Heat balance sheet of a diesel engine

Heat balance sheet

It is an account of the fuel energy supplied to an engine and how it is distributed: brake work, coolant, exhaust gases, and the unaccounted losses (radiation, friction heat to oil, incomplete combustion). It shows where the energy goes and how to improve the engine, and is prepared for a test at a stated load and speed, usually on a per minute or per second (kW) basis.

Heat supplied

$$Q_s = \frac{14}{3600} \times 42\,000 = 163.3\ \text{kW}$$

Heat distribution

$$\begin{aligned} \text{Brake work} &= 50\ \text{kW} \\ Q_w &= \frac{50}{60} \times 4.187 \times 14 = 48.85\ \text{kW} \\ \dot{m}_{exh} &= \dot{m}_f + \dot{m}_a = \frac{14 \times (1 + 22)}{3600} = 0.0894\ \text{kg/s} \\ Q_{exh} &= 0.0894 \times 1.05 \times (380 - 27) = 33.15\ \text{kW} \\ Q_{unacc} &= 163.33 - 50 - 48.85 - 33.15 = 31.33\ \text{kW} \end{aligned}$$

The exhaust heat is the sensible heat above the ambient temperature.

Balance sheet

Answer: brake work 30.6%, cooling water 29.9%, exhaust 20.3%, unaccounted 19.2% of the 163.3 kW supplied.