**5. Nomenclature**



#### **Greek**

42 Heat Exchangers – Basics Design Applications

*<sup>m</sup> cp*)*h*/( .

*m cp*)*min* 

*m cp*)*<sup>h</sup>*

*m cp*)*<sup>c</sup>*

**5. Nomenclature** 

*B* duty parameter *Be* Bejan number

*Cr* capacity ratios *Ctotal* total annual cost, \$

*d* diameter, m

*H* height, m

*L* length, m

*j* Colburn factor *K* Hagenbach factor

 exergy loss rate *Ec* Eckert number

*<sup>P</sup>* pressure-drop factor

*f* Fanning friction factor *G* mass flux, kg/m2.s

*m* mass flow rate, kg/s *N* number of fins

*Nu* Nusselt number

*p* perimeter*, m* 

*Pe* Peclet number = *Re.Pr Pr* Prandtl number =

*Q* heat dissipation rate*,* W

*R* heat capacity ratio

*Ra* Rayleigh number *Re* Reynolds number

*E*∗

*F*

*F\** 

.

.

*S t* .

*A* total heat transfer area, m2

*Br* Brinkman number = *Ec.Pr C* thermal conductivity ratio

*C\** modified ratio of heat capacity rates, ( .

*cp* constant-pressure specific heat, J/kg.K

*Fd* total drag force on the fin (or array), N

*h* heat transfer coefficient, W/m2.K, enthalpy, J/kg

*<sup>P</sup>* modified pressure-drop factor

*k* thermal conductivity, W/m.K

*Ns*, *NM* , *NQ* entropy generation numbers

*NTU* number of heat transfer units, *UoAo*/( .

*NTUh* modified number of heat transfer units, *UoAo*/( .

*/*

*Rfin* resistance of the fin structure as a function of geometry, K/W

entropy generation rate due to thermal effects, W/K

*dq/dx* heat transfer rate per unit length, W/m

*Rsink* overall resistance for the sink array, K/W

*P* temperature effectiveness for a fluid, pressure, Pa


#### **Subscripts**


Thermodynamic Optimization 45

Bejan, A, 1992, Single Correlation for Theoretical Contact Melting Results in Various

Bejan, A., 1996b, Entropy Generation Minimization: The New Thermodynamics of Finite-

Bejan, A., 1996c, Notes on the History of the Method of Entropy Generation Minimization

Bejan, A., 2000, Shape and Structure, from Engineering to Nature, Cambridge University

Bejan, A., 2001, Entropy Generation Minimization: The Method and Its Applications, Strojniski Vestnik/Journal of Mechanical Engineering, 47 (8), pp. 345-355. Bejan, A., 2002, Fundamentals of Exergy Analysis, Entropy Generation Minimization, and

Bejan, A., and Lorente, S., 2001, Thermodynamic Optimization of Flow Geometry in

Bejan, A. and Pfister, P.A., 1980, Evaluation of Heat Transfer Augmentation Techniques

Bejan, A., and Sciubba, E., 1992, The Optimal Spacing of Parallel Plates Cooled by Forced

Bejan, A., and Smith, J. L. Jr, 1974, Thermodynamic Optimisation of Mechanical Supports for

Bejan, A., and Smith, J. L. Jr, 1976, Heat Exchangers for Vapour Cooled Conducting Supports of Cryostats, Advances in Cryogenic Engineering, 21, pp. 247. Benedetti, P., and Sciubba, E., 1993, Numerical Calculation of the Local Rate of Entropy

Chowdhury, K., and Sarangi, S., 1980, A Second Law Analysis of the Concentric Tube

Chowdhury, K., and Sarangi, S., 1983, A Second Law Analysis of the Concentric Tube

Culham, J. R., Khan, W. A., Yovanovich, M. M., and Muzychka, Y. S., 2007, The Influence of

Cryogenic Apparatus, Cryogenics, 14 (3), pp. 158-163.

Journal of Heat and Mass Transfer, 26 (5), pp. 783-786.

Bejan, A., 1996a, Entropy Generation Minimization, CRC Press, Boca Raton, FL.

473-483.

1191-1218.

(3), pp. 239-242.

(7), pp. 545-565.

26 (4), pp. 305-354

(2), pp. 97-106.

November-3 December, 1993.

India, pp. 135-138.

Press, Cambridge, UK.

Bejan, A., 1993, Heat Transfer, Wiley, New York, NY.

Geometries, International Communications in Heat and Mass Transfer, 19 (4), pp.

Size Devices and Finite-Time Processes, Journal of Applied Physics, 79 (3), pp.

(Finite Time Thermodynamics), Journal of Non-Equilibrium Thermodynamics, 21

the Generation of Flow Architecture, International Journal of Energy Research, 26

Mechanical and Civil Engineering, Journal of Non-Equilibrium Thermodynamics,

Based on Their Impact on Entropy Generation, Letters in Heat and Mass Transfer, 7

Convection, International Journal of Heat and Mass Transfer, 35 (12), pp. 3259-3264.

Generation in the Flow Around a Heated Finned Tube, The 1993 ASME Winter Annual Meeting, ASME HTD, 266, pp. 81-91, New Orleans, LA, USA, 28

Balanced Counterflow Heat Exchanger: Optimisation of Wall Conductivity, Proceedings of the 7th National Symposium on Refrigeration and Air Conditioning,

Counterflow Heat Exchanger: Optimisation of Wall Conductivity, International

Material Properties and Spreading Resistance in the Thermal Design of Plate Fin Heat Sinks, ASME Journal of Electronic Packaging, 129 (3), pp. 76-81. Also


#### **Superscripts**

\* at maximum irreversibility
