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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Connect 1-Semester Access Card for Heat and Mass Transfer: Fundamentals and Applications
- Heat is transferred steadily through a 0.2-m-thick, 8 m × 4 m wall at a rate of 2.4 kW. The inner and outer surface temperatures of the wall are measured to be 15°C and 5°C. The average thermal conductivity of the wall is (a) 0.002 W/m·°C (b) 0.75 W/m·°C (c) 1.0 W/m·°C (d) 1.5 W/m·°C (e) 3.0 W/m·°Carrow_forwardIn the context of a Spark Ignition (SI) engine, consider a moment during combustion when there is a heat flux through the wall of the combustion chamber at a specific location, measured at 219 kW/m2. The gas temperature within the cylinder at this time is 2300 K, and the convection heat transfer coefficient within the cylinder is 120 W/m2⋅K. The coolant temperature is 80 °C. The thickness of the cylinder wall is 10mm with a thermal conductivity of 200 W/m⋅K. (a) Determine the temperature of the inner surface of the cylinder wall. (b) Find the temperature on the side of the cylinder wall facing the coolant. (c) Calculate the heat transfer coefficient on the coolant side of the cylinder wallarrow_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_forward
- 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_forwardThe interior of a refrigerator has a surface area of 6.2 m2 . It is insulated by a 2 cm thick material that has a thermal conductivity of 0.0199 J/m · s · ◦ C. The ratio of the heat extracted from the interior to the work done by the motor is 5.5 % of the theoretical maximum. The temperature of the room is 27.6 ◦C, and the temperature inside the refrigerator is 6.6 ◦C. Determine the power required to run the compressor. Answer in units of W.arrow_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_forward
- Consider 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_forwardA 50-L electrical radiator containing heating oil is placed in a well-sealed 75-m3 room. Both the air in the room and the oil in the radiator are initially at the environment temperature of 6°C. Electricity with a rating of 2.4 kW is now turned on. Heat is also lost from the room at an average rate of 0.75 kW. The heater is turned off after some time when the temperatures of the room air and oil are measured to be 20°C and 60°C, respectively. Taking the density and the specific heat of oil to be 950 kg/m3 and 2.2 kJ/kg⋅°C, determine the exergy destruction.arrow_forwardA 50-L electrical radiator containing heating oil is placed in a well-sealed 75-m3 room. Both the air in the room and the oil in the radiator are initially at the environment temperature of 6°C. Electricity with a rating of 2.4 kW is now turned on. Heat is also lost from the room at an average rate of 0.75 kW. The heater is turned off after some time when the temperatures of the room air and oil are measured to be 20°C and 60°C, respectively. Taking the density and the specific heat of oil to be 950 kg/m3 and 2.2 kJ/kg⋅°C, determine how long the heater is kept on.arrow_forward
- A 50-L electrical radiator containing heating oil is placed in a well-sealed 75-m3 room. Both the air in the room and the oil in the radiator are initially at the environment temperature of 6°C. Electricity with a rating of 2.4 kW is now turned on. Heat is also lost from the room at an average rate of 0.75 kW. The heater is turned off after some time when the temperatures of the room air and oil are measured to be 20°C and 60°C, respectively. Taking the density and the specific heat of oil to be 950 kg/m3 and 2.2 kJ/kg⋅°C, determine the second-law efficiency for this process.arrow_forwardA 12-cm × 18-cm circuit board houses on its surface 100 closely spaced logic chips, each dissipating 0.06 W in an environment at 40°C. The heat transfer from the back surface of the board is negligible. If the heat transfer coefficient on the surface of the board is 10 W/m2·K, determine (a) the heat flux on the surface of the circuit board, in W/m2; (b) the surface temperature of the chips; and (c) the thermal resistance between the surface of the circuit board and the cooling medium, in °C/W.arrow_forwardA cylindrical fuel rod (k = 30 W/m•K) of 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel rod generates heat uniformly at a rate of 100 MW/m3, and the average temperature of the cooling water is 115°C with a convection heat transfer coefficient of 2500 W/m2.k. The operating pressure of the cooling water is such that the surface temperature of the fuel rod must be kept below 200°C to avoid the cooling water from reaching the critical heat flux (CHF). The critical heat flux is a thermal limit at which a boiling crisis can occur Determine the temperature at the surface of the rod. What can you do to lower the temperature aty the surface?arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning