A spherical container having an outer radius r2 and inner radius r1 (with thermal conductivity, k) is filled with radioactive material generating constant heat at a rate of qdot. Fluid flows across the container at Tinfinity and convection coefficient h. Obtain a relation for the variation of temperature through the spherical container assuming steady state.

A spherical container having an outer radius r2 and inner radius r1 (with thermal conductivity, k) is filled with radioactive material generating constant heat at a rate of qdot. Fluid flows across the container at Tinfinity and convection coefficient h. Obtain a relation for the variation of temperature through the spherical container assuming steady state.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.60P: 1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a...

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3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.
2.44 To determine the thermal conductivity of a long, solid 2.5-cm-diameter rod, one half of the rod was inserted into a furnace while the other half was projecting into air at . After steady state had been reached, the temperatures at two points 7.6 cm apart were measured and found to be and , respectively. The heat transfer coefficient over the surface of the rod exposed to the air was estimated to be 22.7 . What is thermal conductivity of the rod?
2.2 A small dam, which is idealized by a large slab 1.2 m thick, is to be completely poured in a short Period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m K.
2.43 A turbine blade 6.3 cm long, with cross-sectional area and perimeter , is made of stainless steel . The temperature of the root, , is . The blade is exposed to a hot gas at , and the heat transfer coefficient is K. Determine the temperature of the blade tip and the rate of heat flow at the root of the blade. Assume that the tip is insulated.
A cylindrical liquid oxygen (LOX) tank has a diameter of 1.22 m, a length of 6.1 m, and hemispherical ends. The boiling point of LOX is -179.4C. An insulation is sought that will reduce the boil-off rate in the steady state to no more than 11.3 kg/h. The heat of vaporization of LOX is 214 kJ/kg. If the thickness of this insulation is to be no more than 7.5 cm, what would the value of its thermal conductivity have to be?
3.5 In a ball-bearing production facility, steel balls that are each of 15 mm in diameter are annealed by first heating them to 870°C and then slowly cooling in air to 125°C. If the cooling air stream temperature is 60°C, and it has a convective heat transfer coefficient of , determine the time required for the cooling.
The handle of a ladle used for pouring molten lead is 30 cm long. Originally the handle was made of 1.9cm1.25cm mild steel bar stock. To reduce the grip temperature, it is proposed to form the handle of tubing 0.15 cm thick to the same rectangular shape. If the average heat transfer coefficient over the handle surface is 14 W/m K, estimate the reduction of the temperature at the grip in air at 21C.
2.46 The wall of a liquid-to-gas heat exchanger has a surface area on the liquid side of with a heat transfer coefficient of . On the other side of the heat exchanger wall flows a gas, and the wall has 96 thin rectangular steel fins 0.5 cm thick and 1.25 cm high as shown in the accompanying sketch. The fins are 3 m long and the heat transfer coefficient on the gas side is . Assuming that the thermal resistance of the wall is negligible, determine the rate of heat transfer if the overall temperature difference is .
A 0.6-cm diameter mild steel rod at 38C is suddenly immersed in a liquid at 93C with hc=110W/m2K. Determine the time required for the rod to warm to 88C.
The interior wall of a large, commercial walk-in type meat freezer is covered under normal operating conditions with a 2-cm thick layer of ice. One day, a power outage cuts electricity to the refrigeration system of the freezer. Estimate the time required to melt this layer of ice if it has a mass density of 700kg/m3 and a latent heat of fusion of 334 kJ/kg. Consider the air temperature inside the freezer to be 20C with a heat transfer coefficient of 2W/m2K for convection from the freezer surface to air, and clearly state the assumptions made in your calculations.
Water at a temperature of 77C is to be evaporated slowly in a vessel. The water is in a low-pressure container surrounded by steam as shown in the sketch below. The steam is condensing at 107C. The overall heat transfer coefficient between the water and the steam is 1100W/m2K. Calculate the surface area of the container that is required to evaporate water at a rate of 0.01 kg/s. Problem 1.16
1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a well-insulated 40-L tank of water that is initially at 300 K. If each heater dissipates 500 W, what is the time required for bringing the water temperature in the tank to 340 K? State your assumption for your analysis.