Concept explainers
Consider a medium in which the heat conduction equation is given in its simplest form as
- Is heat transfer steady or transient?
- Is heat transfer one- two-, or three-dimensional?
- Is there heat generation in the medium?
- Is the thermal conductivity of the medium constant or variable?
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- Water flows through a pipe at an average temperature of T = 50°C. The inner and outer radii of the pipe are r1 = 6 cm and r2 = 6.5 cm, respectively. The outer surface of the pipe is wrapped with a thin electric heater that consumes 300 W per m length of the pipe. The exposed surface of the heater is heavily insulated so that the entire heat generated in the heater is transferred to the pipe. Heat is transferred from the inner surface of the pipe to the water by convection with a heat transfer coefficient of h = 55 W/m2· °C. Assuming constant thermal conductivity and one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary conditions) of the heat conduction in the pipe during steady operation and obtain temperature distribution in pipe.arrow_forwardA spherical container with an inner radius r1 = 1 m and an outer radius r2 = 1.05 m has its inner surface subjected to a uniform heat flux of q1=7kw/m^2. The outer surface of the container has a temperature T2 = 25°C, and the container wall thermal conductivity is k = 1.5 W/m·K. Show that the variation of temperature in the container wall can be expressed as and determine the temperature of the inner surface of the container at r = r1.arrow_forwardConsider the process of baking potatoes in a conventional oven. Can the hot air in the oven be treated as a thermal energy reservoir? Explain.arrow_forward
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- Consider a large plane wall of thickness L = 0.15 m, thermal conductivity k = 12.6 W/m · °C, and surface area A=22 m2. The left side of the wall is maintained at a constant temperature of T1= 144 °C while the right side loses heat by convection to the surrounding air at T= 0 °C with a heat transfer coefficient of h = 20 W/m2 · °C. Assuming constant thermal conductivity and no heat generation in the wall. Evaluate the rate of heat transfer through the wallarrow_forward) Consider a solid sphere of radius r=50 cm. The heat is generated steadily inside the sphere at a rate of (15000) W/m3. The conductivity of the sphere is 10 W/m.K. Surface of the sphere is cooled by cooling water whose temperature and convection heat transfer coefficient are 10oC and 125 W/m2.K. Determine the temperatures at the center and surface of the sphere. Find the total heat transfer rate from the surface of the spherearrow_forwardConsider a stainless steel spoon (k = 15 W/m·K) partially immersed in boiling water at 95°C in a kitchen at 25°C. The handle of the spoon has a cross section of 0.2cm x 1.2 cm, and extends 18 cm in the air from the free surface of the water. If the heat transfer coefficient at the exposed surfaces of the spoon handle is 15 W/m2·°C, determine the temperature difference across the exposed surface of the spoon handle. State your assumptions.arrow_forward
- Consider a large 3-cm-thick stainless steel plate in which heat is generated uniformly at a rate eg of 6 x 106 W/m3. Assuming the plate is losing heat from both sides, determine the heat flux on the surface of the plate during steady operation in kW/m2.arrow_forwardTwo surfaces of a 2-cm-thick plate are maintained at 0°C and 100°C, respectively. If it is determined that heat is transferred through the plate at a rate of 500 W/m2 , determine its thermal conductivity.arrow_forwardAn ordinary egg with a mass of 0.1 kg and a specific heat of 3.32 kJ/kg·°C is dropped into boiling water at 95°C. If the initial temperature of the egg is 5°C, the maximum amount of heat transfer to the egg is (a) 12 kJ (b) 30 kJ (c) 24 kJ (d) 18 kJ (e) infinityarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning