HTTA 2017 07 05 Solutions

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Heat T ransfer and Thermal Analysis - A.Y. 2016/17 - Date 05/07/2017 Surname: Name: ID number: Signature: (“matricola” or person code) Part A 1. Derive the general integrals giving the temperature and heat flux profiles as a function of the radius for a hollow sphere with constant and uniform heat source and constant and uniform solicitation on the external surface. 2. Write the definitions and the physical meaning of three principal (not product of other groups) dimensionless groups related to steady-state convection. 3. Sketch (in a qualitatively accurate way) some curves of the blackbody emissive power as a function of temperature and wavelength. 4. Sketch the Nukiyama curve for pool boiling, stating the different phases. 5. Define (it is enough by words) the radiosity and the irradiation. 6. Write the finite difference approximations for the first and second derivatives of temperature with respect to a space direction using the basic centered form. 7. Write the Fourier hypothesis, stating of which quantities the conductivity may be a function. Heat T ransfer and Thermal Analysis - A.Y. 2016/17 - Date 05/07/2017 - Part B Exercise 1 (up to 15 points) A system is made by two very long co-axial cylinders, an internal one that is full (having diameter D1 = 10 mm) and an external one that is hollow (having diameter D2i = 50 mm and thickness s2 = 20 mm). In the interspace between the two cylinders dry air is flowing at atmospheric pressure and wa = 3 m/s; the convective coefficients are h1 = 40 W/m2K with the internal cylinder and h2i = 100 W/m 2K with the external one. The surface of the internal cylinder has emissivity ε1 = 0.75, while its temperature T1 can be determined by knowing that it has the peak of maximum radiative emission at 6.125 µm. The temperature of the internal…