Engineering task and calculation objective
The BIL module carries out the material and heat balancing of heat transfer duties. The balance is the first step of every heat exchanger design: before geometry, overall heat transfer, and pressure drop are considered, it must be established what heat flow is transferred between the media and what mass flows and temperatures result from it on both sides.
The module balances sensible heat as well as phase change (evaporation, condensation) and can optionally account for heat losses to the surroundings. From the selected geometry, the pressure drops on the inside and outside of the apparatus follow in addition – important secondary conditions that in practice often decide the feasibility of a design. To calculate a heat balance always also means closing the fourth unknown quantity (mass flow or temperature of one side) from the three known ones.
Typical applications are the preliminary design of shell-and-tube and double-pipe heat exchangers, the rating of existing apparatus under changed operating data, and the plausibility check of process data from flow sheets.
Calculation workflow
- Define media and operating data: For both sides, the medium, mass flow, and inlet and outlet temperatures are recorded; for phase change, additionally pressure and vapour fraction. The fluid properties (heat capacity, enthalpy of vaporization, density, viscosity) are evaluated at the mean state conditions.
- Balance the heat flow: From the fully determined side, the transferred heat flow follows from mass flow, heat capacity, and temperature change, or from the enthalpy of evaporation or condensation. Heat losses to the surroundings can be taken into account as a deduction.
- Close the unknown quantity of the opposite side: With the balanced heat flow, the missing quantity of the second side is calculated – depending on the task, the required mass flow or the resulting outlet temperature. The temperature cross is checked in the process: the outlet temperature of the cold side cannot exceed the inlet temperature of the hot side.
- Assign the geometry and determine the pressure drops: For the selected apparatus geometry, the flow cross-sections are determined and from them the pressure drops inside and outside are calculated. If they exceed the allowable values, the geometry (number of tubes, baffles, diameter) is adjusted and the balance is checked again.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| innen | mi | kg/s |
| außen | ma | kg/s |
| innen | Vi | m³/s |
| außen | Va | m³/s |
| innen | ρi | kg/m³ |
| außen | ρa | kg/m³ |
| innen | cp,i | J/(kg·K) |
| außen | cp,a | J/(kg·K) |
| innen | ϑi,e | °C |
| innen | ϑi,a | °C |
| außen | ϑa,e | °C |
| außen | ϑa,a | °C |
| innen | Qi | W |
| außen | Qa | W |
| Verlustwärmestrom | Qa,v | W |
| Heat transfer coeffic. inside convective | αi | W/(m²·K) |
| Heat transfer coeffic. outside convective | αa | W/(m²·K) |
| Thermal conductivity | λ | W/(m·K) |
| Fouling resistance | f | m²·K/W |
| Heat transfer area required | Areq | m² |
| Logarithmic temperature difference | Δϑm | K (diff) |
| Overall heat transfer coefficient | k | W/(m²·K) |
| Outside tube diameter | da | m |
| Inside tube diameter | di | m |
Calculation options
Flow arrangement
Countercurrent flow · Cocurrent flow · Cross flow
Geometry
cirular tubes · Channels with arbitrary shape
Worked example
A thermal oil stream is to be cooled with cooling water in a heat exchanger – a worked example of a heat balance calculation. Required are the transferred heat flow and the necessary cooling water mass flow.
Given values
| Mass flow of thermal oil mh | 6.0 kg/s |
| Heat capacity of oil cp,h (mean value) | 2.1 kJ/(kg·K) |
| Oil inlet / oil outlet | 120 °C / 70 °C |
| Cooling water in / out | 20 °C / 45 °C |
| Heat capacity of water cp,c | 4.18 kJ/(kg·K) |
Solution
Heat flow from the balance of the hot side
Q = mh · cp,h · (ϑh,in − ϑh,out) = 6.0 kg/s · 2.1 kJ/(kg·K) · (120 − 70) K = 630 kW
Heat losses to the surroundings are neglected for an insulated apparatus; the entire heat flow is transferred to the cooling water.
Required cooling water mass flow
mc = Q / (cp,c · (ϑc,out − ϑc,in)) = 630 kW / (4.18 kJ/(kg·K) · 25 K) = 6.03 kg/s ≈ 21.7 t/h
Plausibility check: the cooling water outlet temperature (45 °C) lies well below the oil inlet temperature (120 °C) — no temperature cross, so the duty is feasible with any flow arrangement.
Result
| Transferred heat flow Q | 630 kW |
| Cooling water mass flow mc | 6.03 kg/s (≈ 21.7 t/h) |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why should the balance come before the actual heat exchanger design?
The overall heat transfer coefficient and the surface area can only be calculated once the heat flow and the temperature profiles of both sides are fixed – the log mean temperature difference follows directly from the four inlet and outlet temperatures. An erroneous balance propagates through the entire design; it is therefore carried out as a separate, verifiable step.
At which temperature are the fluid properties evaluated?
For the balance, the heat capacity at the mean temperature between inlet and outlet of the respective side is usually sufficient. For large temperature spans or strongly temperature-dependent properties (oils, gases close to saturation), the enthalpy difference should be taken directly from property tables instead of calculating with a constant heat capacity.
How do heat losses to the surroundings enter the balance?
For well-insulated apparatus they are usually negligible (below 1–2 % of the transferred heat flow). For hot, uninsulated, or large-surface apparatus, the loss heat flow is estimated and added to the balance of the hot side: the cold side then receives correspondingly less heat. If the loss is ignored, measurements on a real apparatus appear inconsistent.
What is a temperature cross and when is it permissible?
A temperature cross occurs when the outlet temperature of the cold side lies above the outlet temperature of the hot side. In pure counterflow this is possible, in parallel flow it is not, and in shell-and-tube exchangers with multiple tube passes only to a limited extent – the correction factor of the temperature difference then drops sharply. The balance flags such a constellation early, before an unrealistic design is created.