Laminar viscous dissipation in rectangular ducts

Turkish Journal of Engineering and Environmental Sciences, 2002

Numerical solutions for laminar heat transfer of a non-Newtonian fluid in the thermal entrance region for triangular, square, sinusoidal, etc. ducts are presented for constant wall temperature. The continuity equation and parabolic forms of the energy and momentum equations in Cartesian coordinates are transformed by the elliptic grid generation technique into new non-orthogonal coordinates with the boundary of the duct coinciding with the coordinate surface. The effects of axial heat conduction, viscous dissipation and thermal energy sources within the fluid are neglected. The transformed equations are solved by the finite difference technique. As an application of the method, flow and heat transfer results are presented for ducts with triangular, square, sinusoidal and four-cusped cross sections and square cross sections with four indented corners. The results are compared with the results of previous works.

2019

Today, the study of flow and heat transfer in non-circular ducts are of increasing importance in various industries and applications such as microfluidics, where lithographic methods typically produce channels of square or triangular cross-section. Also, heat transfer in non-circular ducts is important in designing the compact heat exchangers to enhance the heat transfer. In the current study, an EXACT analytical solution for the convective heat transfer in conduits with equilateral triangle cross-section is presented for the first time. The effect of viscous dissipation on heat transfer and temperature distribution through the duct is investigated in detail. This effect is of great importance especially in flow of high viscous fluids in micro-channels. In order to study the effect of viscous dissipation in both cooling and heating cases, the Brinkman number is employed. The exact solution is found by calculating the particular solution which satisfies the thermal boundary conditions. Based on the finite expansion method, an exact analytical solution for temperature distribution and a correlation for dimensionless Nusselt number is obtained as functions of the Brinkman number. The maximum temperature and Nusselt number at the centroid of the conduit for the specific case of Brinkman number equal to zero is calculated equal to 5/9 and 28/9, respectively. The proposed method of solution could be used to find the exact solution for similar problems such as analysis the heat convection in non-circular geometries.

MATEC Web of Conferences

In this work, an analysis of laminar forced convection in a pipe with heated and adiabatic walls for a Newtonian fluid with constant properties is performed by taking the viscous dissipation into account when the axial heat conduction in the fluid is neglected. The Nusselt number versus the Brinkmann, which is based on the total wall heat flux density, have been investigated. In order to determine the temperature field, an analytical solution describing the velocity field in the pipe was used, while the energy equation was determined by the boundary element method (BEM). The results of the calculations of Nusselt numbers as a function of the Brinkman number for different thermal insulation heights to the diameter of the circular duct were presented in the form of diagrams.

International Journal of Heat and Fluid Flow, 1996

Heat transfer to non-newtonian fluids flowing laminarly through rectangular ducts is examined. The conservation equations of mass, momentum, and energy are solved numerically with the aid of a finite volume technique. The viscoelastic behavior of the fluid is represented by the Criminale-Ericksen-Filbey (CEF) constitutive equation. Secondary flows occur due to the elastic behavior of the fluid, and, consequently, heat transfer is strongly enhanced. It is observed that shear thinning yields negligible heat transfer enhancement effect, when compared with the secondary flow effect. Maximum heat transfer is shown to occur for some combinations of parameters. Thus, there are optimal combinations of aspect ratio and Reynolds numbers, which depend on the fluid's mechanical behavior. This result can be usefully explored in thermal designs of certain industrial processes. © 1996 by Elsevier Science Inc.

International Journal of Heat and Mass Transfer, 1997

Abstraet-F~ally developed, constant property, laminar flows of viscous power-law fluids in double-sine shaped ducts are considered. The double-sine cross section represents a limiting inter-plate channel geometry in plate heat exchangers with sinusoidally corrugated plates. The non-Newtonian fluid rheology is described by the power-law or Ostwald-de Waele model, and shear thinning (n < 1) as well as shear thickening (n > 1) flows are considered. Both fluid flow and convective heat transfer problems under (T) and (HI) thermal boundary conditions are analyzed. Analytical solutions based on the Galerkin integral method are presented for a wide range of flow behavior index (0.15 ~< n ~< 2.5) and duct aspect ratio (0.25 ~< 7 ~< .4.0). The effects of fluid rheology (pseudoplasticity or dilatancy), duct geometry, and thermal boundary conditions on the velocity and temperature field, are delineated. Also, isothermal friction factor and Nusselt number results for various conditions are presented, and strategies for predictingfRe and Nu are evaluated.

Energy, 1996

Entropy generation for a laminar viscous flow in a duct subjected to constant heat flux has been investigated. The temperature dependence of the viscosity is taken into consideration. The ratio of pumping power to total heat flux decreases considerably and entropy generation increases along the duct length for viscous fluids. Therefore, it may be shown that an optimum duct length may be obtained which minimizes total energy losses due to both entropy generation and pumping power. For low heat-flux conditions, entropy generation due to viscous friction becomes dominant and the dependence of viscosity on temperature must be considered in order to determine entropy generation accurately.

The Chemical Engineering Journal, 1989

International Journal of Heat and Mass Transfer, 1992

Laminar heat transfer in the entrance region of a circular duct and parallel plates is presented. The velocity profile is fully developed and the iemperature is assumed to be uniform at upstream infinity. The finite difference equation for the energy equation, amounting for axial conduction, was solved by AD1 and QUICK methods and the results extrapolated to zero mesh size with extended Richardson extrapolation. The local Nusselt number, incremental heat transfer number and thermal entrance length are presented for Pe between 1 and 1000; and for constant wall temperature and constant wall heat Aux boundary conditions. Accurate engineering correlations for the P&et number effect on these quantities were also obtained.

Energy Conversion and Management, 2009

A numerical investigation was conducted on the transient behavior of a hydrodynamically, fully developed, laminar flow of power-law fluids in the thermally developing entrance region of circular ducts taking into account the effect of viscous dissipation but neglecting the effect of axial conduction. In this regard, the unsteady state thermal energy equation was solved by using a finite difference method, whereas the steady state thermal energy equation without wall heat flux was solved analytically as the initial condition of the former. The effects of the power-law index and wall heat flux on the local Nusselt number and thermal entrance length were investigated. Moreover, the local Nusselt number of steady state conditions was correlated in terms of the power-law index and wall heat flux and compared with literature data, which were obtained by an analytic solution for Newtonian fluids. Furthermore, a relationship was proposed for the thermal entrance length.

An Overview of Heat Transfer Phenomena, 2012