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Convection and Conduction Heat Transfer Part 8

Tham khảo tài liệu 'convection and conduction heat transfer part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 200 Convection and Conduction Heat Transfer After the temperature field is solved the effective thermal conductivity Ầeff can be determined lỊ qdA Aeff TjdA- 4 where q is the steady heat flux through the cross-section area dA between the temperature difference AT on a distance L. Heat flow through the unit area of the surface with normal n is linked with the temperature gradient in the n-direction by Fourier s law as Q 5 2.2 Composite structure The elementary cell of the considered composite is a cross-sectional square and it is perpendicular to fibres direction. Perfect contact between the matrix and the cell is assumed heat transfer does not depend on time and only conductive transfer is considered. Also none of materials properties depends on temperature so the problem is linear and can be described by Laplace equation in each domain. Fig. 1. Composite elementary cell structure Governing equation of the problem both in the matrix domain and in each fibre domain takes the following form 72T 0. 6 Boundary condition applied to the cell are defined as follows 3Tm _ 0 ỠX for x 0 and x 1 7 Optimization of the Effective Thermal Conductivity of a Composite 201 TC 290K for y 0 8 Th 300K for y 1 9 Tm Tf for dF 10 m 7 f F for dF. 11 ớn ớn Symbols used at the Fig 1. denote as follows TC- cooling temperature at the top of the cell Th- heating temperature at the bottom of the cell Ấ - thermal conductivity indices M and F refer to the matrix and fibres. Hence one can see that the composite is heated from the bottom and cooled from the above. Symmetry condition is applied on the sides of the cell which means that the heat flux on these boundaries equals zero. Thermal continuity and heat flux continuity conditions are applied on the boundary of each fibre. 2.3 Relation between geometry and conductivity As we have already mentioned the geometrical structure of the composite material may have a great impact on the resultant effective conductivity of the composite. Commonly .