2) The temperature distribution in the square chimney is to be analyzed by the finite difference method. Determine the temperature at the nodes of the grid shown. T-120 °C Ta400 °C le 16' 6 cm 12 cm 18 cm
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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.1.77 Explain each in your own words. (a) What is the mode of heat transfer through a large steel plate that has its surfaces at specified temperatures? (b) What are the modes when the temperature on one surface of the steel plate is not specified, but the surface is exposed to a fluid at a specified temperature?2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.
- 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 wall is made from an inhomogeneous (nonuniform) material for which the thermal conductivity varies through the thickness according to k = ax + b, where a and b are constants. The heat flux q"q" is known to be constant. Determine expressions for the temperature gradient and the temperature distribution when the surface at x = 0 is at temperature T1. Use the following values a = 11 W/K b = 25 W/m-K k = 11x + 25 W/m-K q"q" = 104 W/m^2 T1 = 60 CElectrical current flows through a cylindrical cable with a diameter of d = 4 mm generating thermal energy at a uniform rate of 1.6x107 W/m3. There is an insulation of t = 3 mm thickness with a conductivity of 0.2 W/mK. The system is exposed to convection as shown in the figure. Be careful, the outer diameter of the system with insulation becomes d + 2t. Calculate the surface temperature, Ts of the cable in °C. Round your answer to the nearest integer value and write only the numerical value in the provided box, not the units.
- Q1 A field investigation of the thermal environment has been conducted for a room with an external wall facing east. The wall are made of 150 mm brick (k = 0.9 W/m°C) and 15 mm of plaster (k= 0.3 W/m°C) on both sides. The results are as shown in Figure Q1(a) and Figure Q1(b), representing the temporal wall surface temperature and indoor air temperature respectively. (i)Based on the graph in Figure Q1(a), analyze the value of the conductive heat flow (Q) for the wall at 11:00 a.m. and 15:00 p.m. and discuss ONE (1) potential cause of the difference. Given the value of external and internal surface resistance are 0.06 m2°C/W and 0.12 m2°C/W, respectively. Meanwhile, the area of the wall is 12m2 . (ii) Based on your reason in Q1(i), propose TWO (2) practicable strategies that can reduce the external wall surface temperature during that time. (iii) As shown in Figure Q1(b), the indoor air temperature of the room reached its peak (maximum temperature) at about 1.5 hours later than that of…The rate of heat flow (q) through a plane wall of thickness x = 50 mm is 700 watt/m2 . Determine the difference between the temperatures of wall surfaces and the numerical values of the temperature gradient through the wall if it is made from (a) Brass whose k = 78 watt/m-C, (b) If wall is made of red brick whose k = 0.77 watt/m-CThe roof of a building is well insulated on its lower surface and the upper surface is made of black material. The upper surface is exposed to ambient air at 310 K with a convective heat transfer coefficient of 15 W m⁻² K⁻¹. The temperature of clear sky can be taken as 50 K. To the nearest 5 K, what temperature would be measured on the outer surface of the roof by a thermography camera on a clear night once the system had reached a steady state? State clearly the assumptions you are using.
- A copper pipe is used as electrical resistance to generate heat. This generation is equal to A/r per unit ofvolume, where “r” is the measured distance from the pipe axis. determine the profile of temperatures if the temperatures in the pipe walls are respectively T1 and T2.A pressure spring type thermometer having a time constant of 1.7s is placed in boiling water at a temp of 212F after being at a temperature of 69F. Determine the thermometer reading after 3.4s? Show detailed solutionsA steel rod, which is free to move, has a length of 200 mm and diameter of 20 mm at a temperature of 15°C. If the rod is heated uniformly to 115°C, determine the length and the diameter of this rod to the nearest micron at the new temperature if the linear coefficient of thermal expansion of steel is 12.5 x 10 m/m/°C. Wrong solution will be reported instantly