--- title: "Heat balance sheet of a diesel engine" subject: "Internal Combustion Engines" chapter: 8 key: "semester_6/internal_combustion_engines:diesel-engine-heat-balance-numerical" source: https://www.bctengineer.com/q/semester_6/internal_combustion_engines/diesel-engine-heat-balance-numerical site: BCT Engineering --- # Heat balance sheet of a diesel engine Internal Combustion Engines · Chapter 8: Engine performance and testing of engines - Asked in: year not given, 8 marks - Video: [Heat Balance Sheet of Engine](https://www.youtube.com/watch?v=KS-jejQaqfo) — BEST MECHANICAL ENGINEERING - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/internal_combustion_engines/diesel-engine-heat-balance-numerical - Whole chapter: https://www.bctengineer.com/md/semester_6/internal_combustion_engines/chapter-8 ## Question What is a heat balance sheet of an engine? A four-cylinder diesel engine develops a brake power of 50 kW. The fuel consumption is 14 kg/h with a calorific value of 42 000 kJ/kg. The cooling water flow is 50 kg/min with a temperature rise of 14 K. The air-fuel ratio is 22:1 by mass and the exhaust gases leave at 380 degrees C while the ambient temperature is 27 degrees C. Take $c_{pw} = 4.187$ kJ/kg K and $c_{p,exh} = 1.05$ kJ/kg K. Prepare the heat balance sheet in kW and in per cent. ## Short answer Fuel energy 163.3 kW; brake work 50 kW (30.6%), cooling water 48.9 kW (29.9%), exhaust sensible heat 33.2 kW (20.3%), unaccounted losses 31.3 kW (19.2%). ## Answer #### 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 | Item | kW | % | |---|---|---| | Heat in fuel | 163.3 | 100 | | Heat converted to brake work | 50.0 | 30.6 | | Heat to cooling water | 48.9 | 29.9 | | Heat carried by exhaust gas | 33.2 | 20.3 | | Unaccounted losses (by difference) | 31.3 | 19.2 | | Total | 163.3 | 100 | **Answer:** brake work 30.6%, cooling water 29.9%, exhaust 20.3%, unaccounted 19.2% of the 163.3 kW supplied. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does a heat balance sheet show? A. Only the brake work B. How the fuel energy is distributed: work, coolant, exhaust and unaccounted losses C. The compression ratio D. Only the cost of fuel Answer: B. It accounts for the fuel energy supplied and its distribution among useful work and various losses. (Key point: Heat balance sheet meaning) 2. What is the heat supplied by the fuel? A. 163.3 kW B. 14 x 42000 = 588000 kW C. 50 kW D. 98 kW Answer: A. Q_s = 14/3600 x 42000 = 163.3 kW. (Key point: Heat supplied) 3. How is the exhaust heat computed? A. Fuel mass flow x cp x (380 - 27) B. Fuel plus air mass flow x cp x (380 - 27) = 33.15 kW C. Air mass flow x cp x 380 D. Water flow x cp x 14 Answer: B. Exhaust mass = 14 x 23/3600 = 0.0894 kg/s; Q = 0.0894 x 1.05 x 353 = 33.15 kW (sensible heat above ambient). (Key point: Heat to exhaust) 4. How is the unaccounted loss found? A. By difference: 163.3 - 50 - 48.85 - 33.15 = 31.3 kW (19.2%) B. As 50% of brake work C. By measuring with a gauge D. As cooling water heat minus exhaust heat Answer: A. The remainder after brake work, coolant (48.85 kW) and exhaust is the unaccounted portion, about 19.2%. 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