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Consider a short cylinder of radius r0 and height H in which heat is generated at a constant rate of
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- 2.34 Show that the temperature distribution in a sphere of radius . made of a homogeneous material in which energy is released at a uniform rate per unit volume , isarrow_forwardA plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.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
- A 300-ft-long section of a steam pipe whose outer diameter is 4 in passes through an open space at 50°F. The average temperature of the outer surface of the pipe is measured to be 280°F, and the average heat transfer coefficient on that surface is determined to be 6 Btu/h·ft2·°F. Determine (a) the rate of heat loss from the steam pipe and (b) the annual cost of this energy loss if steam is generated in a natural gas furnace having an efficiency of 86 percent, and the price of natural gas is $1.10/therm (1 therm = 100,000 Btu).arrow_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_forwardIn a thermal power plant, a horizontal copper pipe of "D" diameter, "L" length and thickness 0.6 cm enters into the boiler that has the thermal conductivity as 0.33 W/mK. The boiler is maintained at 105C and temperature of the water that flows inside the pipe is at 28C. If the energy transfer (Q) is 118922 kJ in 6 hours. Determine the Heat transfer rate, Surface area of the pipe and Diameter & Length of the pipe, if D = 0.016 L. Change in Temperature (in K) = Heat Transfer Rate (in W) = Surface Area of the Pipe (m2) =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_forwardSteam at T∞ 1 = 320°C flows in a cast iron pipe (k = 80 W/m · °C) whose inner and outer diameters are D1 = 5 cm and D2 = 5.5 cm, respectively (Figure Q2b). The pipe is covered with 3-cm-thick glass wool insulation with k = 0.05 W/m · °C. Heat is lost to the surroundings at T2 = 5°C by natural convection and radiation, with a combined heat transfer coefficient of h2 = 18 W/m2 · °C. Taking the heat transfer coefficient inside the pipe to be h1= 60 W/m2 · °C, determine; i) the rate of heat loss from the steam per unit length of the pipe; and ii) the temperature drops across the pipe shell and the insulation.arrow_forward10 m long pipe is being used to deliver steam through a processing plant. The inner radius of the pipe is r1 = 6 cm and the thickness of the pipe is 2 cm. Thermal conductivity k = 8 W/m⋅K and the average temperature steam flowing through the pipe is 160°C, the average convection heat transfer coefficient on the inner surface is given to be h = 20 W/m2⋅K. If the average temperature on the outer surfaces of the pipe is T2 = 70°C, (a) express the differential equation and the boundary conditions for steady operating conditions, (b) determine a relation for the variation of temperature in the pipe, and (c) evaluate the rate of heat loss (heat of conduction) from the steam through the pipe.arrow_forward
- Two metal rods of equal length-one aluminum, the other stainless steel-are connected in parallel with a temperature of 18.0 ∘C at one end and 110 ∘C at the other end. Both rods have a circular cross section with a diameter of 6.00 cm Determine the length the rods must have if the combined rate of heat flow through them is to be 17.5 JJ per second. If the length of the rods is doubled, by what factor does the rate of heat flow change?arrow_forwardConsider 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_forwardElectric 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/m^ 2 . C and T infty =30^ C , while the left face is exposed to h=75 W/m^ 2 C T infty =50^ C . What is the maximum allowable heat-generation rate such that the maximum tem perature in the solid does not exceed 300 degrees * C ?arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning