Question

Compute the heat transfer rate from the overall energy balance for the hotcold fluid. Do the numbers agree reasonably well? Explain any differences.

Answer 1

Here first we have to assume that working fluid is WATER.

From your data we get information that you working on heat exchanger.

so Overall energy balance equation is,

Heat lost by the hot fluid = -Q = m_H × Cp_H × (To_H - Ti_H) … (1)

Heat gained by the cold side = Q = m_C × Cp_C × (To_C - Ti_C) … (2)

Comparing equations (1) and (2),

m_H × Cp_H × (Ti_H - To_H) = m_C × Cp_C × (To_C - Ti_C) … (3)

where, m_H : mass flow rate of the hot fluid in kg/hr
Cp_H : mass heat capacity of the hot fluid in KJoules/kg⁰C
Ti_H and To_H : Respectively inlet and outlet temperatures on exchanger hot side in ⁰C

m_C : mass flow rate of the cold fluid in kg/hr
Cp_C : mass heat capacity of the cold fluid in KJoules/kg⁰C
Ti_C and To_C : Respectively inlet and outlet temperatures on exchanger cold side in ⁰C

here we consider water density & specific heat Cp constant because its change negligible.

Density of water= 1000 kg/m³ & Cp= 4.2kJ/kgk

Heat transfer rate per Hr= -(m_H /time in hr)× Cp_H × (To_H - Ti_H) = (2*1000/3)*4.2* (47.6-45.2)= -6720 kJ/Hr (here -ve sign indicates that heat is gain by hot fluid which is not possible in heat exchanger)

Mostly in heat exchanger, temperature of hot fluid must be reduce because its transfer heat to cold fluid. But in your case we are found different readings. So you have to perform experiment again. Those readings are not correct.