HTTA 2015 07 22 Solutions

Pagina 1

Heat T ransfer and Thermal Analysis - A.Y. 2014/15 - Date 2014/07/22 Surname: Name: ID number: Signature: Part A 1. Sketch ( in a qualitatively accurate way ) some curves of the blackbody emissive power as a function of temperature and wavelength. 2. Write the definitions of the Nusselt and Biot dimensionless groups, and comment the difference between the two. 3. Write and comment a commonly used rule to determine the Nu value for mixed convection as a function of the Nu values for forced and natural convections. 4. Write the system of equations describing the “energy analysis” for a parallel flow, duct-in-duct heat exchanger. 5. Write the continuity equation for a compressible fluid. 6. Write the finite difference approximations for the first and second derivatives of temperature with respect to a spatial direction using the basic centered form. 7. Put the following materials/substances in correct descending order of thermal conductivity: water, copper, diamond, iron, air, stainless steel. Heat T ransfer and Thermal Analysis - A.Y. 2014/15 - Date 2014/07/22 - Part B Question 1 (up to 10 points) Starting from the energy conservation principle for a closed system and describing the assumptions you make, derive an equation that describes the temperature evolution as a function of time for a small, convex, highly conductive solid body, subject to a single convective exchange with a surrounding fluid for the two cases: 1. a constant and uniform heat source ˙U ′′′ [W/m3] is present within the body; 2. no heat source is present within the body. Analyze and comment the resulting equations. Exercise 1 (up to 10 points) In a homogeneous and isotropic full sphere, made of copper and having radius Rc = 20 mm, a constant and uniform heat source ˙U ′′′ = 10 6 W/m3 is present. Such sphere…