Heat duty
Q = m x cp x (T in - T out), m in kg/s, cp in kJ/(kg K), Q in kW. 50 m3/h of fresh water at 80 °C (971.8 kg/m3) is 13.4972 kg/s; cooled from 80 to 70 °C with cp 4.18: 13.4972 x 4.18 x 10 = 564.18 kW.
Reference tool — arithmetic, not exchanger selection
Work out the duty of a cooler.
Heat duty · heat balance · LMTD · counterflow and parallel · UA
Flow, temperatures, LMTD.
Type a line (fresh water 50 m3/h 80 to 70 C, sea water 32 C 60 m3/h; or Q 500 kW hot 80/70, cold 32/? 60 m3/h) or fill in the fields: the line and the fields stay in step.
Examples:
Leave one field empty, a flow or a temperature, and the calculator finds it from the heat balance. The cp and density of fresh water and sea water are filled in as picks; for lube oil and other liquids, enter them from the data sheet.
All 130 engineering tools
Enter the flow and the inlet and outlet temperatures of one side of a cooler, plate or shell-and-tube, and the calculator gives the heat duty, Q = m x cp x (T in - T out). From the heat balance it finds the missing outlet temperature or flow of the other side, and from the end temperatures the log-mean temperature difference (LMTD) for counterflow and, when chosen, parallel flow, with UA = Q / LMTD. A volume flow is turned into a mass flow with the density; for fresh water and sea water the cp and density are picks, for lube oil and other liquids you enter them from the data sheet. The working is shown with your numbers, and the result is a line you can copy.
Arithmetic only: no fouling factors, no typical heat transfer coefficients, no approach temperature advice and no exchanger sizing. No correction factor F for multi-pass or cross-flow exchangers is applied. The size and build of the exchanger come from the data of its maker and the design of the plant.
How it is worked out
Duty, balance, LMTD.
Heat balance
What the hot side gives, the cold side takes. 60 m3/h of sea water (17.0833 kg/s, cp 4.00) warms by 564.18 / (17.0833 x 4.00) = 8.26 K: from 32 to 40.26 °C. A missing flow: m = Q / (cp x temperature change).
LMTD and UA
LMTD = (dT1 - dT2) / ln(dT1 / dT2). Counterflow: 80 - 40.26 = 39.74 K and 70 - 32 = 38 K give 38.87 K; parallel flow: 48 K and 29.74 K give 38.15 K. UA = Q / LMTD = 564.18 / 38.87 = 14.52 kW/K, with no correction F.
| Flow, m3/h | Fresh water, kg/s | Fresh water, kW per 10 K | Sea water, kg/s | Sea water, kW per 10 K |
|---|---|---|---|---|
| 5 | 1.378 | 57.6 | 1.424 | 56.9 |
| 10 | 2.756 | 115.2 | 2.847 | 113.9 |
| 20 | 5.512 | 230.4 | 5.694 | 227.8 |
| 50 | 13.781 | 576.0 | 14.236 | 569.4 |
| 100 | 27.561 | 1152.1 | 28.472 | 1138.9 |
| 200 | 55.122 | 2304.1 | 56.944 | 2277.8 |
| 500 | 137.806 | 5760.3 | 142.361 | 5694.4 |
The figures are the arithmetic Q = m x cp x 10 K with the picks of this page: fresh water at 992.2 kg/m3 (40 °C) and cp 4.18 kJ/(kg K), sea water at 1025 kg/m3 and cp 4.00 kJ/(kg K). For another temperature change the duty scales in proportion.
Sources
The working is the definition of the heat duty, Q = m x cp x temperature change, and of the log-mean temperature difference, LMTD = (dT1 - dT2) / ln(dT1 / dT2), for counterflow and parallel flow, as in the heat transfer textbooks. The fresh water cp of 4.18 kJ/(kg K) between 20 and 60 °C and the densities of 999.1 kg/m3 at 15 °C, 992.2 at 40 °C, 983.2 at 60 °C and 971.8 at 80 °C are each checked against two independent references. The sea water cp of 4.00 kJ/(kg K) at 35 g/kg near 20 °C is checked against two independent references; the typical density of 1025 kg/m3 (about 1020 to 1029 kg/m3 at the surface) against two references. Lube oil has no pick: two references gave no common typical value. 1 kcal = 4.1868 kJ exactly (the International Table calorie), so 1 kcal/h = 1.163 W. The data sheet of the liquid and the data of the exchanger maker always come first.
Before you work it out
Questions about heat exchanger duty
How is the heat duty of a cooler worked out?
Q = m x cp x (T in - T out) on one side, with the mass flow m in kg/s and cp in kJ/(kg K), which gives kW. A volume flow is turned into a mass flow with the density: 50 m3/h of fresh water at 80 °C, 971.8 kg/m3, is 50 / 3600 x 971.8 = 13.4972 kg/s. Cooled from 80 to 70 °C with cp 4.18 kJ/(kg K), Q = 13.4972 x 4.18 x 10 = 564.18 kW.
How is the missing outlet temperature or flow found?
From the heat balance: what the hot side gives, the cold side takes. With 564.18 kW and 60 m3/h of sea water at 1025 kg/m3 (17.0833 kg/s) and cp 4.00 kJ/(kg K), the sea water warms by 564.18 / (17.0833 x 4.00) = 8.26 K, from 32 to 40.26 °C. A missing flow comes the same way: m = Q / (cp x temperature change).
What is the LMTD, and how do counterflow and parallel flow differ?
LMTD = (dT1 - dT2) / ln(dT1 / dT2), with dT1 and dT2 the temperature differences at the two ends. In counterflow they are hot inlet less cold outlet and hot outlet less cold inlet: 80 - 40.26 = 39.74 K and 70 - 32 = 38 K give 38.87 K. In parallel flow they are hot inlet less cold inlet and hot outlet less cold outlet: 48 K and 29.74 K give 38.15 K. When both differences are equal, the LMTD is that difference: 38 K and 38 K give 38 K.
What is UA, and why is there no correction factor?
UA = Q / LMTD, the product of the overall heat transfer coefficient and the area that the duty and the temperatures call for: 564.18 kW / 38.87 K = 14.52 kW/K in counterflow. It is the UA of true counterflow or true parallel flow. A multi-pass shell-and-tube or a cross-flow exchanger needs a correction factor F on the LMTD, from the method of its maker; this page leaves F out.
Which cp and density are used?
For fresh water, cp 4.18 kJ/(kg K), the value between 20 and 60 °C, and the density from a short table (999.1 kg/m3 at 15 °C, 992.2 at 40 °C, 983.2 at 60 °C, 971.8 at 80 °C) at the point nearest the inlet temperature. For sea water, cp 4.00 kJ/(kg K) at 35 g/kg near 20 °C and a typical 1025 kg/m3. For lube oil and other liquids there is no pick: enter cp, and the density for a volume flow, from the data sheet of the liquid.
Why does the calculator refuse some temperatures?
Heat goes only from the hotter stream to the colder one. In counterflow the cold outlet may rise above the hot outlet but never above the hot inlet; in parallel flow the cold outlet stays below the hot outlet. Hot water 80 to 50 °C with cold water 30 to 60 °C works in counterflow (20 K at both ends, LMTD 20 K) but not in parallel flow. Fouling, the U value and the exchanger size come from the maker of the exchanger and the plant design; this page gives no figures for them.
Plates, gaskets or a tube bundle?
Send the line with a photograph of the exchanger nameplate.
The calculator works out the duty from the figures you enter. When plates, gaskets, a tube bundle or seals for a cooler are needed, attach a photograph of the exchanger nameplate, and Vessel Core checks the details before an offer goes back.
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