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CHAPTER SEVEN

Irreversible engines—Closed

cycles

7.1 Introduction

The endoreversible heat engines discussed in Chapter 6 were assumed
to experience external irreversibility only. The present chapter extends the
analysis of the preceding chapter to heat engines which undergo both exter-
nal and internal irreversibilities. The analysis will specifically focus on four
widely known gas cycles, including Brayton, Otto, Atkinson, and Diesel
engines operating in a closed cycle while exchanging heat with two thermal
reservoirs. Expressions were derived in Chapter 5 for the efficiencies of the
ideal design of these cycles. The performance of each engine at maximum
thermal efficiency, maximum power output, and minimum entropy gener-
ation rate will individually be investigated.
The underlying assumptions to be adopted for simplicity of the analysis
include (i) air is assumed to be the working gas with constant properties, (ii)
the air behaves like an ideal gas, (iii) pressure drop is negligible, (iv) external
irreversibilities are due to heat transfer processes between the engine and the
high- and low-temperature thermal reservoirs characterized by T H and T L ,
(v) internal irreversibilities are due to the compression and expansion pro-
cesses, (vi) the temperatures of the thermal reservoirs are fixed. As depicted
in Fig. 7.1, all four cycles have a similar T-s diagram.
The irreversible compression and expansion processes take place through
lines 1!2 and 3!4, respectively. The dotted lines 1!2s and 3!4s show
the isentropic compression and expansion processes. Lines 2!3 and 4!1
represent the heat addition and heat removal processes, respectively. In the
Brayton cycle, the heat transfer processes are isobaric whereas they are
isochoric in the Otto cycle. In the Atkinson cycle, heat is added to the
engine at constant volume (isochoric), and heat is removed at constant

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