Solve the heat conduction equation a?u 1 ди əx²¯ 2 at over 0 0 for the boundary conditions u(0,t) = u(3,t) = 0 and initial condition u(x, 0) = 5 sin 4nx – 3sin 2nx +si sinnx %3D -
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- 1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.A 10-cm diameter pipe is covered by 2 layers of lagging. The insidelayer is 4 cm thick and has a coefficient of thermal conductivity of 0.08W/m-K. The outside layer is 3cm thick and has a coefficient of thermalconductivity of 0.15 W/m-K. The steam main conveys steam apressure of 1.7 MPa with 25 C superheat. The outside temperature ofthe lagging is 27 C. If the steam main is 30 m long, determine theinterface temperature of the lagging and overall coefficient of heattransfer based on outside area.Steam flows in an insulated pipe at a temperature 130 C. The insideheat transfer coefficient is 79 W/m2-K and the outside coefficient is 15W/m2-K. The pipe is mild steel (k=57 W/m-K) and has an inside radiusof 50 mm and an outside radius of 57 mm. the pipe is covered with a25.4 mm layer( k=0.09 W/m-K). Determine the overall heat transfercoefficient if the surrounding air temperature is 21.1 C.
- In a thermal power plant, a horizontal copper pipe of "D" diameter, "L" length and thickness 1.2 cm enters into the boiler that has the thermal conductivity as 0.37 W/mK. The boiler is maintained at 113C and temperature of the water that flows inside the pipe is at 29C. If the energy transfer (Q) is 118779 kJ in 7 hours. Calculate: 4-Length of the pipe, if D = 0.017 L. 5-Pipe Diameter (in mm)A cylindrical reactor made of copper with a radius of a= r=5mm has a heat conduction coefficient of k=386 W/moC, and there is heat generation at e ̇= (q ) ̇= 4x10^8 W/m3 inside this reactor. The cylindrical reactor convection heat transfer coefficient is h=2000 W/m0C and 〖T_(ambient= ) T〗_∞= 30 oC by convection, it cools down from the reactor surface to the center. According to the given boundary conditions a)Find the reactor surface temperature and the temperature T(a) at r=a. (VARIABLES: r=1-10mm, T_∞= 0-100oC) b) q(a) =((q ) ̇ * a )/ 2 = (e ̇ * a )/ 2 then find the heat flux amount in kW/m2A cylindrical tube with inner and outer radius are 10 mm and 20 mm respectively and the temperature of the inner surface is 300 C while for the outer surface is 100 C . If the rate of heat transfer per unite length is 3625.88 W/m , the tube conductivity is :
- In a thermal power plant, a horizontal copper pipe of "D" diameter, "L" length and thickness 1.9 cm enters into the boiler that has the thermal conductivity as 0.37 W/mK. The boiler is maintained at 102 °C and temperature of the water that flows inside the pipe is at 34°C. If the energy transfer (Q) is 100735 kJ in 7 hours. Determine the Heat transfer rate, Surface area of the pipe and Diameter & Length of the pipe, if D = 0.015 L .The thermal conductivities of human tissues vary greatly. “Fat” and “skin” have conductivities of approximately 0.200 W /m 0K and 0.0200 W /m 0K, respectively, while other “tissues” inside the body have conductivities of approximately 0.500 W /m 0 Assume that between the core region of the body and the skin surface lies a “skin” layer of 1.00mm, a “fat” layer of 0.500 cm., and 3.20 cm. layer of other “tissues”. A)Find the R-factor for each of these three layers, and the R-factor for all layers taken togetherIn a thermal power plant, a horizontal copper pipe of "D" diameter, "L" length and thickness 1.7 cm enters into the boiler that has the thermal conductivity as 0.3 W/mK. The boiler is maintained at 107degreeC and temperature of the water that flows inside the pipe is at 31degreeC. If the energy transfer (Q) is 124925 kJ in 7 hours. Determine the Heat transfer rate, Surface area of the pipe and Diameter & Length of the pipe, if D = 0.012 L.Change in Temperature (in K) Heat Transfer Rate (in W) Surface Area of the Pipe (m2) Pipe Length (in m) Pipe Diameter (in mm)
- Steam passes at 250 ° C through a steel pipe with an inner diameter of 60 mm and an outer diameter of 75 mm. Pipe The heat transfer coefficients inside and outside are 500 and 25 W / m2K, respectively. Ambient temperature 20 ° C and The heat conduction coefficient of the pipe is 56.5 W / mK. a)Find the heat loss from the 5 m length of the pipe. b)What thickness of material with heat transfer coefficient 0.035 W / mK to reduce heat loss by 95%? insulation should be made.The average rate at which energy is conducted outward through the ground surface in North America is 54.0 mW/m2, and the average thermal conductivity of the near surface rocks is 2.50 W/m K. Assuming a surface temperature of 10.0oC, find the temperature at a depth of 10.0 km. Ignore the heat generated by the presence of radioactive elements.A steel tube (k = 15 W/m.K) 3 m long carries a refrigerated liquid at 5°C. The inner diameter of the tube is 4 cm and the thickness is 1.5 cm. The convection heat transfer coefficient inside the tube is 80 W/m².K. The fluid receives heat from the external environment, which is at 28°C with a convection heat transfer coefficient of 20 W/m².K. To reduce the gain, it is studied to add a layer of insulating foam to the tube with a thickness of 5 cm and thermal conductivity k = 0.08 W/m².K. The placement of insulation pays off financially if the heat transfer rate is reduced by at least 30% and if the outside surface temperature is above 15°C. Ignoring the effects of radiation, verify that these conditions are met.