Convective heat transport in yield stress nanofluids in a differentially heated square enclosure

This article presents an experimental study of magnetohydrodynamic convection in a tall vertical slot under the influence of a horizontal magnetic field. The test fluid is an eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr ≈ 0:02. The experimental setup covers Rayleigh numbers in the range 103 [lsim ] Ra [lsim ] 8×104 and Hartmann numbers 0 < M < 1600. The effect of the magnetic field on the convective heat transport is determined not only by damping as expected from Joule dissipation but also, for magnetic fields not too strong, the convective heat transfer may be considerably enhanced compared to ordinary hydrodynamic (OHD) flow. Estimates of the isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport accompanies the formation of strong local anisotropy of the turbulent eddies in the sense of an alignment of the main direction of vorticity with the magnetic field. The reduced three-dimensional nonlinearities in non-isotropic flow favour the formation of largescale vortex structures compared to OHD flow, which are more effective for convective heat transport. Along with the formation of quasi-two-dimensional vortex structures, temperature fluctuations may be considerably enhanced in a magnetic field that is not too strong. However, above Hartmann numbers M [gsim ] 400 the formerly strongly time-dependent flow suddenly becomes stationary with an extended region of high convective heat transport at stationary flow. Finally, for very high Hartmann numbers the convective motion is strongly suppressed and the heat transport is reduced to a state close to pure heat conduction.

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Numerical Study of Convective Heat Transfer of Multiple Internal Isolated Blocks in an Enclosure

Solar Energy ◽

10.1115/isec2005-76108 ◽

2005 ◽

Author(s):

Xutao Zhang ◽

Jianing Zhao ◽

Fusheng Gao ◽

Jun Gao ◽

Songling Wang

Keyword(s):

Heat Transfer ◽

Mixed Convection ◽

Convective Heat Transfer ◽

Forced Convection ◽

Convective Heat ◽

Numerical Study ◽

Thermal Design ◽

Square Enclosure ◽

Forced Convective Heat Transfer ◽

Low Reynolds

The treatment of Convective Heat Transfer Coefficients (CHTCs) in an enclosure has a significant impact on the thermal design of electronic appliance, especially the CHTCs in an enclosure with internal isolated blocks. The CHTCs of the isolated blocks for pure natural convection are usually used, while it may not be applicable to any practice. Combined convective heat transfer, even forced convective heat transfer, is sometime more applicable in reality. In our present work, first of all, validation of the turbulence model for CFD simulation of natural convective flows in a square enclosure is performed. The values of CHTCs for vertical walls obtained by using a low Reynolds k-ε model agree well with the existed correlations. The simulation also indicates that the distance from the first grid to the wall has a significant impact on the CHTCs. Using this low Reynolds k-ε model, computer simulations of natural and forced convective heat transfer within a square enclosure containing ten isolated blocks are performed. For both the natural and forced convection, the dimensionless Nusselt numbers are derived by the obtained results. For the case of mixed convection, the CHTCs are established by blending those for natural and forced convection using the Churchill-Usagi approach, which is a general expression combines the asymptotic solutions of independent CHTCs into the mixed convection by using a Churchill-Usagi blending coefficient.

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Natural convection of Casson fluid in a square enclosure

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-11-2019-0192 ◽

2020 ◽

Vol 16 (5) ◽

pp. 1245-1259

Author(s):

Mohammad Saeid Aghighi ◽

Christel Metivier ◽

Hamed Masoumi

Keyword(s):

Natural Convection ◽

Yield Stress ◽

Casson Fluid ◽

Small Degree ◽

Content Type ◽

Square Enclosure ◽

Casson Model ◽

Side Walls ◽

The Mean ◽

Viscoplastic Models

PurposeThe purpose of this paper is to analyze the natural convection of a yield stress fluid in a square enclosure with differentially heated side walls. In particular, the Casson model is considered which is a commonly used model.Design/methodology/approachThe coupled conservation equations of mass, momentum and energy related to the two-dimensional steady-state natural convection within square enclosures are solved numerically by using the Galerkin's weighted residual finite element method with quadrilateral, eight nodes elements.FindingsResults highlight a small degree of the shear-thinning in the Casson fluids. It is shown that the yield stress has a stabilizing effect since the convection can stop for yield stress fluids while this is not the case for Newtonian fluids. The heat transfer rate, velocity and Yc obtained with the Casson model have the smallest values compared to other viscoplastic models. Results highlight a weak dependence of Yc with the Rayleigh number: Yc∼Ra0.07. A supercritical bifurcation at the transition between the convective and the conductive regimes is found.Originality/valueThe originality of the present study concerns the comprehensive and detailed solutions of the natural convection of Casson fluids in square enclosures with differentially heated side walls. It is shown that there exists a major difference between the cases of Casson and Bingham models, and hence using the Bingham model for analyzing the viscoplastic behavior of the fluids which follow the Casson model (such as blood) may not be accurate. Finally, a correlation is proposed for the mean Nusselt number Nu¯.

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