HTTA 2016 09 07 Solutions

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Heat T ransfer and Thermal Analysis - A.Y. 2015/16 - Date 2016/09/07 Surname: Name: ID number: Signature: Part A 1. Write the continuity equation for a compressible fluid. 2. Write the Newton law and state the quantities of which the convective coefficient may be a function. 3. Write the expression of the logarithmic mean temperature difference, stating the meaning of the involved terms. 4. Write the expression (in cylindrical coordinates) 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. 5. Write the Young equation, stating the meaning of the involved terms. 6. Write the definitions of the Nusselt and Biot dimensionless groups, and comment the difference between the two. 7. Write the definitions of the void fraction and interfacial area concentration in volume-averaged terms. Heat T ransfer and Thermal Analysis - A.Y. 2015/16 - Date 2016/09/07 - Part B Exercise 1 (up to 15 points) A hot wire anemometer is a device used to measure the local speed of a fluid stream. It consist of a thin electrical wire heated by Joule heating and placed in the region of interest of the fluid stream whose speed is to be measured. From the value of the power absorbed to keep the wire surface at a fixed temperature, it is possible to estimate the mean speed in the measurement region. Calculate the value of the fluid speed knowing that: • the fluid is dry air; • the metal wire has diameter D = 0.25 mm and length L = 12.5 mm; • an electrical power ˙L = 0.56 W is needed to keep it at a surface temperature TP = 100◦C; • the fluid stream is at T∞ = 15◦C; • radiation is negligible; • the convective coefficient between the wire and the fluid can be estimated using the correlation by Hilpert: Nu D = CRe m DPr 1/3…