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Optimization of energy systems using the concept of balance in the nature

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Abstract

In this paper, a concept of balance is used to improve the important parameters of the thermal systems. In fact, using this concept give the designer to propose some new configuration which is more efficient. To show the benefit of this concept, firstly, the proposed balancing method is introduced for a simple case study after that its application is used in optimization of thermal systems. In this regard, to achieve the better optimal results in each problem, the unbalanced factors are detected and some solutions are presented to reduce the system unbalancing. Three case studies including Rankine cycle, plate fin heat exchanger, and double pipe heat exchanger are discussed and optimized to show the benefits of this method.

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Abbreviations

A flow :

Free flow cross-sectional area(m2)

A tot :

Total heat transfer area(m2)

af :

Annualized factor (-)

b :

Fin height(m)

c :

Specific heat(j/kgK)

c :

Fin pitch(m)

C min :

Minimum of Ch and Cc (W/K)

C max :

Maximum of Ch and Cc (W/K)

C ∗ :

Heat capacity rate ratio (Cmin/Cmax)

C in :

Investment cost ($/year)

C op :

Operational cost ($/year)

D e :

Heat transfer equivalent diameter (m)

D h :

Hydraulic diameter (m)

d i :

Tube inside diameter (m)

d o :

Tube outside diameter (m)

\( {\dot{E}}_D \) :

Rate of exergy destruction (kW)

e :

Specific exergy destruction (kj/kg)

f :

Friction factor (−)

h :

Heat transfer coefficient (W/m2K)

h :

Specific enthalpy (kj/kgK)

j :

Colburn number (−)

k W :

Wall conductivity (W/mK)

L :

Tube length (m)

L c :

Cold stream flow length(m)

L h :

Hot stream flow length(m)

L n :

No-flow length(m)

\( \dot{m} \) :

Mass flow rate (kg/s)

N :

Operational hours in a year

Nu :

Nusselt number (−)

NTU :

Number of transfer units (−)

Pr :

Prandtl number (−)

\( \dot{Q} \) :

Rate of heat transfer (W)

Re:

Reynolds number (−)

R f :

Fouling resistance (m2K/W)

St :

Stanton number (−)

TAC :

Total annual cost ($/year)

t f :

Fin thickness(m)

U :

Overall heat transfer coefficient (W/m2K)

V :

Volumetric flow rate (m3/s)

\( \dot{W} \) :

Power (W)

x :

Fin length(m)

ε :

Heat exchanger effectiveness(−)

η :

Efficiency(−)

β :

Ratio of hot and cold surface area(−)

μ :

Viscosity (Pa.s)

ΔP :

Pressure drop (Pa)

σ :

Ratio betweenAflow and Afront (Aflow/Afront)

ϕ e :

Unit price of electrical ($/kWh)

a :

Actual

b :

Boiler

c :

Cold or condenser

h :

Hot

e:

Exhaust

i :

Inlet

P :

Pump

s :

Isentropic

T :

Turbine

tot :

Total system

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

    Hassan Hajabdollahi & Mohammad Shafiey Dehaj

Authors
  1. Hassan Hajabdollahi
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  2. Mohammad Shafiey Dehaj
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Contributions

H. Hajabdollahi suggested the idea and stated the theory. M. Shafiey performed optimization. M. Shafiey wrote the manuscript with support from H. Hajabdollahi. All authors discussed the results and contributed to the final manuscript. All authors read and approved the final manuscript.

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Correspondence to Mohammad Shafiey Dehaj.

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The authors declare that they have no competing interests.

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Hajabdollahi, H., Shafiey Dehaj, M. Optimization of energy systems using the concept of balance in the nature. Environ Sci Pollut Res 28, 37580–37591 (2021). https://doi.org/10.1007/s11356-021-13421-8

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