Sensible Heat Duty Calculator

Calculate the sensible heating or cooling duty of a flowing stream from its mass flow rate, specific heat capacity, and inlet and outlet temperatures. See the signed heat-transfer rate, temperature change, and intermediate steps in SI or engineering units.

Formula and method

For a single-phase stream at steady flow, with an approximately constant or appropriate mean mass-specific heat capacity:

Q̇ = ṁ × c_p × (T_out − T_in) = ṁ × c_p × ΔT

The engine converts mass flow to kg/s, specific heat to J/(kg·K), and temperature change to K. Multiplying gives J/s, or W. It also reports the specific enthalpy change, Δh ≈ c_pΔT, and heat-capacity rate, Ċ = ṁc_p.

Sign convention: positive duty means heat is added to the stream; negative duty means heat is removed. The required heating or cooling magnitude is |Q̇|. Equal inlet and outlet temperatures give zero sensible duty. Zero mass flow gives zero duty, without representing an operating flowing stream.

Units and input basis

• Enter mass flow, not volumetric or molar flow. Convert volume flow using the density at its actual conditions before using this tool.
• Use mass-specific c_p for your material, composition, phase, and temperature range. No material property is looked up automatically; the example value is an assumption.
• Mass-flow, heat-capacity, and temperature units are independent. For example, kJ/(kg·K) can be used with temperatures entered in °F; the engine converts the temperature difference correctly.
• A temperature difference of 1 °C equals 1 K; a difference of 1 °F or 1 °R equals 5/9 K. Offset conversions apply to absolute inlet/outlet temperatures, not to ΔT.
• Btu_IT denotes International Table Btu (1055.05585262 J); kcal_th denotes thermochemical kilocalorie (4184 J). One lbm is 0.45359237 kg, one tonne is 1000 kg, and one hour is 3600 s.

Assumptions and validity

• Steady flow, no phase change or reaction, negligible shaft work, and negligible kinetic and potential energy changes. Pressure effects on enthalpy are neglected.
• c_p must be positive and representative of the temperature interval. When c_p varies significantly, use a justified mean value or calculate Δh from property data or ∫c_p(T) dT instead.
• This is the duty associated with the stream temperature change. Heat losses, equipment efficiency, latent heat, and utility consumption require additional calculations.
• Temperature inputs must be at or above absolute zero. These numerical checks do not establish the material phase, property validity, or equipment operating limits.

Worked example

A stream flows at 2 kg/s and is heated from 20 to 80 °C. Assume its mean c_p is 4.18 kJ/(kg·K). Then ΔT = 60 K, Δh ≈ 4.18 × 60 = 250.8 kJ/kg, and Ċ = 2 × 4.18 = 8.36 kW/K.

Q̇ = 2 × 4.18 × 60 = +501.6 kW. Add 501.6 kW to the stream. Reversing the temperatures gives −501.6 kW: remove 501.6 kW. Select “Load example” to reproduce the heating case.

For heat exchanger calculations, use the LMTD Calculator to find the temperature driving force. Exchanger area also requires a suitable overall coefficient and, where applicable, a configuration correction factor.

Sources and calculation version

• U.S. Department of Energy, Thermodynamics, Heat Transfer, and Fluid Flow, DOE-HDBK-1012/1-92, Volume 1, module HT-01, page 21: specific heat and the mass-flow heat-transfer equation.
• NIST SP 811, Appendix B.9: mass, energy, and heat-flow unit conversions and definitions of International Table Btu and thermochemical calorie.

Changelog: engine 1.0.0 introduces signed heating/cooling duty, independent unit conversion, intermediate results, zero-flow and equal-temperature handling, and input validation. Parameter source: your stream conditions and heat capacity; no property dataset is used. Engineering review status: independent review pending.