13.4 The rod of 1-in. radius shown in Figure P13-4 generates heat internally at the rate of uniform Q = 10,000 Btu/(h-ft) throughout the rod. The left edge and perimeter of the rod are insulated, and the right edge is exposed to an environment of T = 100°F. The convection heat-transfer coefficient between the wall and the environment is h = 100 Btu/(h-ft²°F). The thermal conductivity of the rod is K = 12 Btu/(h-ft-°F). The length of the rod is 3 in. Calculate the temperature distribution in the rod. Use at least three elements in your finite element model. 1-in. radius L= 3 in. T = 100 F Figure P13-4

13.4 The rod of 1-in. radius shown in Figure P13-4 generates heat internally at the rate of uniform Q = 10,000 Btu/(h-ft) throughout the rod. The left edge and perimeter of the rod are insulated, and the right edge is exposed to an environment of T = 100°F. The convection heat-transfer coefficient between the wall and the environment is h = 100 Btu/(h-ft²°F). The thermal conductivity of the rod is K = 12 Btu/(h-ft-°F). The length of the rod is 3 in. Calculate the temperature distribution in the rod. Use at least three elements in your finite element model. 1-in. radius L= 3 in. T = 100 F Figure P13-4

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.

Chapter7: Forced Convection Inside Tubes And Ducts

Section: Chapter Questions

Problem 7.1DP

See similar textbooks

Similar questions

In an absorption refrigerator, the energy driving the process is sllPplied not as work, but as heat from a gas flame. (Such refrigerators commonly use propane as fuel, and are used in locations where electricity is unavailable. *) Let us define the following symbols, all taken to be positive by definition: Qf = heat input from flame Qe = heat extracted from inside refrigerator Qr = waste heat expelled to room Tf = temperature of flame Te temperature inside refrigerator Tr = room temperature Explain why the "coefficient of performance" (COP) for an absorption refrigerator should be defined as Qc/Qf.
Goal Solve for the performance coefficient of a refrigerator using a five-step process the includes:1. Making a state table.2. Making a process table.3. Calculating the totals for Work, Heat, and Internal-Energy-Change.4. Identifying the heat input (cold reservoir) and output (hot reservoir).5. Calculating the performance coefficient of the refrigerator.Problem Shown in the figure to the right is a cyclic process undergone by a refrigerator. Your refrigerator shall use 5.0 moles of helium gas (monatomic). During the process a->b, the volume increases by a factor of 3.0. Solution- (1) Fill in the State Table (all pressures in Pascals, all volumes in cubic meters, all temperatures in K). Pressure Volume Temperature a b c (2) Fill in the Process Table (all entries in Joules). Work Heat dU a->b b->c c->a (3) Find the Totals: Work = J Heat = J dU = J (4) Find the heat input (from "cold…
Calculate the power of the submarine’s electrical heater needed, to maintain the interior of outer hull at 30°C. The exterior of outer hull is 10°C. (Assume heat of the submarine is only lost across the outer hull)
In an absorption refrigerator, the energy driving the process is sllPplied not as work, but as heat from a gas flame. (Such refrigerators commonly use propane as fuel, and are used in locations where electricity is unavailable. *) Let us define the following symbols, all taken to be positive by definition: Qf = heat input from flame Qe = heat extracted from inside refrigerator Qr = waste heat expelled to room Tf = temperature of flame Te temperature inside refrigerator Tr = room temperature Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Tf, Te, and Tr alone.
1. A heat exchanger is located on the roof of a warehouse to heat the air in winter. It is a coil-shaped pipe into which water vapor enters at 0.1 MPa and 300 °C and leaves with a quality of 30%. The warehouse has the following dimensions: 80m x 160m x 10m. The air must be heated from 5°C to 22°C. a. What must be the mass flow rate of the water to heat the air in less than half an hour? b. We want to cool the steam from the exchanger outlet and bring it up to 50 °C. For this, a mixing chamber with water at 20 °C is used, what will be the proportion of the steam mixture? c. The exchanger is damaged and only liquid water can be used at the same pressure (inlet T. 1 °C below saturation and outlet T. at 30°C). How long does it take to heat the air with the same flow of water?
3. A steel pipeline 2”sch 40 (k = 45W/mK) contains saturated steam at 121.1oC. the line is insulated with 25.4 mm asbestos (k = 0.182W/mK). Assuming that the inside temperature of the metal wall is at 121.1oC and the outer surface of the insulation is at 26.7oC, calculate the heat loss for 30.5m of pipe.
You are designing a 3m x 3m floor with radiant heating. The floor has 12 parallel pex pipes (k = 40 W/mK) of L = 3m, OD = 25mm and ID = 20mm. Hot water (TInfintiy 1 = 90oC, h = 200 W/m2K) runs through the pipes continuously. The surface below the pipes is perfectly insulated. Above the pipes, there is a 3mm layer of bonding material (? = 12 W/mK) and a 9mm layer of tile (k = 2 W/mK). Above the tile, there is air (TInfinity 2 = 25oC, h = 20 W/m2K). Properties of Air: k = 0.025 W/mK, Pr = 0.72, v = 1.847 x 10−5, u = 16.84 x 10−6, p = 1.2 kg/m3, B = 1/Tf (ideal gas), Hint: Assume that the “layer” of pipe starts at the center point (e.g. for conduction purposes, the pipe is OD divided by 2 thick). For convection, consider the entire pipe surface. a) What is the total heat rate entering the room above the floor? b) What is the temperature of the top of the tile?
A solar-energy collector produces a maximum temperature of 200 C. The collected energy is used in a cyclic heat engine that operates in a 7 C environment. What is the maximum thermal efficiency? What-if Scenario What would the maximum efficiency be if the collector were redesigned to focus the incoming light to enhance the maximum temperature to 500 C ?
(a) Compare flat plate, parabolic collectors to be used for a solar thermal plant with respect to (i) temperature, (ii) concentration ratio, (iii) suitability, and (iv) absorber type. (b) A tidal power plant of single basin type, has a basin area of 25 x 10 to power 6 m2. The tide has a range of 10m. The turbine however, stops operating when the head on it falls below 2 m. Calculate the energy generated in one filling process, in KWh if the turbine generator efficiency is 75%. (Density of sea water = 1025 kg/m2)
A six-cylinder refrigerant 22 compressor operating at 29 r/s indicate a refrigerating capacity of 96.4 kW and a power requirement of 28.9 kW at an evaporating temperature of 5°C and condensing temperature of 50°C. The performance data are based on 3°C liquid sub-cooling and 8°C superheating of the suction gas entering the compressor. The cylinder bore is 67 mm and the piston stroke is 57 mm. Compute (a) the clearance volumetric efficiency if the clearance volume is 4.8 percent, (b) the actual volumetric efficiency, and (c) the compression efficiency.
An ammonia compressor of an ice plant is driven by 175 kW electric motor. The belt transmission efficiency is 94.5% while the mechanical efficiency of the compressor is 85%. The water used in making ice is supplied to the 300-lb block ice per can at 18OC temperature and ice leaves the plant at -6.5OC. The coefficient of performance is 2.0. Heat losses conducted into the brine are 15% of the chilling and freezing load. Calculate: a) The refrigeration capacity b) The ice plant capacity c) The number of ice cans needed if brine temperature is -7.50OC.
The heat transfer rate from a refrigerator consuming 9 kJ of electrical energy per minute to the room environment is 400 W. In this case:a) The heat extraction rate from the internal environment of the refrigerator (kJ/s),b) Calculate the performance coefficient of the refrigerator.