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HEAT TRANSFER PROBLEMS

Environmental. Physics. HEAT TRANSFER PROBLEMS. Equipo docente : Alfonso Calera Belmonte Antonio J. Barbero. Departamento de Física Aplicada UCLM. Environmental. Physics. PROBLEM 1.

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HEAT TRANSFER PROBLEMS

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  1. Environmental Physics HEAT TRANSFER PROBLEMS Equipo docente: Alfonso Calera Belmonte Antonio J. Barbero Departamento de Física Aplicada UCLM

  2. Environmental Physics PROBLEM 1. The differential equation giving the profile of temperature through a hollow cylinder infinitely long at steady state is Where r is the radious Find out the heat flux per unit of length in a cylindrical pipe with the boundary conditions T=T1 at r = r1, T=T2 at r=r2 (the border effects are neglected, and it is assumed that conductivity k is constant). From boundary conditions

  3. Environmental Note that r L Physics PROBLEM 1 (continued) Here Ar means the curved surface of a cylindrical area, given by Heat flux From Fourier’s equation

  4. Environmental r2 T3 T2 T1 r1 d r3 km ki Physics PROBLEM 2. A metallic cylindrical pipe (thermal conductivity km) having an inner radious r1 and an outer radious r2 is covered by a d-cm thickness insulation of thermal conductivity ki. The pipe carries a fluid at T1 temperature, and the external temperature is T’. Calculate the losses of heat per meter of isolated pipe. T’ = T3 From the solution of the prior problem: we use the concept of thermal resistence The heat flux is given by a set of terms having each the form Thermal resistences are given in this case by terms of the form Numerical application: km = 40 W/mºC, ki = 0.75 W/mºC, r1 = 5 cm, r2 = 7 cm, d = 3 cm, T1 = 80 ºC, T’ = 25 ºC. Find out the intermediate temperature T2.

  5. PROBLEM 3. A metallic cylindrical pipe (thermal conductivity km= 40 W/mºC) having an inner radious r1 = 5 cm and an outer radious r2 = 7 cm carries a fluid at T1 = 80 ºC. The inner and outer heat transfer coefficients are 2500 W m-2 ºC and 1600 W m-2 ºC. The external temperature is 25 ºC. Find out the losses of heat per meter of pipe. PROBLEM 4. Consider three panes of glass, each of thickness 5 mm. The panes trap two 2.5 cm layers of air in a large glass door. How much power leaks through a 2.0 m2 glass door if the temperature outside is -40 ºC and the temperature inside is 20 ºC? Data: kglass= 0.84 W/mºC, kair= 0.0234 W/m ºC (discuss if we can consider air in the same way we consider glass). PROBLEM 5. If the temperature of the Sun fell 5%, and the radius shrank 10%, what would be the percentage change of the Sun’s power output? PROBLEM 6. We know that the sun radiates 3.74·1026 W. We also know that the distance from Sun to Earth is 1.5·1011 m and the radius of Earth is 6.36·106 m. • What is the intensity (power/m2) of sunlight when it reaches Earth? • How much power is absorbed by Earth in sunlight? (assume that none of the sunlight is reflected) • What average temperature would allow Earth to radiate an amount of power equal to the amount of sun power absorbed?

  6. PROBLEM 5. If the temperature of the Sun fell 5%, and the radius shrank 10%, what would be the percentage change of the Sun’s power output? The power output would decrease 34% PROBLEM 6. We know that the sun radiates 3.74·1026 W. We also know that the distance from Sun to Earth is 1.5·1011 m and the radius of Earth is 6.36·106 m. • What is the intensity (power/m2) of sunlight when it reaches Earth? • How much power is absorbed by Earth in sunlight? (assume that none of the sunlight is reflected) • What average temperature would allow Earth to radiate an amount of power equal to the amount of sun power absorbed?

  7. PROBLEM 6. We know that the sun radiates 3.74·1026 W. We also know that the distance from Sun to Earth is 1.5·1011 m and the radius of Earth is 6.36·106 m. From the radiated power • What is the intensity (power/m2) of sunlight when it reaches Earth? • How much power is absorbed by Earth in sunlight? (assume that none of the sunlight is reflected) • What average temperature would allow Earth to radiate an amount of power equal to the amount of sun power absorbed? we get the power of sunlight at the Earth’s orbit From the Sun, the Earth appears as a tiny disk whose radious is 6.36·106 m The power intercepted by Earth is If Earth would behave as a perfect blackbody TEarth = 276 ºK s =5.67051 x 10-8 W/m2K4

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