Formula used
Heat capacity rate (also called heat capacity flow rate) links energy transfer to temperature change in flowing streams:
- Ċ = ṁ × cp where ṁ is mass flow rate and cp is specific heat.
- Ċ = Q̇ / ΔT where Q̇ is heat transfer rate and ΔT is stream temperature change.
Units: Ċ is typically W/K (or kW/K). Larger Ċ means the stream temperature changes less for the same heat duty.
How to use this calculator
- Select a method that matches your available data.
- Choose the unknown in the “Solve for” dropdown.
- Enter the known values and pick their units.
- Optionally choose output units for each quantity.
- Press Calculate to see results above the form.
Example data table
| Case | ṁ (kg/s) | cp (kJ/kg·K) | Ċ (kW/K) | Q̇ (kW) | ΔT (K) |
|---|---|---|---|---|---|
| Water heating | 2.00 | 4.18 | 8.36 | 100 | 11.96 |
| Air cooling | 1.20 | 1.01 | 1.21 | 25 | 20.66 |
| Oil loop | 0.80 | 2.10 | 1.68 | 45 | 26.79 |
Values are illustrative. Use fluid-property data for your operating temperature.
Technical article
1) Meaning of heat capacity rate
Heat capacity rate, Ċ, describes how strongly a flowing stream resists temperature change. It is the product of mass flow and specific heat, so it scales with both how much fluid moves and how much energy each kilogram stores per kelvin.
2) Why Ċ matters in real equipment
In heaters, coolers, and recuperators, Ċ links duty to temperature rise through Q̇ = ĊΔT. A large Ċ stream warms or cools slowly for a given heat load, often becoming the “stiff” side that sets achievable outlet temperatures.
3) Typical specific heat data ranges
Liquid water near room temperature has cp ≈ 4.18 kJ/kg·K, while air is commonly near 1.00 kJ/kg·K at moderate conditions. Many hydrocarbon oils fall around 1.8–2.5 kJ/kg·K, and glycols typically sit between water and oils.
4) Example: water heating with measured flow
If ṁ = 2.0 kg/s and cp = 4.18 kJ/kg·K, then Ċ = 8.36 kW/K. With a 100 kW heater, the expected temperature increase is ΔT = Q̇/Ċ = 100/8.36 ≈ 12 K. This matches the example table.
5) Example: air cooling and larger temperature swings
For ṁ = 1.2 kg/s and cp = 1.01 kJ/kg·K, Ċ ≈ 1.21 kW/K. A modest 25 kW load gives ΔT ≈ 20.7 K, showing why gases often experience larger temperature changes than liquids at comparable duties.
6) Link to heat exchanger effectiveness
Heat exchanger analysis commonly uses the minimum and maximum heat capacity rates, Ċmin and Ċmax. The capacity ratio Cr = Ċmin/Ċmax influences achievable effectiveness, and Ċmin sets the upper bound for heat transfer: Q̇max = Ċmin(Th,in − Tc,in).
7) Unit discipline and conversion checks
This calculator converts to base SI internally (kg/s, J/kg·K, W, K) to prevent mixed-unit errors. For temperature difference, degrees Celsius and kelvin are equivalent, while degrees Fahrenheit must be converted using the 5/9 factor for differences.
8) Measurement and modeling cautions
Use cp values at your operating temperature and composition; cp can vary with temperature, pressure, and mixture ratio. For two-phase flow, an effective cp may be misleading unless phase change is treated explicitly. When using Q̇/ΔT, ensure ΔT is the stream change, not the exchanger approach temperature.
FAQs
1) What is the difference between cp and Ċ?
cp is a material property per kilogram per kelvin. Ċ includes flow rate, so it represents the whole stream’s capacity to absorb or release heat per kelvin of temperature change.
2) When should I use Ċ = ṁ × cp?
Use it when you know the mass flow rate and can obtain cp from property tables or datasheets. It is the most direct way to characterize a stream for heat exchanger sizing.
3) When should I use Ċ = Q̇ / ΔT?
Use it when you have measured heat duty and the stream temperature change. This is common during commissioning or testing, where flow may be uncertain but temperatures and duty are logged.
4) Is ΔT the same in °C and K?
Yes. Temperature differences in degrees Celsius and kelvin are numerically identical. Differences in °F or °R must be converted to kelvin using the 5/9 factor.
5) Does Ċ change with temperature?
It can. Mass flow may vary with operating point, and cp often changes with temperature and composition. For accurate work, use cp evaluated near the stream’s mean temperature.
6) How do I handle mixtures or solutions?
Use an appropriate mixture cp from reliable data, or a validated correlation for your concentration and temperature. Then compute Ċ with the actual mass flow rate of the mixture stream.
7) How does Ċ help compare hot and cold sides?
Compare Ċ values to find Ċmin and Ċmax. The side with smaller Ċ experiences larger temperature change and typically limits the maximum possible heat transfer.