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Cost Optimization of Heat Exchanger Inventory in Cascade Refrigeration Cycles

  • Research Article-Mechanical Engineering
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Abstract

In this work, the cost optimal distribution of the overall conductance of all the heat exchangers is investigated from a thermoeconomic point-of-view in cascade refrigeration cycles using the endoreversible case. Non-dimensional cost functions are developed and investigated for a constant value of the rate of work, rate of cooling, rate of heat rejection and heat transfer rate for the cascade heat exchanger. These can be used to predict the minimum initial cost of the heat exchangers under the specified thermal conditions. All the cost functions showed an optimum point in relation to the absolute condenser temperature ratio (θ1) wherein the case of fixed heat rejection rate from the condenser gave the lowest cost values and the case of constant rate of work gave the highest cost values with it being 3 times higher at the optimum point. For the former case, a 1% increase in evaporator to condenser fluid temperature ratio (Φ) resulted in an average increase of 4.7% in the cost function value. For the case of fixed cooling rate, the corresponding cost function had an optimum value with respect to the non-dimensional temperature difference in the cascade heat exchanger. In this case, for a 5% increase in θ1, the cost value decreased by ~ 7%; although this decrease was larger for lower values of Φ. Also, investigation into the unit cost ratio of the system showed that the condenser contributed the most (42%-65%) to the total overall conductance.

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Abbreviations

A :

Area (m2)

F :

Non-dimensional cost ratio (–)

G :

Unit cost conductance ratio (–)

\(\dot{m}\) :

Mass flow rate (kg s−1)

\(\dot{Q}\) :

Heat transfer rate (kW)

T :

Absolute temperature (K)

U :

Overall heat transfer coefficient (W m−2 K−1)

Γ:

Total cost ($)

γ :

Unit conductance cost ($ W−1 K)

Φ:

Low-side Carnot absolute temperature ratio \(\left( { = {{T_{LC} } \mathord{\left/ {\vphantom {{T_{LC} } {T_{HC} }}} \right. \kern-0pt} {T_{HC} }}} \right)\)

θ 1 :

High-side absolute temperature ratio for topping cycle \(\left( { = {{T_{HC} } \mathord{\left/ {\vphantom {{T_{HC} } {T_{H} }}} \right. \kern-0pt} {T_{H} }}} \right)\)

θ 2 :

High-side absolute temperature ratio for cascade heat exchanger \(\left( { = {{T_{{{\text{CHX}},h}} } \mathord{\left/ {\vphantom {{T_{{{\text{CHX}},h}} } {T_{H} }}} \right. \kern-0pt} {T_{H} }}} \right)\)

θ 3 :

Low-side absolute temperature ratio for cascade heat exchanger \(\left( { = {{T_{{{\text{CHX}},l}} } \mathord{\left/ {\vphantom {{T_{{{\text{CHX}},l}} } {T_{H} }}} \right. \kern-0pt} {T_{H} }}} \right)\)

ξ :

Absolute temperature ratio \(\left( { = {{T_{L} } \mathord{\left/ {\vphantom {{T_{L} } {T_{H} }}} \right. \kern-0pt} {T_{H} }}} \right)\)

a :

Fixed work rate

b :

Fixed cooling rate

C :

Reversible compartment

c :

Fixed condenser heat rejection rate

CHX:

Cascade heat exchanger

d :

Constant heat transfer in the cascade heat exchanger

H :

Hot end

h :

High-side

L :

Cold end

l :

Low-side

tot:

Total

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Acknowledgements

The authors would like to acknowledge the support provided by King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through project # SB191026.

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Authors and Affiliations

  1. Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Bilal A. Qureshi & Syed M. Zubair

  2. IRC for Renewable Energy and Power Systems, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Bilal A. Qureshi & Syed M. Zubair

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  1. Bilal A. Qureshi
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Correspondence to Syed M. Zubair.

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Qureshi, B.A., Zubair, S.M. Cost Optimization of Heat Exchanger Inventory in Cascade Refrigeration Cycles. Arab J Sci Eng 48, 12513–12522 (2023). https://doi.org/10.1007/s13369-023-07865-y

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