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Cooling heat-balance calculator

Compare hot- and cold-stream heat duties; examine flow, temperature, units and energy-balance assumptions together.

From flow to heat, step by step

Calculate a stream’s sensible-heat rate, rearrange the equation or compare two separate streams. Each result retains its units, substitutions and assumptions.

Q̇ = ṁ × cp × ΔT ṁ = ρ × V̇

Inputs and fluid assumptions

What would you like to calculate?

kg/s × kJ/(kg·K) × K = kW. Use a decimal point or comma; do not use thousands separators.

Stream

Flow reading0 or 10⁻⁹–10⁹; select its unit alongside.

Flow unitDistinguish mass flow from volume flow.

Assumed density ρ kg/m³10⁻⁶–100,000. Match the volume reading’s reference conditions.

Assumed specific heat cp kJ/(kg·K)10⁻⁶–1,000. Treated as constant throughout.

Temperature change ΔT KTout − Tin. 0 or magnitude 10⁻⁹–10,000.

For one stream, ΔT = Tout − Tin. Positive Q̇ means heat gained by the stream; negative Q̇ means heat removed. The two-side comparison reports hot-side removal and cold-side gain separately.

4.18 kJ/(kg·K) and 1,000 kg/m³ are assigned constant properties for this teaching example only. They are not universal seawater, glycol-mixture or temperature/pressure values. Enter cp and ρ appropriate to your fluid and measurement conditions. With mass-flow input, ρ is used only for volume-flow equivalents.

Calculations use finite numerical ranges, and input bounds differ by mode. An extreme result from one mode may not be accepted as an input to another. The display rounds to six significant figures; CSV preserves computed numeric values.

Result and reproducible steps

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This calculator processes inputs in your browser. A CSV is created only when you select Download; the calculator does not send or store data.

What does this model calculate?

Draw the boundary around one stream’s inlet and outlet. For steady single-phase flow with suitable constant cp, ṁcpΔT gives its sensible-enthalpy change rate. Interpreting this as heat exchange requires other terms, such as shaft work, kinetic/potential energy change and storage, to be negligible.

Because cp is entered in kJ/(kg·K) and mass flow in kg/s, the result is directly in kW. A 10 °C temperature difference equals a 10 K difference; this equivalence does not apply to absolute temperatures. Volume flow is first converted to m³/s, then multiplied by suitable density.

Heat-rate mode uses Q̇ = ṁcpΔT; flow mode uses ṁ = Q̇/(cpΔT); temperature-change mode uses ΔT = Q̇/(ṁcp). Inverse calculations explicitly handle zero denominators and conflicting signs. Numerical bounds are not a physical validity envelope; this tool does not determine fluid phase or pressure.

The comparison uses R = Q̇removed from hot side − Q̇gained by cold side. If storage and external heat exchange are negligible, the duties are expected to be close across that boundary. R alone cannot identify leakage, fouling, sensor failure or adequate cooling capacity.

Reproduce the guide’s examples

These invented water-stream examples assume cp = 4.18 kJ/(kg·K) on both sides and ρ = 1,000 kg/m³ where volume conversion is needed. They are not vessel measurements or seawater design data.

Explicit assumptions, units and results
Case	Calculation	Value
Hot stream · 60 → 50 °C	2 × 4.18 × (60 − 50)	83.60 kW removed
Cold stream · 20 → 25 °C	4 × 4.18 × (25 − 20)	83.60 kW gained
Cold outlet 24.5 °C	4 × 4.18 × (24.5 − 20)	75.24 kW; residual 8.36 kW
Volume flow · 36 m³/h	36/3,600 × 1,000 = 10 kg/s	10 × 4.18 × 5 = 209 kW

The first two rows agree at 83.6 kW. This checks energy consistency for the supplied numbers; no exchanger area, UA or fouling state has been calculated.
Reducing only the cold outlet by 0.5 °C lowers its apparent duty by 8.36 kW. The displayed relative residual becomes 10%; this does not establish 10% efficiency loss or a leakage rate.
To carry 83.6 kW with a 5 K rise, ṁ = 83.6/(4.18 × 5) = 4 kg/s. For the same target and a 4.5 K rise, about 4.44444 kg/s is required algebraically. This demand does not establish that a pump can deliver the flow.

Before applying the result

Identify density and specific heat for the actual fluid composition, temperature, pressure and volume-meter reference conditions. Do not extrapolate teaching constants into unsuitable conditions.
Both sides’ flow and temperature readings must represent the same time interval and appropriate measurement locations. Bypass, mixing and an incorrect boundary can create an apparent imbalance.
Before interpreting a residual, assess measurement uncertainty and correlation, timing, thermal storage and external heat loss. The ±10% table here is not an uncertainty analysis.
Phase change, boiling, condensation, transients, detailed enthalpy/property calculations, LMTD/ε-NTU, area, UA, pressure drop and equipment sizing are outside scope. Actual installations require manufacturer data, approved procedures and qualified engineering judgment.

Method and property references

The DOE source is an archived educational handbook, not a current marine design-approval standard. IAPWS supports condition-dependent properties; NIST supports uncertainty assessment. This tool does not run those sources’ property correlations. Links checked 8 October 2026.

Full guide: Cooling-system heat balances

Model 1.0.0

Read the method and its limits

Related project: ShipExact

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