PREDICTION OF HEAT TRANSFER COEFFICIENT BASED ON EDDY DIFFUSIVITY CONCEPT Q. J. Slaiman 1 , M. M. Abu-Khader 2, and B. O. Hasan 1 1 Department of Chemical Engineering, Nahrain University, Baghdad, Iraq. 2 Department of Chemical Engineering, FET, Al-Balqa Applied University, Amman, Jordan. Abstract: The concept of eddy diffusivity is reviewed, and theoretical comparison study is per- formed to predict heat transfer coefficient using various proposed models for eddy diffusivity at wide range of Prandtl (7– 800) and Reynolds numbers (5000 – 100 000) in pipe flow. The modi- fied Reynolds analogy equation is employed to start the analysis for predicting the heat transfer coefficient. The influence of Re, Pr and the distance from the wall (y þ ) on the eddy diffusivity and consequently on the heat transfer coefficient and temperature profile is studied and discussed. The results are compared with experimental data. A new expression of thermal eddy diffusivity is been developed by comparing modified form of Reynolds analogy correlation with experimen- tal heat transfer data. Using this new expression more accurate results can be obtained. For future research work, It is interesting to include links to other models and to examine the beha- viour of this empirical model in complex flow configurations. Keywords: eddy diffusivity; heat transfer coefficient; pipe flow; turbulence. INTRODUCTION Practically all engineering processes invol- ving fluids depend on the interaction of a fluid with a phase boundary. Fluid friction over extended surfaces, heat and mass trans- fer to fluids in evaporation, distillation and gas absorption are some of the processes invol- ving the transport of momentum, heat and mass from a phase boundary to a fluid in turbulent flow. The understanding of turbulent transport mechanism and the subsequent ability to predict the relevant transport rates are essential to the development of rational design procedures for various processes. Despite many years of intensive research into turbulent diffusion, it is still poorly under- stood and can only be rather crudely predicted in many cases (Robert and Webster, 2001). Because of highly complex turbulent flow mechanism, the prediction of the transport rates necessarily involves the formulation of conceptual models which embody many simplifying assumptions (Gutfinger, 1975). Various models proposed in the literature constitute the framework of present day predictive theory and may be broadly divided into three general classes: (1) models based on film theory, (2) models based on eddy or turbulent diffusivity, and (3) models based on the surface renewal concept (Danckwerts, 1951). The develop- ment of the theory of transfer of heat and mass between a solid surface and a turbulent fluid has been handicapped by the lack of data on the manner in which the eddy diffusiv- ities vary with distance from the surface. Data on eddy diffusivity very close to the surface are particularly important in order to under- stand the mechanism of transfer at high Prandtl and Schmidt numbers. The eddy diffu- sivity for heat may be obtained from tempera- ture profiles and measured heat fluxes. Data very near the wall are difficult to obtain by either of these procedures, since the Pitot tubes and thermocouples employed affect the nature of the flow being studied (Sherwood et al., 1968). Interferometric tech- niques have been used giving values of eddy diffusivity at y þ as low as 0.5–1. The various empirical constants introduced in the formu- lation of the turbulence models must be evalu- ated through comparison with experimental data (Gutfinger, 1975; Gurniki et al., 2000). The eddy diffusivity behavior in the viscous sub-layer, damped turbulence layer, and turbulent core affect greatly the rate of heat (or mass) transport between the wall and bulk. Previous studies (Von Karman, 1939; Lin et al., 1953; Deissler, 1955; Van Driest, 1956; Wasan and Wilke, 1964; Rosen and Tragardh, 1995; Meignen and Berthoud, 455 Vol 85 (A4) 455–464  Correspondence to: Dr M.M. Abu-Khader, Department of Chemical Engineering, FET, Al-Balqa Applied University, Amman- Jordan. E-mail: mak@accessme.com DOI: 10.1205/cherd06002 0263–8762/07/ $30.00 þ 0.00 Chemical Engineering Research and Design Trans IChemE, Part A, April 2007 # 2007 Institution of Chemical Engineers