HTTA 2017 02 06 Solutions

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Heat T ransfer and Thermal Analysis - A.Y. 2015/16 - Date 2017/02/06 Surname: Name: ID number: Signature: Part A 1. Derive the general integrals giving the temperature and heat flux profiles as a function of the radius for a very long, homogeneous cylinder with constant and uniform heat source and constant and uniform solicitation on the external surface. Comment the boundary condition on the axis in the case of a full cylinder. 2. Write the Richardson number and the criterion to distinguish between forced, natural and mixed convection. 3. Write the conduction equation for a system in steady-state conditions, with constant and uniform conductivity, in presence of a uniform heat source, expanding the Laplacian operator in three-dimensional cartesian coordinates. 4. Define the number of transfer units (NTU) and the heat capacity ratio (R) used in the ε-NTU method. 5. State the spectral band in which a surface has its maximum emission if its temperature is T = 6000 K. 6. For the lumped parameter approach to give good results, the Biot number has to be: A) ≪ 1, B) ≈ 1, C) ≫ 1 ? 7. Write the Kirchhoff law for real (non-diffuse) opaque emitters, stating the meaning of the symbols. Heat T ransfer and Thermal Analysis - A.Y. 2015/16 - Date 2017/02/06 - Part B Exercise 1 (up to 15 points) The system sketched in the picture is made by a central slab where a uniform heat source is present, and two passive external slabs. Vacuum was realized between the central slab and the external ones, while air (at atmospheric pressure) is flowing over the outer faces of the external slabs. The radiative heat transfer between the outer faces and the room that contains the whole system is negligible. The quantities for which the values are known are the ones written in the figure in normal font, with…