tailieunhanh - Developments in Heat Transfer Part 18

Tham khảo tài liệu 'developments in heat transfer part 18', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 670 Developments in Heat Transfer source may be a black-body emitter incandescent lamp light emitting diode or laser to name a few. The rod absorbs the radiation converting it to heat. In order to approximate cases of 1 rod with evenly spaced side heating and varying axial heating rate or boundary condition and 2 end heating with arbitrarily distributed source or boundary conditions it is sufficient to assume an axisymmetrical case with a finite rod. Then the governing equation becomes -T-r-7-ớír K- r0 r z Q r 0 13 r âr âr v âz2 v v a b c Fig. 1. Three cylindrical optical devices a rod held by heatsink mounts on both ends with radially symmetrical side induction heaters b rod held by a heatsink along its length with end induction heater and c end induction heated thin disk dark with a cap Side heating The boundary conditions for a rod may model various cooling configurations including conductive and convective cooling means. A possible configuration is conduction cooling where a heat sink with a mount holds the rod over part of its length. Tills configuration justifies the assumption of either Dirichlet or Neumann boundary conditions or their combination specified around the rod circumference T ri V 1 or 14 The Dirichlet boundary condition is particularly suitable for cases where the boundary is held at a set temperature such as the case of heat sinking to Peltier junction or cryogenic cooling. In terms of the function ớit becomes ớ rỊV ln 1 To 15 Then the Neumann condition is suitable for cases where the boundary provides a certain heat flux across it as specified in Eq. 14. At the rod ends the facets are assumed insulated specified by Neumann condition such that Heat Conduction in Nonlinear Media 671 ae_ Zz o 0 z Z L 2 16 where the origin is at the rod center and z L 2 is half the rod length. Modeling of the heat source assumes a region confined both radially and axially inside the rod Q r z P 0 17 2 2 where 1 is the length of the source region in the rod .

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