raccolta1415

Page 1

Heat Transfer and Thermal Analysis - A.A. 2013/14 - Date 2015/02/11 Surname: Name: ID number: Signature: Part B (sufficient if ≥ 16) Exercise 1 (up to 8 points) A microprocessor has the shape of a thin parallelepiped, with base 30x30 mm and height 3 mm, and its lower base is glued to a plate which can be assumed as adiabatic. Its equivalent thermophysical properties are density ρ = 3500 kg/m 3, heat capacity c = 200 J/kgK, conductivity λ = 50 W/mK, and during average operation its surface temperature is 45 ◦C. 1. When the computer is switched off, the microprocessor is immersed in stagnant air (properties given in the table on the side of sketch of ex. 3) at atmospheric pressure and T∞ = 25◦C. Neglecting radiation and explaining the other assumptions you decide to make, determine the time required for the microprocessor to cool down to 1 K over the air temperature. 2. When the computer is switched on, the microprocessor starts receiving ˙WE of electric power (constant in time), which is dissipated by Joule effect. Write the differential equation to be solved to determine the temperature profile with time T (τ). For both cases, the effect of the sides of the parallelepiped can be neglected. Exercise 2 (up to 11 points) A hollow sphere, whose external diameter is Ds = 100 mm, is made by two layers, having thickness and conductivity s1 = 10 mm, λ1 = 0.5 W/mK, s2 = 20 mm, λ2 = 1 W/mK respectively. In the internal layer 1, a uniform heat source ˙U ′′′ = 106 W/m3 is present. The external surface of the sphere can be assumed as gray with emissivity εs = 0.75. Knowing that the system is in steady-state conditions, that convection outside the sphere is negligible and that the temperature of the interface between the two solid layers is T12 = 875◦C: 1. calculate how much radiative heat…