Abstract
Versatile applications of plate heat exchangers (PHE's) in various industrial processes signify their command over other types of heat exchangers. The objective of this work was to derive Nusselt number correlations using dimensional analysis in terms of all the parameters to determine the heat transfer coefficients in a PHE for various concentrations of carboxymethyl cellulose (CMC) solution and it was also compared with the available models in literature. The heat transfer coefficient increases with increase in concentration of CMC from 0.1 to 0.6 %w/w and also increases with increase in mass flow rates of both cold and hot fluids from 0.016 to 0.099 kg/s. The Nusselt number correlation developed using dimensional analysis has predicted the Nusselt number for the given PHE with a RMS deviation of 14.61.
Similar content being viewed by others
Abbreviations
- PHE:
-
Plate heat exchanger
- CMC:
-
Carboxymethyl cellulose
- RTD:
-
Resistance temperature detector
- A p :
-
Effective plate heat transfer area (m2)
- \(c^{*}\) :
-
Capacity ratio \(c^{*}\) < 1, dimensionless
- F T :
-
Log-mean temperature difference correction factor, 0 < FT < 1 dimensionless
- N c :
-
Number of channels
- C p :
-
Specific heat of fluid at constant pressure (J/kg K)
- D h :
-
Hydraulic diameter (m)
- l :
-
Plate length (m)
- d :
-
Port diameter (m)
- Cs :
-
Channel spacing (m)
- h :
-
Convective heat transfer coefficient (W/m2 K)
- K :
-
Fluid thermal conductivity (W/m K)
- m :
-
Mass flow rate (kg/s)
- NTU :
-
Number of transfer units
- N Re :
-
Reynolds number, dimensionless
- N Nu :
-
Nusselt number, dimensionless
- N Pr :
-
Prandtl number, dimensionless
- N Gr :
-
Grashoff number, dimensionless
- Q :
-
Rate of heat transfer (W)
- T :
-
Temperature (K)
- ∆T :
-
Temperature difference (K)
- ∆x :
-
Plate thickness (m)
- U exp :
-
Experimental overall heat transfer coefficient, including correction factor (W/m2 K)
- \(U^{*}\) :
-
Overall heat transfer coefficient (W/m2 K)
- v :
-
Velocity (m2/s)
- w :
-
Width of the plate (m)
- k :
-
Consistency index (Pa sn)
- n :
-
Flow behavior index
- K :
-
Plate thermal conductivity (W/m K)
- y :
-
Dependent variable
- a :
-
Coefficient of x
- x :
-
Independent variable
- b :
-
Constant
- i, j and k :
-
Model parameters, dimensionless
- βg :
-
Thermal expansion with acceleration due to gravity (*m/s2 K)
- ρ :
-
Density of the fluid (kg/m3)
- ∆T lm :
-
Logarithmic mean temperature difference (LMTD) (K)
- ε :
-
Exchanger thermal effectiveness
- h :
-
Hot
- c :
-
Cold
- i :
-
Fluid inlet
- o :
-
Fluid outlet
- ss :
-
Stainless steel
- max :
-
Maximum
References
Focke WW, Zachariades J, Olivier I (1985) The effect of the corrugation inclination angle on the thermo hydraulic performance of PHEs. Int J Heat Mass Transf 28:1469–1497
Shah RK, Focke WW (1988) Plate heat exchangers and their design theory. In: Shah RK, Subbarao EC, Mashelkar RA (eds) Heat transfer equipment design. Hemisphere, Washington, pp 227–254
Cabral RAF, Gut JAW, Telis VRN, Romero TJ (2010) Non-Newtonian flow and pressure drop of pineapple juice in a PHE. Braz J Chem Eng 27(4):563–571
Carr JM (1993) Hydrocolloids and stabilizers. Food Technol 47(10):100
Hegedusi V, Herceg Z, Rimac S (2000) Rheological properties of carboxymethylcellulose and whey model solutions before and after freezing. Food Technol Biotechnol 38(1):19–26
Speers RA, TungM A (1986) Concentration and temperature dependence of flow behavior of xanthan gum dispersions. J Food Sci 51(1):96–98
Reilly IG, Tien C, Adelman M (1965) Experimental study of natural convective heat transfer from a vertical plate in a non-Newtonian fluid. Can J Chem Eng 43(4):157–160
Cooper A (1974) Recover more heat with plate heat exchangers. Chem Eng 285:280–285
Clark DF (1974) Plate heat exchanger design and recent development. Chem Eng 285:275–279
Edwards MF, Changal VaieAA, Parrott DL (1974) Heat transfer and pressure drop characteristics of a plate heat exchanger using Newtonian and non-Newtonian liquids. Chem Eng 285:286–288
Marriott J (1971) Where and how to use plate heat exchangers. Chem Eng 78:127–134
Afonso IM, Maia L, Melo LF (2003) Heat transfer and rheology of stirred yoghurt during cooling in plate heat exchangers. J Food Eng 57:179–187
Afonso IM, Cruz P, Maia JM, Melo LF (2008) Simplified numerical simulation to obtain heat transfer correlations for stirred yoghurt in a plate heat exchanger. J Food Eng 86(4):296–303
Fernandes CS, Dias RP, Noberga JM, Maia JM (2005) Effect of corrugation angle on the hydrodynamic behaviour of power-law fluids during a flow in plate heat exchanger. In: Shah RK, Ishizuka M, Rudy TM, Wadekar VV (eds) Proceedings of the fifth international conference on enhanced, compact and ultra compact heat exchangers: science engineering and technology, Engineering Conferences International, USA
Fernandes CS, Dias RP, Nobrega JM, Afonso IM, Melo LF, Maia JM (2005) Simulation of stirred yoghurt processing in plate heat exchangers. J Food Eng 69:281–290
Fernandes CS, Dias RP, Nobrega JM, Afonso IM, Melo LF, Maia JM (2006) Thermal behaviour of stirred yoghurt during cooling in plat heat exchangers. J Food Eng 76:433–439
Fernandes CS, Dias RP, Nobrega JM, Maia JM (2007) Laminar flow in chevron-type plate heat exchangers: CFD analysis of tortuosity, shape factor and friction factor. Chem Eng Process 46:825–833
Fernandes CS, Dias RP, Nobrega JM (2008) Maia friction factors of power-law fluids in chevron-type plate heat exchangers. J Food Eng 89:441–447
Gut JAW, Pinto JM, Gabas AL, Romer JT (2003) Pasteurization of egg yolk in plate heat exchangers thermo-physical properties and process simulation, Annual meeting, CA 123:16–21
Jokar A, Hosni M, Mohammad H, Eckels SJ (2006) Dimensional analysis on the evaporation and condensation of refrigerant R-134a in minichannel plate heat exchangers. Appl Therm Eng 26(17–18):2287–2300
Carezzato A, Alcantara MR, Romero TJ, Tadini CC, Gut JAW (2007) Non-Newtonian heat transfer on a plate heat exchanger with generalized configurations. Chem Eng Technol 30(1):21–26
Lin JH, Huang CY, Su CC (2007) Dimensional analysis for the heat transfer characteristics in the corrugated channels of plate heat exchangers. Int Commun Heat Mass Transf 34(3):304–312
Warnakulasuriya FSK, Worek WM (2008) Heat transfer and pressure drop properties of high viscous solutions in plate heat exchangers. Int J Heat Mass Transf 51:52–67
Mahdi Y, Mouheb A, Oufer L (2009) A dynamic model for milk fouling in a plate heat exchanger. Appl Math Model 33:648–662
Khan TS, Khan MS, Chyu MC, Ayub ZH (2012) Experimental investigation of single phase convective heat transfer coefficient in a corrugated plate heat exchanger for multiple plate configurations. Appl Therm Eng 30:1058–1065
Pandey SD, Nema VK (2012) Experimental analysis of heat transfer and friction factor of nanofluid as a coolant in a corrugated plate heat exchanger. Exp Thermal Fluid Sci 38:248–256
Ray DR, Das DK, Vajjha RS (2014) Experimental and numerical investigations of nanofluids performance in a compact minichannel plate heat exchanger. Int J Heat Mass Transf 71:732–746
Rohsenow WM, Hartnett JP, Cho YI (1998) Handbook of heat transfer, 3rd edn. McGraw-Hill, New York
Gut JAW, Fernandes R, Pinto JM, Tadinia CC (2004) Thermal model validation of plate heat exchangers with generalized configurations. Chem Eng Sci 59:4591–4600
Vlasogiannis P, Karagiannis G, Argyropoulos P, Bontozoglou V (2002) Air–water two-phase flow and heat transfer in a plate heat exchanger. Int J Multiph Flow 28:757–772
Wanchoo RK, Sharma SK, Bansal R (1996) Rheological parameters of some water-soluble polymers. J Polym Mater 13:49–55
Moradi M, Etemad SG, Moheb A (2006) Laminar flow heat transfer of a pseudoplastic fluid through a double pipe heat exchanger. Iran J Chem Eng 3(2):13–19
Manjula P, Kalaichelvi P, Dheenathayalan K (2009) Development of mixing time correlation for a double jet mixer. J Chem Technol Biotechnol 85(1):115–120
Sopa C, Cumnueng W, Thavachai T, Juntanee U, Jatuphong V (2008) Effects of temperature and concentration on thermal properties of cassava starch solutions. Songklanakarin J Sci Technol 30(3):05–411
Acknowledgments
The authors wish to express their appreciation to Council of Scientific and Industrial Research (CSIR) for the financial support given for carrying out this investigation (Ref. No. 22/514/10-EMR-II).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Muthamizhi, K., Kalaichelvi, P. Development of Nusselt number correlation using dimensional analysis for plate heat exchanger with a carboxymethyl cellulose solution. Heat Mass Transfer 51, 815–823 (2015). https://doi.org/10.1007/s00231-014-1455-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00231-014-1455-5