HTTA 2018 01 16 Solutions

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Heat T ransfer and Thermal Analysis - A.Y. 2016/17 - Date 16/01/2018 Surname: Name: ID number: Signature: (“matricola” or person code) Part A 1. Write the Laplace-Young equation for a cylinder, stating which quantities are indicated by the used symbols. 2. Put the following substances in correct ascending order of heat capacity: water, air, copper. 3. Draw the temperature profiles T (x) for the two fluids and write the expression of the logarithmic mean tem- perature difference (evidencing the involved temperatures in the drawing) for a counter-current parallel-flow double-pipe heat exchanger if no fluid is undergoing a phase change and the heat capacity of the hot fluid is the largest one. 4. Write the general equation for conduction in a medium having conductivity which varies with temperature. 5. Derive the general integrals (before application of any b.c.) giving the temperature and heat flux profiles as a function of the radius for a homogeneous sphere with heat source. 6. Write the definitions of the void fraction for a two-phase flow in local, section-averaged and volume-averaged terms. 7. Write the expression of the total heat transfer resistance in a double-pipe heat exchanger where fouling is present on both sides of the wall separating the two fluids. Heat T ransfer and Thermal Analysis - A.Y. 2016/17 - Date 16/01/2018 - Part B Exercise 1 (up to 15 points) In a full cylinder having radius R = 0.1 m, homogeneous and of infinite length, a heat source ˙U ′′′ = 10 5 W/m3 is present. The cylinder is placed horizontally and it is immersed in a cross-flow stream of dry air with T∞ = 290 K and velocityw∞ = 10 m/s. Determine: • the type of convection (forced/free/mixed) occurring (using a quantitative criterion, and if necessary making reasonable assumptions to avoid iterative…