*NC P <sup>I</sup> P* **II** *Yh*

194 Heat Transfer Studies and Applications

■ Optimal configurations

**7. Conclusions**

**Table 9.** Thermal effectiveness of RS for both mathematical models

consisting of assemblies of single-pass PHEs.

*E* **(differential equation model)** *E* **(closed-form model)** *ϕ* =1 *ϕ* =2 *ϕ* =3 *ϕ* =4 *ϕ* =1 *ϕ* =2 *ϕ* =3 *ϕ* =4

 80 1 2 0 80.1 80.3 80.3 80.1 80.4 80.4 80.4 80.4 80 2 1 1 80.3 80.1 80.3 80.1 80.4 80.4 80.4 80.4 81 1 2 0 80.3 80.3 80.3 80.3 80.6 80.6 80.6 80.6 83 2 1 1 80.5 80.5 80.5 80.5 80.8 80.8 80.8 80.8 84 1 2 0 80.5 80.8 80.8 80.5 80.9 80.9 80.9 80.9 84 2 1 1 80.8 80.5 80.8 80.5 80.9 80.9 80.9 80.9 85 1 2 0 80.8 80.8 80.8 80.8 81.0 81.0 81.0 81.0 87 2 1 1 80.9 80.9 80.9 80.9 81.2 81.2 81.2 81.2 88 1 2 0 80.9 81.2 81.2 80.9 81.3 81.3 81.3 81.3 88 2 1 1 81.2 80.9 81.2 80.9 81.3 81.3 81.3 81.3 89 1 2 0 81.2 81.2 81.2 81.2 81.4 81.4 81.4 81.4 91 2 1 1 81.4 81.4 81.4 81.4 81.6 81.6 81.6 81.6 92 1 2 0 81.3 81.6 81.6 81.3 81.7 81.7 81.7 81.7 92 2 1 1 81.6 81.3 81.6 81.3 81.7 81.7 81.7 81.7 93 1 2 0 81.6 81.6 81.6 81.6 81.8 81.8 81.8 81.8 95 2 1 1 81.7 81.7 81.7 81.7 82.0 82.0 82.0 82.0 96 1 2 0 81.7 81.9 81.9 81.7 82.1 82.1 82.1 82.1 96 2 1 1 81.9 81.7 81.9 81.7 82.1 82.1 82.1 82.1 97 1 2 0 81.9 81.9 81.9 81.9 82.2 82.2 82.2 82.2 **144 2 3 0** 71.8 71.7 **92.8 92.9** 71.8 71.8 **93.0 93.0 144 3 2 1** 71.7 71.8 **92.8 92.9** 71.8 71.8 **93.0 93.0** 149 3 2 1 71.7 71.7 93.0 93.0 71.7 71.7 93.2 93.2

In this chapter it was presented the development of two models for the design and optimization of plate heat exchangers. Both mathematical models were used to accomplish the heat exchanger design simulations. These methods use differential equations and closed-form equations based on the notion that a multi-pass PHE can be reduced to an arrangement



#### Greek symbols



#### Subscripts

*m*˙ mass velocity per channel (kg/s)

*N* Number of channels per pass

*M*˙ Mass flow rate, kg/s

196 Heat Transfer Studies and Applications

<sup>=</sup> Tri-diagonal matrix

*NC* Number of channels *NP* Number of plates

*Nu* Nusselt number

*P* Number of passes

*Pr* Prandtl number *Q* Heat transfer rate(J/s) *R* Heat capacity rate ratio *Rf* Fouling factor, K/W *Re* Reynolds number

*NTU* Number of transfer units

OS Optimal set of configurations

*PC* Temperature effectiveness

RS Reduced set of configurations *si* Binary parameter for flow direction

*U* Overall heat transfer coefficient, W/m2

*Yh* Binary parameter for hot fluid location *Yf* Binary parameter for type of channel flow *zi* Eigenvector of the tri-diagonal matrix

*α* Heat transfer coefficient

*ΔP* Pressure drop, Pa

*β* Chevron corrugation inclination angle, degrees

*ΔTlm* Log-mean temperature difference (K)

*v* Fluid velocity inside channels, m/s

·K

*tP* Plate thickness, m

*WP* Plate width, m

Greek symbols

*M*


#### Superscripts


#### **Author details**

Fábio A.S. Mota1,2, E.P. Carvalho2 and Mauro A.S.S. Ravagnani2\*


2 Chemical Engineering Graduate Program - State University of Maringá, Maringá, PR, Brazil

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**Provisional chapter**
