Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 36Citation - Scopus: 39The Natural Emergence of Asymmetric Tree-Shaped Pathways for Cooling of a Non-Uniformly Heated Domain(American Institute of Physics, 2015) Çetkin, Erdal; Oliani, AlessandroHere, we show that the peak temperature on a non-uniformly heated domain can be decreased by embedding a high-conductivity insert in it. The trunk of the high-conductivity insert is in contact with a heat sink. The heat is generated non-uniformly throughout the domain or concentrated in a square spot of length scale 0.1 L0, where L0 is the length scale of the non-uniformly heated domain. Peak and average temperatures are affected by the volume fraction of the high-conductivity material and by the shape of the high-conductivity pathways. This paper uncovers how varying the shape of the symmetric and asymmetric high-conductivity trees affects the overall thermal conductance of the heat generating domain. The tree-shaped high-conductivity inserts tend to grow toward where the heat generation is concentrated in order to minimize the peak temperature, i.e., in order to minimize the resistances to the heat flow. This behaviour of high-conductivity trees is alike with the root growth of the plants and trees. They also tend to grow towards sunlight, and their roots tend to grow towards water and nutrients. This paper uncovers the similarity between biological trees and high-conductivity trees, which is that trees should grow asymmetrically when the boundary conditions are non-uniform. We show here even though all the trees have the same objectives (minimum flow resistance), their shape should not be the same because of the variation in boundary conditions. To sum up, this paper shows that there is a high-conductivity tree design corresponding to minimum peak temperature with fixed constraints and conditions. This result is in accord with the constructal law which states that there should be an optimal design for a given set of conditions and constraints, and this design should be morphed in order to ensure minimum flow resistances as conditions and constraints change.Article Citation - WoS: 33Citation - Scopus: 35Experimental and Numerical Investigation of Constructal Vascular Channels for Self-Cooling: Parallel Channels, Tree-Shaped and Hybrid Designs(Elsevier Ltd., 2016) Yenigün, Onur; Çetkin, ErdalIn this paper, we show experimentally and numerically how a plate which is subjected to a constant heat load can be kept under an allowable temperature limit. Vascular channels in which coolant fluid flows have been embedded in the plate. Three types of vascular channel designs were compared: parallel channels, tree-shaped and their hybrid. The effects of channel design on the thermal performance for different volume fractions (the fluid volume over the solid volume) are documented. In addition, the effects of the number of channels on cooling performance have been documented. Changing the design from parallel channels to tree-shaped designs decreases the order of pressure drop. Hence increase in the order of the convective heat transfer coefficient is achieved. However, tree-shaped designs do not bathe the entire domain, which increases the conductive resistances. Therefore, additional channels were inserted at the uncooled regions in the tree-shaped design (hybrid design). The best features of both parallel channels and tree-shaped designs are combined in the hybrid of them: the flow resistances to the fluid and heat flow become almost as low as the tree-shaped and parallel channels designs, respectively. The effect of design on the maximum temperature shows that there should be an optimum design for a distinct set of boundary conditions, and this design should be varied as the boundary conditions change. This result is in accord with the constructal law, i.e. the shape should be varied in order to minimize resistances to the flows.Article Citation - WoS: 1Citation - Scopus: 1Revised Distributional Forms of the Laplacian and Poisson's Equation, Their Implications, and All Related Generalizations(Taylor and Francis Ltd., 2015) Kuştepeli, AlpThe theory of distributions of L. Schwartz is a very useful and convenient way for the analysis of physical problems since physical distributions, especially charge distributions yielding the discontinuity of the potential and boundary conditions, can be correctly described in terms of mathematical distributions. To obtain the charge distributions, the distributional form of the Laplacian is applied to the Poisson's equation; therefore, for the correct representations and interpretations, the distributional forms and their proper applications are very important. In this article, it is shown that the distributional form of the Laplacian has been presented by Schwartz and also others with a missing term, leading to confusing and wrong results mathematically, and as a result electromagnetically; and the revised, correct, and complete distributional representations of the Laplace operator, the Poisson equation, and double layers, defined as the dipole layer and equidensity layer, are obtained and presented with detailed discussions and explanations including boundary conditions. By using the revised form of the Laplacian, Green's theorem is obtained explicitly with special emphases about important points and differences with previous works. The generalized forms of the Laplacian, Poisson's equation, charge densities, boundary conditions, and Greens theorem are also presented when there is a multi-layer on the surface of discontinuity.Letter Citation - WoS: 2Citation - Scopus: 3A Comment on Change of Nusselt Number Sign in a Channel Flow Filled by a Fluid-Saturated Porous Medium With Constant Heat Flux Boundary Conditions(Springer Verlag, 2013) Uçar, Eren; Mobedi, Moghtada; Özerdem, Barış; Pop, IoanThe aim of this Letter is to show that, the Nusselt number sign might be changed without changing of heat transfer direction at the wall of channels, even for flows without viscous dissipation. The sign of the Nusselt number is important for deciding on heat transfer direction at a solid wall. The change of the Nusselt number signmay be interpreted as the change of the direction of the heat transfer at a wall. There are studies, such as internal heat and fluid flow in a channel with viscous dissipation (Hung and Tso 2008, 2009; Mitrovic and Maletic 2007; Mobedi et al. 2010) or with an asymmetric heat flux boundary conditions (Cekmer et al. 2011) in which the sign of the wall Nusselt number changes. Nield and Kuznetsov (2008) studied in a very interesting paper the counter flow in a channel whose boundaries are asymmetrically heated and is consisted of two porous layers with different permeability values. These authors showed that even the sign of an overall Nusselt number defined based on the average wall temperatures and heat fluxes, and the mean permeability values of the two porous layers can also be changed and it can take negative values when a strong asymmetry heat flux is imposed to the boundaries. The change of Nusselt number sign at the walls are also observed in other studies of Kuznetsov (Kuznetsov and Nield 2010; Xiong and Kuznetsov 2000).