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Politecnico di Milano – A.Y. 2025–2026 Master Programme in Energy/Nuclear Engineering Heat and Mass Transfer Examination – 12 January 2026 Surname: Name: Student ID number: Grade 1 -. . . . . . . . . /10 2 -. . . . . . . . . /10 3 -. . . . . . . . . /10 Total . . . . . . . . . /30 The time available is 2.5 hours . Only the material provided as Supplementary Material may be used. No textbooks, notes, or electronic devices are allowed. The maximum score is 30/30. At the end of the exam, this text must be submitted with the numerical results written next to each question , and only one protocol sheet (four written pages) with the detailed solution must be handed in. Exercise 1 (10 points) An isothermal (Tc = 85 ◦C) silicon chip of widthW = 20 mm on a side is soldered to an aluminum heat sink (λ = 180 W /m K) of equivalent width. The heat sink has a base thickness ofLb = 3 mm and an array of 11 rectangular fins, each of lengthLf = 15 mm. An air flow atT∞ = 25 ◦C and with a velocity ofu∞ = 8.9 m/s is maintained through the channels formed by the fins and a cover plate. The fin spacing isδ = 1.8 mm. The solder joint has a thermal resistanceR′′ t,c = 6 · 10−5 m2 K/W. An adiabatic fin tip condition may be assumed, and airflow along the outer surfaces of the heat sink may be assumed to provide a convection coefficient equivalent to that associated with airflow through the channels. The air properties should be evaluated atT∞. Find: 1. the mean convective heat transfer coefficient, assuming an almost uniform fin temperature 2. the power dissipated to the air 3. the temperature at the base of a fin and the effectiveness of a single fin Accounting for the increase in air temperature as it flows through the heat sink, find: 4. the outlet temperature of the air exiting each channel…