of water is 299.65 K and for air is 300.267 K.


Have I made any mistake in calculations?
or is this practically possible?
Please help me!


Thank you!

[Sam-I-am]

Originally Posted by aadicfd

Hello everyone,
(This is an urgent problem so please have a look at it and suggest me if you have a solution as soon as possible)

I am having a trouble calculating the final temperatures of fluid in a heat exchanger. The problem is as follows:


I have a heat exchanger with effectiveness of 0.67
The fluid inside the tube is water with following properties:
inlet temperature: 303 K
Specific heat capacity (water) = 4184 J/kg K
flow rate (water)= 0.00002 m^3/sec
density = 1000 kg/m³


The fluid outside is air with following properties

inlet temperature: 298 K
Specific heat capacity (air) = 1006.3 J/kg K
flow rate (water)= 0.10372 m^3/sec
density = 1.1845 kg/m^3

My approach:


Cp_water = 4184 * 1000 * 0.00002 = 83.68

Cp_air = 1006.3 * 1.1845 * 0.10372 = 123.63



Q_max = Cp_min * (T_water_inlet - T_air_inlet) =83.68 * 5


Q_max = 418.4 W


Actual heat flow = Q_act = Q_max * Effectiveness = 418.4* 0.67 = 280.328 W


For both the fluids the difference in outlet and inlet temperatures is referred below as T_diff with _a and _w as suffix for air and water respectively


T_diff = T_inlet - T_outlet


Q_act = Cp_water * T_diff


Thus,

T_diff_w = Q_act / Cp_water = 280.328 / 83.68 = 3.35 K


T_diff_a = Q_act / Cp_air = 280.328 / 123.63 = 2.267


Here as you can see the final temperature of water is 299.65 K and for air is 300.267 K.


Have I made any mistake in calculations?
or is this practically possible?
Please help me!


Thank you!

Yes, it is possible for thout_out < tcold_out and I dont see any mistake. However, it is not possible for thot_out < tcold_in, since that would imply an effectiveness > 1.

[evcelica]

This is possible on a counter-flow heat exchanger only.
If the two fluids are traveling the same way, then no it is not possible.
With a counter flow heat exchanger, the outlet of one fluid is exchanging heat with the inlet of the other.