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- 1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder (0.1 m diameter, thermal conductivity of 0.2 W/m K) with uniform internal heat generation. By dimensional analysis, determine the relation between the steady-state temperature at the center of the cylinder , the diameter, the thermal conductivity, and the rate of heat generation. Take the temperature at the surface as your datum. What is the equation for the center temperature if the difference between center and surface temperature is when the heat generation is ?1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.
- A hot water pipe is 100 mm in diameter and 80 m long. This pipe is insulated in two layers. First layer is 25 mm thick, thermal conductivity is 0.12 W/m C material, second layer is 45 mm thick It is made of material with a thermal conductivity of 0.05 W/m C. T1, T2 and T3 are the surface temperatures in the pipe. One With the acceptance of heat transfer in dimensional and continuous conditions, transfer from the pipe in case T1= 600 OC and T3= 35 C Find the amount of heat released and the temperature T2. 2.tabaka 1.tabaka 100 mm T₁ T₂ T34x F2 # 3 E 4, F3 54 $ R F4 Ac = 1m² ▬ H DII x= 1 m (4) Consider a wall (as shown above) of thickness L-1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h= 1 W/m²K and an ambient temperature T. 1 K. There is no heat generation inside the wall. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). % To,1 = 1 K h₁ = 1 W/m²K 5 Q Search F5 T T₁ A 6 x=0 F6 à = 0 W/m³ k= 1W/mK L=1m Y 994 F7 & 7 T₂ U Ton2 = 1 K h₂ = 1 W/m²K1 PrtScn F8 Page of 7 ) 0 PgUp F11 P#m 3 E D C F3 $ 4 R F Ac = 1m² V Too,1=1 K h₁ = 1 W/m²K (5) Consider a wall (as shown above) of thickness L=1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h = 1 W/m²K and an ambient temperature T.= 1 K. Heat generation inside the wall is q=1W/m³. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). 44 % 5 Q Search F5 T G T₁ B x=0 * A 6 q=1 W/m³ k= 1W/mK L=1m F6 Y H F7 & 7 T₂ x= 1 m U N Top 2 = 1 K h₂=1 W/m²K PrtScn F8 8 Home M F9 ( 9 K End F10 0 L PgUp
- One-dimensional heat transfer through a composite wall is shown in the following figure. Please calculate the heat flow through the composite wall according to the equivalent thermal circuit. It is known that the thermal conductivity are ka=46.5 W/(m.K), kp=1.1 W/(m.K), kc =0.06 W/(m.K), respectively. The thickness of the three materials is Ax,=Axg=Axc=10mm. The temperature of wall 1 and wall 4 are t=80°C, t4=15°C, respectively. (Please give the compution process and the result.) A - Temperature profile RA Rg Rc T3 Axc A B 1 4 Figure for question 9A Multi-layer wall of a building is shown in the following figure. The thermal conductivity of A, B, C, D, and E are: 30, 5, 1.67, 10.5, 6 W/m k, respectively. Assume one dimentional heat transfer. The area of A = D = E =4 m?, and B = C= 2 m². The thickness of each layer is 10 cm. The temperature of surface A is 25 °C, and the temperature of surface E is 38 °C. Calculate the heat transfer rate through the wall. B A D E C2. The slab shown is embedded in insulating materials on five sides, while the front face experiences convection off its face. Heat is generated inside the material by an exothermic reaction equal to 1.0 kW/m'. The thermal conductivity of the slab is 0.2 W/mk. a. Simplify the heat conduction equation and integrate the resulting ID steady form of to find the temperature distribution of the slab, T(x). b. Present the temperature of the front and back faces of the slab. n-20- 10 cm IT- 25°C) 100 cm 100 cm
- Consider a copper plate that has dimensions of 3 cm x 3 cm x 7 cm (length, width, and thickness, respectively). As shown in the following figure, the copper plate is exposed to a thermal energy source that puts out 126 J every second. The density of copper is 8,900 kg/m³. Assume there is no heat loss to the surrounding block. 126 J Copper Insulation Ⓡ What is the specific heat of copper (in J/(kg K))? J/(kg. K) What is the mass of the copper plate (in kg)? kg How much energy (in J) will be consumed during 11 seconds? J Determine the temperature rise (in K) in the plate after 11 seconds.Consider 1D heat conduction in a Cu rod with an average temperature of 25C. Does there exist a maximum (or upper-limit value) temperature gradient for heat conduction. If so, what is that value with justification on the derivation/scientific reasoning. The thermal conductivity is k=385 W/m*K. The diameter of the rod is left in terms of d.2-88 A 1.5-mm-diameter stainless-steel rod [k = 19 W/m.°C] protrudes from a wall maintained at 45°C. The rod is 12 mm long, and the convection coefficient is 500 W/m² . °C. The environment temperature is 20°C. Calculate the temperature of the tip of the rod. Repeat the calculation for h = 200 and 1500 W/m² . °C.