Question

Consider two double-pipe counter-flow heat exchangers that are identical except that one is twice as long as the other. Is the longer heat exchanger more likely to have a higher effectiveness

Answer 1

Both pipes will have the same effectiveness

Step-by-step explanation:

Heat exchanger effectiveness is defined as the ratio of the actual amount of heat transferred to the maximum possible amount of heat that could be transferred with an infinite area.

The actual amount of heat transferred for counter-flow heat exchangers is given as;

`q = C_h(T_h,_i -T_h,_o)`

where;

Ch is the specific heat capacity

Th,i is the inlet temperature of the hot fluid

Th,o is the outlet temperature of the hot fluid

The maximum possible amount of heat that could be transferred with an infinite area, is given as;

`q_(max) = C_(min)(T_h,_i-T_c,_i)`

where;

Cmin is the minimum heat transfer coefficient for hot and cold fluid

Heat exchanger effectiveness is calculated as;

`\epsilon = (q)/(q_(max))`

From the formula above, Heat exchanger effectiveness is independent of the pipe length.

Therefore, both pipes will have the same effectiveness