Benchmark solutions for the natural convective heat transfer problem in a square cavity with large horizontal temperature differences

Vierendeels, Jan; Merci, Bart; Dick, Erik

doi:10.1108/09615530310501957

Cited by 56 publications

(84 citation statements)

References 3 publications

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“…The internal flow was considered to be two dimensional, steady and laminar (Baïri et al 2007;Khezzar et al 2011;Lartigue et al 2000;Davis 1983;Souza et al 2003;Vierendeels et al 2003;Corcione 2003;Lee and Ha 2005). The external flow was also considered to occur in the laminar regime because the Reynolds number along the geometry length is always lower than the critical value of 3.5×10 5 , for all conditions considered in this study (Coulson et al 1999;Lienhard and Lienhard 2003).…”

Section: Modelling Assumptions and Approachmentioning

confidence: 99%

Advanced modelling of the transport phenomena across horizontal clothing microclimates with natural convection

et al. 2015

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The ability of clothing to provide protection against external environments is critical for wearer's safety and thermal comfort. It is a function of several factors, such as external environmental conditions, clothing properties and activity level. These factors determine the characteristics of the different microclimates existing inside the clothing which, ultimately, have a key role in the transport processes occurring across clothing. As an effort to understand the effect of transport phenomena in clothing microclimates on the overall heat transport across clothing structures, a numerical approach was used to study the buoyancy-driven heat transfer across horizontal air layers trapped inside air impermeable clothing. The study included both the internal flow occurring inside the microclimate and the external flow occurring outside the clothing layer, in order to analyze the interdependency of these flows in the way heat is transported to/from the body. Two-dimensional simulations were conducted considering different values of microclimate thickness (8, 25 and 52 mm), external air temperature (10, 20 and 30 °C), external air velocity (0.5, 1 and 3 m s(-1)) and emissivity of the clothing inner surface (0.05 and 0.95), which implied Rayleigh numbers in the microclimate spanning 4 orders of magnitude (9 × 10(2)-3 × 10(5)). The convective heat transfer coefficients obtained along the clothing were found to strongly depend on the transport phenomena in the microclimate, in particular when natural convection is the most important transport mechanism. In such scenario, convective coefficients were found to vary in wavy-like manner, depending on the position of the flow vortices in the microclimate. These observations clearly differ from data in the literature for the case of air flow over flat-heated surfaces with constant temperature (which shows monotonic variations of the convective heat transfer coefficients, along the length of the surface). The flow patterns and temperature fields in the microclimates were found to strongly depend on the characteristics of the external boundary layer forming along the clothing and on the distribution of temperature in the clothing. The local heat transfer rates obtained in the microclimate are in marked contrast with those found in the literature for enclosures with constant-temperature active walls. These results stress the importance of coupling the calculation of the internal and the external flows and of the heat transfer convective and radiative components, when analyzing the way heat is transported to/from the body.

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Section: Modelling Assumptions and Approachmentioning

confidence: 99%

Advanced modelling of the transport phenomena across horizontal clothing microclimates with natural convection

et al. 2015

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“…A uniform mesh of 80×80 B27 elements is used to discretize the domain, and the steady-state solution is found directly using Equation (5) in five 'loadsteps' with about six iterations per loadstep. The vertical velocity and temperature variations (normalized as v y /0.05021228 and ( −600)/600, respectively) along the line y = 0.5 are shown in Figure 10, and should be compared with the benchmark solutions in Reference [21] (p. 1067). One can see that the agreement is very good inspite of using a uniform and coarse mesh.…”

Section: Two-dimensional Natural Convectionmentioning

confidence: 99%

A finite element method for compressible viscous fluid flows

Jog

2011

Numerical Methods in Fluids

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SUMMARYThis work presents a mixed three-dimensional finite element formulation for analyzing compressible viscous flows. The formulation is based on the primitive variables velocity, density, temperature and pressure. The goal of this work is to present a 'stable' numerical formulation, and, thus, the interpolation functions for the field variables are chosen so as to satisfy the inf-sup conditions. An exact tangent stiffness matrix is derived for the formulation, which ensures a quadratic rate of convergence. The good performance of the proposed strategy is shown in a number of steady-state and transient problems where compressibility effects are important such as high Mach number flows, natural convection, Riemann problems, etc., and also on problems where the fluid can be treated as almost incompressible.

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“…Additionally heat and fluid flow in a square cavity are a standard test case for code validation. This is well-known in the field of applied mathematics and numerical methods [2,3].…”

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confidence: 94%

Modelling of the mixed convection in a lid-driven cavity with a constant heat flux boundary condition

Błasiak

Kolasiński

2015

Heat Mass Transfer

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Benchmark solutions for the natural convective heat transfer problem in a square cavity with large horizontal temperature differences

Cited by 56 publications

References 3 publications

Advanced modelling of the transport phenomena across horizontal clothing microclimates with natural convection

Advanced modelling of the transport phenomena across horizontal clothing microclimates with natural convection

A finite element method for compressible viscous fluid flows

Modelling of the mixed convection in a lid-driven cavity with a constant heat flux boundary condition

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