HTTA 2018 06 18 Solutions

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Heat T ransfer and Thermal Analysis - A.Y. 2017/18 - Date 18/06/2018 Surname: Name: ID number: Signature: (“matricola” or person code) Part A 1. Write the Laplace-Young and the Young equations, stating which quantities are indicated by the used symbols. see Wikipedia 2. For a homogeneous hollow sphere that exchanges uniformly by convection on the external surface, is the heat flux in steady-state conditions decreasing within the sphere as 1 /r? Motivate the answer. No, it varies with 1 r2, see integration of the Poisson equation. 3. Write a finite difference approximation of the Fourier equation for 1D, transient conduction using the implicit approach. ρc T p+1 i −T p i ∆τ = λ ( T p+1 i+1 +T p+1 i−1 − 2T p+1 i ∆x2 ) + ˙U ′′′ 4. Write the radiosity of a diffuse and gray surface as a function of its black-body emissive power and of the total irradiation of the surface. For an opaque diffuse gray surface radiosity = emissivity · blackbody emissive power + reflectivity · irradi- ation. If transparent, transmitted part should also be added. 5. Sketch a multi-layer insulation clothing, indicating in the drawing which heat transfer contribution is reduced by each of the parts. see p. 24/25 of the slides about thermal control 6. Sketch the Nukiyama curve indicating the different phases and the points where the heat flux is maximum and minimum. see Fig. 9.2 p. 462 Lienhard & Lienhard 4th ed. 7. Write the expression of three dimensionless groups involved in steady-state convection, stating which quantities are indicated by the used symbols. see the chapters about free or forced convection on the Lienhard & Lienhard textbook Heat T ransfer and Thermal Analysis - A.Y. 2017/18 - Date 18/06/2018 - Part B INSTRUCTIONS - Read them very carefully! • test duration is 1 h 45’. After 35’ part A…