A Simple, Effective Viscosity Formulation for Turbulent Flow and Heat Transfer in Compact Heat Exchangers

A simple algebraic methodology for computing turbulent stresses and fluxes in arrays of heat exchanger elements is proposed. An effective Reynolds number is computed from the back-projection of the friction or heat transfer factor onto the low-Reynolds-number profile. This is then used to obtain the turbulent viscosity for fluid friction, or turbulent Prandtl number, for heat transfer. It is shown that under certain circumstances, the resulting mathematical expression is consistent with the Brinkman–Forchheimer modified form of Darcy's law and also with the Reynolds quadratic form for frictional/heat transfer resistance. The model is critically appraised in comparison to empirical data for compact and tube bank heat exchangers. The circumstances where it renders a good predictive measure are highlighted and discussed critically.

[1]  P. J. Coelho.  Mathematical modeling of the convection chamber of a utility boiler -- The theory , 1999 .

[2]  C. L. Tien,et al.  Boundary and inertia effects on flow and heat transfer in porous media , 1981 .

[3]  Osborne Reynolds,et al.  On the extent and action of the heating surface of steam boilers , 1961 .

[4]  M. J. Andrews,et al.  Three dimensional numerical simulation of shell-and-tube heat exchangers. Part I: Foundation and fluid mechanics , 1998 .

[5]  P. Coelho.  MATHEMATICAL MODELING OF THE CONVECTION CHAMBER OF A UTILITY BOILER AN APPLICATION , 1999 .

[6]  D. H. Schwarz,et al.  Calculations of transport phenomena and reaction distribution in a polymer electrolyte membrane fuel cell , 2009 .

[7]  R. K. Shah,et al.  Offset Rectangular Plate-Fin Surfaces—Heat Transfer and Flow Friction Characteristics , 1968 .

[8]  Adrian E. Scheidegger,et al.  The physics of flow through porous media , 1957 .

[9]  Antonio C. M. Sousa,et al.  Flow field predictions in a model heat exchanger , 1988 .

[10]  W. R. Gardner.  Physics of Flow through Porous Media , 1961 .

[11]  Steven Beale,et al.  Fluid flow and heat transfer in tube banks. , 1992 .

[12]  S. Beale.  Use of Streamwise Periodic Boundary Conditions for Problems in Heat and Mass Transfer , 2007 .

[13]  Steven Beale,et al.  A Distributed Resistance Analogy for Solid Oxide Fuel Cells , 2005 .

[14]  Naim Afgan,et al.  Heat exchangers: design and theory sourcebook , 1974 .

[15]  V. Gnielinski,et al.  Equations for calculating heat transfer in single tube rows and banks of tubes in transverse flow , 1979 .

[16]  R. Ulinskas,et al.  Heat transfer in tube banks in crossflow , 1988 .

[17]  D. B. Spalding,et al.  NUMERICAL STUDY OF FLUID FLOW AND HEAT TRANSFER IN TUBE BANKS WITH STREAM-WISE PERIODIC BOUNDARY CONDITIONS , 1998 .

[18]  D. Butterworth.  The development of a model for three-dimensional flow in tube bundles , 1978 .

[19]  M. J. Andrews,et al.  THREE-DIMENSIONAL NUMERICAL SIMULATION OF SHELL-AND-TUBE HEAT EXCHANGERS. PART II: HEAT TRANSFER , 1998 .

[20]  Joel Koplik,et al.  Nonlinear flow in porous media , 1998 .

[21]  R. Shah,et al.  Compact Heat Exchangers , 1990 .

[22]  R. de Boer,et al.  Theory of Porous Media , 2020, Encyclopedia of Continuum Mechanics.

[23]  Kuppan Thulukkanam.  Heat Exchanger Design Handbook , 2013 .

[24]  Norberto Fueyo,et al.  Modelling and simulation of fluid flow and heat transfer in the convective zone of a power-generation boiler , 2008 .