Thermally Developing Forced Convection of NonNewtonian Fluids Inside Elliptical Ducts
ABSTRACT Laminarforced convection inside tubes of various crosssection shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumptions used in this work are a nonNewtonian fluid, laminar flow, constant physical properties, and negligible axial heat diffusion (high Peclet number). Most of the previous research in elliptical ducts deal mainly with aspects of fully developed laminar flow forced convection, such as velocity profile, maximum velocity, pressure drop, and heat transfer quantities. In this work, we examine heat transfer in a hydrodynamically developed, thermally developing laminar forced convection flow of fluid inside an elliptical tube under a second kind of a boundary condition. To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as SturmLiouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform, where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number, and the average Nusselt number for various crosssection aspect ratios.

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ABSTRACT: The present review covers the heat transfer literature published in 2004 in English language, including some translations of foreign language papers. Though extensive, some selection is necessary. Only articles published by a process of peer review in archival journals are reviewed. Papers are grouped into subjectoriented sections and further divided into subfields. Many papers deal with the fundamental science of heat transfer, including experimental, numerical and analytical work; others relate to applications or natural systems. In addition to reviewing journal articles, this Review also takes note of important conferences and meetings on heat transfer and related areas, major awards presented in 2004, and relevant books published in 2004.07/2010; 53(21222122):43434396. DOI:10.1016/j.ijheatmasstransfer.2010.05.004 
Article: Heat transfer in CouettePoiseuille flow between parallel plates of the Giesekus viscoelastic fluid
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ABSTRACT: In this work, the heat transfer to the CouettePoiseuille flow of a nonlinear viscoelastic fluid obeying the Giesekus model between parallel plates for the case where the lower plate is at rest and the upper one moves at constant velocity is studied. The momentum equation is analytically solved and the effect of dimensionless pressure gradient (G), Giesekus model parameter (α) and Deborah number (De) on the velocity profile is investigated. To analyze the influence of viscous dissipation on the heat transfer, the energy equation is solved by a finite volume method for two different thermal boundary conditions: uniform wall heat flux (Case 1) and constant wall temperature (Case 2). The results show strong effects of the viscoelastic parameters on the velocity and temperature profiles. It is observed that the viscous dissipation is responsible for the variation in the bulk fluid temperature and the effect of viscous heating depends on the values of dimensionless pressure gradient.Journal of NonNewtonian Fluid Mechanics 06/2013; 196. DOI:10.1016/j.jnnfm.2013.01.007 · 1.94 Impact Factor 
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ABSTRACT: A numerical investigation of heat transfer with viscoelastic FENEP fluid in circular and noncircular ducts is carried out to study the effect of the solvent contribution on heat transfer in the absence of viscous dissipation by assuming temperatureindependent model parameters. The numerical simulation is conducted using the finite element software POLYFLOW and results are compared with analytical and semianalytical solutions available in the literature for the 2D axisymmetric pipes. The analysis considers a constant wall heat flux boundary condition and shows that an increase in fluid elasticity raised the normalized heat transfer coefficient due to the increased level of shearthinning behavior. However, increasing the extensibility parameter L2 leads to a decrease in Nusselt number. Local and average Nusselt number values are obtained for the axisymmetric pipe flows for several values of polymer concentration and the study confirms quantitatively that polymer concentration enhances heat transfer rates in FENEP fluids. Nusselt number distribution in the fully developed region of tubes of equilateral triangular, square and rectangular crosssections is reported for the first time for nonlinear viscoelastic fluids of the FENEP type with solvent contribution.Journal of NonNewtonian Fluid Mechanics 05/2014; 207. DOI:10.1016/j.jnnfm.2014.03.003 · 1.94 Impact Factor