Final answer:
To find the heat exchange area and the rate of heat transfer for a counter flow heat exchanger, the rate of heat transfer formula Q = mcΔT is used, with the conversion for heat transfer rate to watts and the heat exchanger equation Q = UAΔT_lm facilitating the calculation for the required heat exchange area.
Step-by-step explanation:
Heat Exchanger Calculations
The problem at hand is to compute two primary variables in a double pipe counter flow heat exchanger scenario: the heat exchange area and the rate of heat transfer. Given are the flow rate of water, the temperature change of the water and the oil, the specific heat of the oil, and the overall heat transfer coefficient.
To calculate the rate of heat transfer (Q), we apply the formula Q = mcΔT, where m is the mass flow rate of water, c is the specific heat capacity of water (which is 4.186 kJ/kg.K for water), and ΔT is the temperature change of water. Inserting the known values, we have Q = (65 kg/min) × (4.186 kJ/kg.K) × (25 K), since the water is heated from 50°C to 75°C. To convert the heat transfer rate to watts, we multiply by 60 seconds and 1000 to convert kJ to J, and the final unit will be in watts (W).
To determine the heat exchange area (A), we use the heat exchanger equation Q = UAΔT_lm, where U is the overall heat transfer coefficient and ΔT_lm is the log mean temperature difference (ΔT_lm) between the two fluids at the inlet and outlet. ΔT_lm can be calculated using the inlet and outlet temperatures of both fluids. Since U is given as 340 W/m2.K, once ΔT_lm is calculated, we can rearrange the equation to solve for A as A = Q / (UΔT_lm).
Note that you will need to ensure that the mass flow rate of oil is sufficient to provide the calculated heat transfer rate, as the temperature change of the oil is already given.