A thin electrical heater is wrapped around the outer surface of a long cylindrical tube whose inner surface is maintained at a temperature of
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Fundamentals of Heat and Mass Transfer
- 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.arrow_forwardCalculate the overall heat transfer coefficient of the steel pipe based on the inner surface. The inner diameter of the pipe is 12.7 cm, and the thickness of the pipe is 2.4 cm. The convective heat transfer coefficient in the pipe is 350 W / (m² °C), the convective heat transfer coefficient outside the pipe is 25 W / (m² °C), the thermal conductivity of the steel pipe is 15 W / (m °C) . If a pipe is used to deliver steam at 110 °C and the ambient temperature is 30 °C, determine the rate of heat transfer from the pipe per meter. q = AnswerWatts/marrow_forwardStainless steel pipes with a thermal conductivity of 17 W/ (m° C) are used to transport hot oil. The temperature inside the tube is 130 ° C. The inner diameter of the pipe is 8 cm and the thickness of the pipe wall is 2 cm. The pipe is then insulated with 4 cm thick insulation with a thermal conductivity of 0.035 W / (m° C). The ambient temperature of the pipe is 25 ° C. Calculate the temperature between the steel and the insulation if we assume a steady state. A picture of the pipe can be seen below.arrow_forward
- 1. For a steam pipe with a given diameter of 10 cm covered by two (2) layers of insulation. The first insulation has a thickness of 4 cm and a coefficient of thermal conductivity of 0.08 W/m.K. and the second insulation has a thickness of 3 cm and a thermal conductivity of 0.15 W/m.K. The steam main conveys steam at a pressure of 1.70 MPa with 25°C superheat. Outside temperature is 27°C. The pipe is 30 meters in length. (tsat @ 1.70 MPa = 204°C). Determine the following: a) The heat loss in KW b) Explain the concepts/principles that were considered and the factors that affected the condition of the above mentioned items (a & b).arrow_forwardQ1. Consider a plane wall (thermal conductivity, k = 0.8 W/mK, and thickness, fb1 = 100 mm) of a house as shown in Fig. Q1(a). The outer surface of the wall is exposed to solar radiation and has an absorptivity of a = 0.5 for solar energy, or=600 W/m². The temperature of the interior of the house is maintained at T1 = 25 °C, while the ambient air temperature outside remains at T2 = 5 °C. The sky, the ground and the surfaces of the surrounding structures at this location can be modelled as a surface at an effective temperature of Tsky = 255 K for radiation exchange on the outer surface. The radiation exchange inside the house is negligible. The convection heat transfer coefficients on the inner and the outer surfaces of the wall are h₁ = 5 W/m²-K and /1₂ = 20 W/m².K, respectively. The emissivity of the outer surface is = 0.9. T1 = 25 °C Ţ₁ Too1 = 25 °C T₁ k 100 mm Fig. Q1(a) Assuming the heat transfer through the wall to be steady and one-dimensional: (a) Solve the steady 1D heat…arrow_forwardA 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/m2arrow_forward
- An electric cable consists of an inner core and an outer protection layer. The shape of the cable can be approximated as a cylinder. The diameter of the inner core is D1 = 1.6 cm and the total diameter of the cable is D2 = 2 cm. The thermal conductivities for the cable inner core and outer layer are k = 50 W/m·K and k = 0.1 W/m·K, respectively. The electric current in the inner core causes a volumetric thermal energy generation rate of q ̇ = 10^(6) W/(m^(3)) . The cable is placed in an air crossflow of u∞ = 2 m/s and T∞ = 300 K. The air in the film around the cylinder has a kinematiccrossflow of u∞ = 2 m/s and T∞ = 300 K. The air in the film around the cylinder has a kinematic viscosity of ν = 2 × 10^(−5 )(m^2)/s, thermal conductivity of kf = 0.025 W/m · K, and Prandtl number of Pr=0.7. Assume one-dimensional and steady-state conduction heat transfer along the radial direction of the cable cross section. Perform heat transfer analysis for a section of the cable with length L = 10 cm.…arrow_forwardQuestion No. 11: a) Derive the general heat conduction equation in Cartesian coordinates. b) Electric heater wires are installed in a solid wall having a thickness of 8 cm and k =2.5W/m ◦C.The right face is exposed to an environment with h=50W/m2◦C and T∞ = 30°C, while the left face is exposed to h=75W/m2◦C and T∞ =50◦C. What is the maximum allowable heat-generation rate such that the maximum temperature in the solid does not exceed 300◦C?arrow_forwardA 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.arrow_forward
- 2. A steel plate of k=50W/mK and thickness 10cm passes a heat flux by conduction of 25kW/m2. If the temperature of hot surface of plate is 100 C, then what is the temperature of the cooler side of plate? 1. 30 C 2. 40 C 3. 50 C 4. 60 Carrow_forwardA hot fluid (60° C) flows inside an copper tube with 1.7 cm OD and 1.5 cm ID. The inside of the pipe has a heat transfer coefficient of 130 W/m2-K. The tube is exposed to a room with air and surrounding walls of 23° C. The heat transfer coefficent between the outside of the walls and the room air is 15 W/m2 K. Draw an equivalent circuit diagram of the heat transfer, and quantify the resistance to heat flow by each of the two convective processes, conduction in the tube, and radiation between the outside of the tube and the room walls. Are any of the resistances negligible to the overall heat transfer, and if so, which ones?arrow_forward6. a. The heat flux applied to the walls of the biomass combustion furnace is 20 W/m2. The furnace walls have a thickness of 10 mm and a thermal conductivity of 12 W/m.K. If the wall surface temperature is measured to be 50oC on the left and 30oC on the right, prove that conduction heat transfer occurs at a steady state!b. Heating the iron cylinder on the bottom side is done by placing the iron on the hotplate. This iron has a length of 20 cm. The surface temperature of the hotplate is set at 300oC while the top side of the iron is in contact with the still outside air. To reach the desired hotplate temperature, it takes 5 minutes. Then it takes 15 minutes to measure the temperature of the upper side of the iron cylinder at 300oC. Show 3 proofs that heat transfer occurs transientlyarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning