Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section

Maia, Cássio Roberto Macedo; Aparecido, J. B.; Milanez, Luiz Fernando

doi:10.1016/j.ijthermalsci.2006.02.001

Cited by 32 publications

(21 citation statements)

References 7 publications

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“…Their results demonstrated that the heat transfer coefficient can be improved dramatically when reducing aspect ratio and increasing nanoparticle concentration. The same method had been adopted by Maia et al [28] to obtain the temperature distribution and the convective heat transfer coefficient of non-Newtonian fluids at the entrance region in elliptical ducts. They found that the aspect ratio of the elliptical section has a marked influence on the heat transfer parameters and the peak value of Nusselt number arises as the aspect ratio is near 0.3, which agrees well with the results in Shah and London [21].…”

Section: Introductionmentioning

confidence: 99%

Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature

Duan

et al. 2019

Micromachines

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Laminar convective heat transfer of elliptical minichannels is investigated for hydrodynamically fully developed but thermal developing flow with no-slip condition. A three-dimensional numerical model is developed in different elliptical geometries with the aspect ratio varying from 0.2 to 1. The effect of Reynolds number (25 ≤ Re ≤ 2000) on the local Nusselt number is examined in detail. The results indicate that the local Nusselt number is a decreasing function of Reynolds number and it is sensitive to Reynolds number especially for Re less than 250. The effect of aspect ratio on local Nusselt number is small when compared with the effect of Reynolds number on local Nusselt number. The local Nusselt number is independent of cross-section geometry at the inlet. The maximum effect of aspect ratio on local Nusselt number arises at the transition section rather than the fully developed region. However, the non-dimensional thermal entrance length is a monotonic decreasing concave function of aspect ratio but a weak function of Reynolds number. Correlations for the local Nusselt number and the thermal developing length for elliptical channels are developed with good accuracy, which may provide guidance for design and optimization of elliptical minichannel heat sinks.

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Section: Introductionmentioning

confidence: 99%

Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature

Duan

et al. 2019

Micromachines

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“…Forced heat convection of non-Newtonian fluids in ducts has been increasingly investigated. Some authors [1][2][3][4][5][6][7][8][9] have studied heat transfer of fluids through ducts by neglecting the viscous dissipation effect. One of the earliest studies of viscoelastic fluid flow obeying the Phan-Thien-Tanner (PTT) model was conducted by Oliveira and Pinho [10].…”

Section: Introductionmentioning

confidence: 99%

Analysis of forced convection of Phan–Thien–Tanner fluid in slits and tubes of constant wall temperature with viscous dissipation

Daghighi

Norouzi

2019

J Braz. Soc. Mech. Sci. Eng.

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In the present work, analytical solutions are presented for thermal convection of the linear Phan-Thien-Tanner fluid (LPTT) in slits and tubes of constant wall temperature by taking account of the viscous dissipation term. Unlike the similar previous studies in which the advection term was neglected in the heat transfer equation, it is considered in this investigation. A continuous relation between the Nusselt number and the Brinkman number is obtained. Expressions for the temperature distribution are derived in closed form and in terms of a Frobenius series for the slit and tube flows, respectively. Based on these solutions, the effects of fluid elasticity and Brinkman number on thermal convection of LPTT fluid flows are studied in detail. It is shown that at negative Brinkman numbers (fluid cooling), increasing the Deborah number leads to a decrease in the Nusselt number, but an increase in the centerline temperature. Nonetheless, this trend is opposite for positive Brinkman numbers (fluid heating), i.e., an increase in the Nusselt number and a decrease in the centerline temperature. Also, there is a Brinkman number beyond which the Nusselt number is smaller than zero, meaning that there is weak heat convection in the flow. Also, the results confirm that the extensibility parameter affects the temperature profile in the same way as the Deborah number. Keywords Viscoelastic fluid • Phan-Thien-Tanner model • Forced convection • Constant wall temperature tube and slit • Viscous dissipation List of symbols A Area of cross section, m 2 Br Brinkman number, Br = U 2 ∕k(T w −T m) c p Specific heat, J kg −1 K −1 d h Hydraulic diameter, d h = 2R for tube flow and d h = 4H for slit flow, m Deformation rate tensor, Eq. (8) De Deborah number, defined as De = U∕R for tube case and De = U∕H for slit case F Dimensionless function h Heat transfer coefficient, W m −2 K −1 H Half of the distance between two parallel plates, m J Equals 0 for slit and 1 for tube k Conductivity coefficient, W m −1 K −1 K Equals 1.5 and 2 for slit and tube, respectively Nu Nusselt number, Nu = hd h ∕k p Pressure, Pa P Perimeter of cross section, m R Tube radius, m T Fluid temperature, K u Axial velocity, ms −1 U Mean velocity, ms −1 Velocity vector y Radial (tube) or transverse (slit) direction, m z Axial direction, m Greek symbols Equals 1 for pure entropy elasticity and 0 for pure energy elasticity 1 1 =1.5U N ∕U for slit and 1 =2 U N ∕U for tube Constant, Eq. (12) Extensibility coefficient Constant viscosity coefficient, Pa s Relaxation time, s Density, Kg m −3 ∇ Upper-convected derivative of stress tensor, Eq. (9) Viscous dissipation, Eq. (15)

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“…Abdel-Wahed and Attia [25] evaluated hydrodynamic and thermal characteristics of fully developed laminar flow in an arbitrarily shaped triangular duct using a finite difference technique. Maia et al [26] solved the heat transfer problem in thermally developing laminar flow of a non-Newtonian fluid in elliptical ducts by using the generalized integral transform technique. They transformed the axes algebraically from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the wall in the elliptical duct.…”

Section: Introductionmentioning

confidence: 99%

Convective Heat Transfer in Microchannels of Noncircular Cross Sections: An Analytical Approach

Shahsavari

Tamayol

Kjeang

et al. 2012

Journal of Heat Transfer

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Analytical solutions are presented for velocity and temperature distributions of laminar fully developed flow of Newtonian, constant property fluids in micro/minichannels of hyperelliptical and regular polygonal cross sections. The considered geometries cover several common shapes such as ellipse, rectangle, rectangle with round corners, rhombus, star-shape, and all regular polygons. The analysis is carried out under the conditions of constant axial wall heat flux with uniform peripheral heat flux at a given cross section. A linear least squares point matching technique is used to minimize the residual between the actual and the predicted values on the boundary of the channel. Hydrodynamic and thermal characteristics of the flow are derived; these include pressure drop and local and average Nusselt numbers. The proposed results are successfully verified with existing analytical and numerical solutions from the literature for a variety of cross sections. The present study provides analytical-based compact solutions for velocity and temperature fields that are essential for basic designs, parametric studies, and optimization analyses required for many thermofluidic applications.

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Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section

Cited by 32 publications

References 7 publications

Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature

Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature

Analysis of forced convection of Phan–Thien–Tanner fluid in slits and tubes of constant wall temperature with viscous dissipation

Convective Heat Transfer in Microchannels of Noncircular Cross Sections: An Analytical Approach

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