1) A square isothermal chip is of width w=5 mm on a side and is mounted in a subtrate such that its side and back surfaces are well insulated, while the front surface is exposed to the flow of a coolant at T amb. From reliability considerations, the chip temperature must not exceed T=85 C. Coolant w Circuits Chip t If the coolant is air and the corresponding convection coefficient is h_air, what is the maximum allowable chip power (Q maxair )? If the coolant is a dielectric liquid with h_ref, what is the maximum allowable power (Q maxref)? Assumption: Negligible heat transfer by radiation Personal number (yy mm ddnnnn) h_ref : W/ m 2.K h_air : W/ m 2.K Tamb : W/ m 2.K Q maxair : Q maxref : Tamb5 Tamb=20 Tamb=30 2 2 h_air50 h_ref=2000 h_ref=3000 h_ref=4000 h_air=200 h_air=250
2) Air at P kpa and 35 C flows across a square flat plate with length of L, meter, at velocity of u, m/s. The plate is maintained at 65 C. Estimate the heat lost from the plate. (Fluid properties at T film are given μ=2.02*10 5 kg/m.s, K.028 W/m.K, Pr.71) Personal number (yy mm ddnnnn) P : kpa L : m u : m/s u=5 u=7.5 u=9 2 2 P=5 L.1 L.3 L.5 P=7 P=9 Q : W 3) Steel balls at diameter D meter are annealed by heating to Ti and then slowly cooling to 400 K in an air environment for which T =325 K and at given heat transfer coefficient of h. Assuming the properties of the steel to be k= 40 W/m.K, ρ=7800 kg/m 3, and cp=600 J/kg.K, estimate the time required for the cooling process. (Negligible radiation effects and constant properties) Personal number (yy mm ddnnnn) D : m Ti : C h : W/ m 2.K Ti000 Ti150 Ti300 2 D.012 D.015 D.02 2 h0 h=20 h=30
t : second 4) Water at the rate of m, kg/s is heated from 5 to 15 C by passing it through a D, cm inner diameter copper tube. The tube wall temperature is maintained at T wall C. What is the length of the tube? (Fluid properties: Cp=4.195*10 3 J/kg.K; k.582 W/m.K; μ.31*10 3 kg/m.s; Pr=9.4) Personal number (yy mm ddnnnn) Twall=75 Twall=90 Twall00 2 m=2.5 m=3 m=3.5 2 D=3 D=5 D=7 D : cm T wall : C m : kg/s L : m 5) Find the apparent conductivity of the air in between the glasses of a doubleglassed window if the distance between them is δ cm, and the height of the window is L m. Assume that the surface temperatures are given according to your personal data.(the properties of the air are ν2.10 6 m 2 /s; k.024 W/m.K; Pr.72) Personal number (yy mm ddnnnn) =4 2 L.8 L L.2 2 Surface temperature 014 Surface temperature 216 Surface temperature 420
δ : cm L : m Surface temperature : C ke : W/m.K 6) Parallel flow of atmospheric air over a flat plate of length L is disrupted by an array of stationary rods placed in the flow path over the plate. Laboratory measurements of the local convection coefficient at the surface of the plate are made for a prescribed value of air velocity and Ts>T. The results are correlated by an expression of the form given from your personal data h x, where h x has units of W/ m 2.K and x is in meters. Evaluate the average convection coefficient ћ L for the entire plate and the ratio ћ L /h L at the trailing edge. (Ts is surface temperature and T is ambient temperature) L : m hx : W/ m 2.K ћ L ћ L /h L : W/m.K : 7) Calculate the surface temperature of a thin roof on a Sunny day with air temperature of +20 C, the radiation heat flux is 600 W/ m 2. The surface has the absorptivity α. The total film heat transfer coefficient between the surface and the air is h W/m 2.K. The inside of roof is insulated by δ cm cork (k.04 W/m.K) and the inside surface temperature is +20 C.
Personal number (yy mm ddnnnn) =5 0 5 δ : cm h : W/ m 2.K α : T roof : C 2 2 h0.65.8.9 h5 h=20 8) Two large parallel planes having emissivities of ε 1 and ε 3 are maintained at temperatures of T 1 K and T 3 K, respectively. A radiation shield having an emissivity of ε 2 on both sides is placed between the two planes. Calculate (a) the heat transfer rate per unit area if the shield were not present, (b) the heat transfer rate per unit area with the shield present, and (c) the temperature of the shield. Personal number (yy mm ddnnnn) 0.03 0.05 2.07 2.2 and.4.3 and.5.4 and.6 2 T1=700 and T3=300 T1=800 and T3=400 T1=900 and T3=500 ε 1 and ε 3 : T 1 and T 3 : K ε 2 : a) (Q/A) 13 2 : W/m b) (Q/A) 13 : W/m 2 T shield : K
9) In a water cooler, horizontal tubes with an inside diameter of d mm are used. Inside the tubes, boiling refrigerant HCFC22 is flowing. It is desired that the inside surface temperature does not fall bellow +2 C and the evaporation temperature does not fall bellow 3 C. Calculate the tube length required to maintain a cooling capacity of Q W. At the tube inlet vapour quality is x.15, while at the tube outlet the refrigerant is slightly superheated. For HCFC 22, μ= 250*10 6 Ns/m 2.K; k.09 W/m.K; h fg =209 kj/kg. d : mm Q : W L : m 10) The inlet temperatures to a parallel flow heat exchanger are 80 and 40 C respectively. The UAvalue and the heat capacity rates are given according to your personal number for the hot and cold fluid, respectively. Find the outlet temperatures of the two fluids. UA : W/ C Heat capacity rates : W/ C T 2h : C T 2c : C