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A thin electrical heater is wrapped around the outer surfaceof a long cylindrical tube whose inner surface ismaintained at a temperature of
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Chapter 3 Solutions
Introduction to Heat Transfer
- 1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.arrow_forwardShow that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinderarrow_forward2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)arrow_forward
- 2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.arrow_forwardA high-speed computer is located in a temperature-controlled room at 26C. When the machine is operating, its internal heat generation rate is estimated to be 800 W. The external surface temperature of the computer is to be maintained below 85C. The heat transfer coefficient for the surface of the computer is estimated to be 10W/m2K. What surface area would be necessary to assure safe operation of this machine? Comment on ways to reduce this area.arrow_forwardQ1: Consider one-dimensional conduction in a plane composite wall (Im x Im) as shown in the figure below. The outer surfaces are exposed to a fluid at 25°C and a convection heat transfer coefficient of 1000 W/m K. The middle wall B experiences uniform heat generation dg, while there is no generation in walls A and C. The temperatures at the interfaces are T=261°C and T; -211°C. Assuming negligible contact resistance at the interfaces: A) Determine the outside surface temperature of walls A and C? B) Compute the value of dg? (20 M) A B. ーム k= 25 Wim-K A = 50 W/m-K L = 30 mm Le= 30 mm L = 20 mm %3Darrow_forward
- Q1: Consider one-dimensional conduction in a plane composite wall (1m x Im) as shown in the figure below. The outer surfaces are exposed to a fluid at 25°C and a convection heat transfer coefficient of 1000 W/m2.K. The middle wall B experiences uniform heat generation dB, while there is no generation in walls A and C. The temperatures at the interfaces are T1=261°C and T2=211°C. Assuming negligible contact resistance at the interfaces: A) Determine the outside surface temperature of walls A and C? B) Compute the value of q;? T2 T h 25 241 A B -2LB Lc .03 Ta kA = 25 W/m-K kc = 50 W/m-K LA = 30 mm Lg = 30 mm Lc = 20 mm %3Darrow_forwardConsider a plate whose thickness is 2L=20 cm and thermal conductivity is 20 W/mK. Heat generation inside the plate (104 W/m³) is uniform. The plate is placed in an environment at T=20°C and convective heat transfer coefficient is h=16 W/m²K. Find the temperature at the center of plate. h To -L O a. 45 °C O b. 75 °C O c. 67 °C O d. 85 °C О е. 90 °Сarrow_forwardHEAT TRANSFER (a) Determine the thermal conductivity of an insulating material given the following data: steel pipe with 0.1025 m inner diameter and 0.1150 m outer diameter, insulation thickness 3 cm, heat flow per meter is 150 W/m, steel thermal conductivity 55 W/m-°C, and overall temperature difference of 72.2°C. If the temperature of the steam inside the pipe is 128°C, (b) find the outside temperature of the insulating material.arrow_forward
- Please help solve the following heat transfer problem. You are to use a resistance model in your solution. Thank you.arrow_forwardQ2. Steam pumped through a long- insulated pipe at a temperature of T= 500 K and provides a convection coefficient of h, = 100 W/m?K at the inner surface of the pipe. The inner and outer radius of the pipe and insulation material are r1 = 10, r2 = 12 and r3 = 17 cm, respectively. The thermal conductivity of the pipe is 100 W/mK. The insulation material is glass fiber and its outer surface is exposed to ambient air at 300 K. If the ambient air provides a convection coefficient of ho = 20 Internal flow Ambient air W/m?K, determine the followings: a. What are the thermal resistance coefficients for convections and conductions b. What is the heat transfer rate per unit length of the pipe c. If the pipe is 30 m long, what will be total heat transfer rate from the pipe. t00 noints)arrow_forward1- A solid infinitely long cylinder, radius 2 cm, has uniform internal heat generation. The temperature distribution in the cylinder is T(r) = = 256 – 8.6 x 104 r² where r is in meters, T in °C and the thermal conductivity of the cylinder material is 16 W/ m °C. Determine: (a) The temperature at the centerline. (b) The surface temperature. (c) The heat flux at the surface. (d) The rate of heat transfer to the surrounding per unit meter of cylinder length.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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