Conjugate natural convection boundary layers

Khatamifar, Mehdi (2018) Conjugate natural convection boundary layers. PhD thesis, James Cook University.

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In this study, the unsteady behavior of conjugate natural convection ow and heat transfer in a differentially-heated square cavity divided by a partition with finite thickness and thermal conductivity is studied using direct numerical simulation. A series of numerical simulation is carried out for three values of dimensionless partition thickness (i.e., Tₚ = 0:05; 0:1; and 0:2), two values of dimensionless partition position (i.e., Xₚ = 0:25 and 0:5), five values of the thermal conductivity ratio (i.e., kᵣ = 0:1; 1; 100; 500 and 1000) and six values of the Rayleigh value (i.e., Ra = 10³; 10⁴; 10⁵; 10⁶; 10⁷ and 10⁸). For all these cases, the aspect ratio of the cavity A = H=L = 1, and the Prandtl number Pr = 0:71 were used.

A computer code written in Visual C# programming language is developed in this study for all numerical simulations. The code operates by solving the conservation equations for heat, mass and momentum with the finite volume method. The main variables used throughout the code are velocities and pressure, and the SIMPLE algorithm is employed to solve the velocity and pressure fields. Each equation can be solved by TDMA (as a default algorithm) or other methods. The developed code can solve steady/unsteady, compressible/incompressible, and turbulent/laminar flows in a Cartesian coordinate system. The nomenclature of the TEACH code (originated at the Imperial Collage) is mainly used in this code to increase readability. To further improve the readability of this code, the code structure has been designed to have separate and independent sections. Another code has been written in Visual C# to do the post-processing of data using already produced binary files by the main code. The code is verified and validated against the published results of partitioned (data from two studies) and non-partitioned (data from 14 studies) cavities.

Empirical correlations are developed for the average Nusselt number by the iterative non-linear curve fitting (i.e., the Levenberg-Marquardt algorithm) which include the effects of Ra, Tₚ and Xₚ . It is found that the effect of Xₚ is negligible. For high kᵣ cases, the number of isotherms in the partition is very low or is not present. The low temperature difference in the partition leads to a negligible heat flux through the partition. In this situation, the partition can be considered as an isothermal wall and the heat transfer characteristics are similar to those of non-partitioned cavity cases, and consequently, the scaling relations for isothermals of a non-partitioned cavity can be used. However, higher temperature gradients are present in the partition in the low kᵣ cases, compared to that in the high kᵣ cases. Therefore, the temperature difference between the left and right sides of the partition is dependent on both kᵣ and Tₚ. In this situation, the thermal behavior of the partition shifts from an isothermal wall like to isoflux wall type. This type of partition has uniform heat flux, and the thermal resistance parameter role becomes important and the scaling relations extracted for isoflux wall in a non-partitioned cavity are more appropriate.

The overall behaviour of Nu(Ave) as kᵣ varies is identified to have three distinctive regions; thermal resistance, thermal transient and isothermal regions. The effect of Tₚ on Nu(Ave) is trivial for low Ra values. Tₚ and kᵣ have opposite effects on the thermal resistance parameter of the partition. Therefore, there is a point where kᵣ nullifies the effect of Tₚ and the increased thermal conductivity of the partition overcomes the thermal damping effect of the partition thickness. This situation happened around kᵣ = 100 for both the centrally positioned and off-centre partitioned cavities.

The transient Nu(Ave) at the hot sidewall (or cold sidewall) of a centrally partitioned cavity characterized by four regimes; conduction, quasi-steady, decaying and steady-state regimes. For cavities with off-centre partitions (in this study partition is close to the hot sidewall) this classification is different. The cold sidewall was characterized by the same four regimes presented for a centrally partitioned cavity. However, for the hot sidewall, a regime identified after decaying region and is called filling regime. Consequently, the five distinct regimes of Nu(Ave) at the hot wall of an off-centre partitioned cavity are conduction, quasi-steady, decaying, filling and steady-state.

Item ID: 54302
Item Type: Thesis (PhD)
Keywords: conjugate natural convection, differentially-heated cavity, heat transfer, partition, numerical simulation
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Publications arising from this thesis are available from the Related URLs field. The publications are:

Khatamifar, Mehdi, Lin, Wenxian, Armfield, S.W., Holmes, David, and Kirkpatrick, M.P. (2017) Conjugate natural convection heat transfer in a partitioned differentially-heated square cavity. International Communications in Heat and Mass Transfer, 81. pp. 92-103.

Date Deposited: 25 Jun 2018 00:18
FoR Codes: 09 ENGINEERING > 0915 Interdisciplinary Engineering > 091505 Heat and Mass Transfer Operations @ 50%
09 ENGINEERING > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics @ 30%
09 ENGINEERING > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics @ 20%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970109 Expanding Knowledge in Engineering @ 100%
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