Spheres of 40-mm diameter heated to a uniform temperature of 400°C are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of 300 W/m² K on the sphere surfaces. The thermophysical properties of the sphere material are p = 3000 kg/m³, c = 850 J/kg-K, and k = 15 W/m.K. (a) How long must the spheres remain in the air bath for 80% of the thermal energy to be removed?
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- 3.10 A spherical shell satellite (3-m-OD, 1.25-cm-thick stainless steel walls) re-enters the atmosphere from outer space. If its original temperature is 38°C, the effective average temperature of the atmosphere is 1093°C, and the effective heat transfer coefficient is , estimate the temperature of the shell after reentry, assuming the time of reentry is 10 min and the interior of the shell is evacuated.a) A 50 mm diameter carbon steel tube (ρ=7833 kg/m³; Cp = 465 J/kg.K, k = 54 W/mK) at an initial uniform temperature of 18°C is heated in an oven with air circulation that is at a temperature of 250°C and has a convection heat transfer coefficient of 45 W/m².K. How long must the tube be in the oven for the surface temperature to reach 100°C? b) The figure below illustrates the temperature distribution inside a flat solid at two instants for two different situations (A and B). In both situations is there heat transfer? What causes them to behave differently?A grandmother is concerned about reducing her winter heating bills. Her strategy isto loosely fit rigid polystyrene sheets of insulation over her double-pane windows rightafter the first freezing weather arrives. Identify the relevant heat transfer processes on acold winter night when the foamed insulation sheet is placed:(a) on the inner surface, and (13)3(b) on the outer surface of her window.
- Question 1: A glass window of width W = 1 m and height H = 2m is 5 mm thick and has a thermal conductivity of kg =1.4 W/m.K. If the inner and outer surface temperatures of the glass are 15 °C and -20 C, respectively, on a cold winter day, what is the rate of heat loss through the glass? To reduce heat loss through windows, it is customary to use a double pane construction in which adjoining panes are separated by an air space. If the spacing is 10 mm and the glass surfaces in contact with the air have temperatures of (last two digit of your Registration number) °C and -15 °C, what is the rate of heat loss from a 1 mx2mwindow? The thermal conductivity of air is ka = 0.024 W/m.K.16 mm in diameter mild steel sphere initially at 6000 C is exposed to a current of air at 300C with a convection coefficient of 90 W/m2.K. Calculate the time required to cool thesphere to 1000 C, Initial rate of cooling in 0C/s, Instantaneous heat transfer rate at the endof one minute after the start of cooling, and total energy transferred during the first oneminute. Take properties of mild steel as k = 43 W/m.K, C = 474 J/kg.K, ρ = 7850 kg/m3,α = 0.045 m2/sAn electrical heater 114 mm long and 7 mm in diameter is inserted into a hole drilled normal to the surface of a large block of material having a thermal conductivity of 9 W/m · K. Estimate the temperature reached by the heater when dissipating 54 W with the surface of the block at a temperature of 27°C.
- Circular cooling fins of diameter D = 1 mm andlength L = 25.4 mm, made of copper (k = 400 W/m·K), areused to enhance heat transfer from a surface that is maintainedat temperature Ts1 = 132°C. Each rod has one end attached tothis surface (x = 0), while the opposite end (x = L) is joinedto a second surface, which is maintained at Ts2 = 0°C. Theair flowing between the surfaces and the rods is also at T` =0°C, and the convection coefficient is h = 100 W/m2·K.(a) Express the function u(x) = T(x) - T` along a fin, andcalculate the temperature at x = L/2. (b) Determine the rate of heat transferred from the hot surface through each fin and the fin effectiveness. Is the use of fins justified? Why? (c) What is the total rate of heat transfer from a 10-cm by 10-cm section of the wall, which has 625 uniformly distributed fins? Assume the same convection coefficient for the fin and for the unfinned wall surface.A long wire of diameter D = 2 mm is submerged in an oil bath of temperature T∞ = 23°C. The wire has an electrical resistance per unit length of Re′=0.01 Ω/m. If a current of I = 180 A flows through the wire and the convection coefficient is h = 529 W/m2 · K, what is the steady-state temperature of the wire? From the time the current is applied, how long does it take for the wire to reach a temperature that is within 2°C of the steady-state value? The properties of the wire are ρ = 2,334 kg/m3, c = 537 J/kg · K, and k = 43 W/m · K.Find out the diameter of the spherical product being frozen in an air-blast wind tunnel. The initial product temperature is 100C & cold air in the tunnel is at -120C. The product density is 1000 kg/m3 and the convective heat transfer coefficient for the air blast is 50 W/m2K. The thermal conductivity of the product is 1.25 W/mK and the initial freezing temperature is -20C. The latent heat of fusion is 300 kJ/kg. Freezing time is 2.2 hrs
- b. A short cylindrical aluminium bar, having thermal conductivity, 200W/m.K and thermal diffusivity, 8.4 X 10-5 m2 /s of diameter 6 cm and height 3 cm is initially at a uniform temperature of 175°C. Suddenly the surfaces are subjected to convective cooling with a heat transfer coefficient of 250 W/m2 .K into an ambient at 25°C. Calculate the center temperature of the cylinder one minute after the start of coolingA sphere of 80 mm diameter (k=50 W/m.K and α=1.5x10-6 m2/s) is initially at a uniform, elevated temperature, and is quenched in an oil bath maintained at 30 °C. The convection coefficient for the cooling process is 1100 W/m2K. At a certain time, the surface temperature of the sphere is measured to be 120 °C. What is the corresponding center temperature of the sphere?The wall of a box furnace is made of a composite material. Layer A is directly in contact with the combustion gases inside the furnace and it has a thickness of 0.023 m, a thermal conductivity of 132 W/m-K, and a cross-sectional area of 0.42 m2. On the other hand, Layer C corresponds to the outermost layer that is in direct contact with the ambient air. It has a thickness of 0.036 m, a thermal conductivity of 2 W/m-K, and has the same cross-sectional area as Layer A. In between Layer A and Layer C are two parallel layers: LayerB and Layer D. Layer B has the same cross-sectional area as Layer D. The thickness of Layer B and Layer D is 0.066 m. Layer B has a thermal conductivity of 13 W/m-K; while, Layer D has a thermal conductivity of 23 W/m-K. The combustion gases inside the furnace has a temperature of 373 ; while, the ambient air has a temperature of 30 . Finally, the convection heat transfer coefficients at the inside and outside of the wall are 111 W/m2-K and 22 W/m2-K…