Question

In: Physics

A long solid bar (k = 28 W/m·K and α = 12 × 10−6 m2/s) of...

A long solid bar (k = 28 W/m·K and α = 12 × 10−6 m2/s) of square cross section is initially at a uniform temperature of 32°C. The cross section of the bar is 20 cm × 20 cm in size, and heat is generated in it uniformly at a rate of ??̇ = 8 × 105 ??⁄??2. All four sides of the bar are subjected to convection to the ambient air at T∞ = 30 °C with a heat transfer coefficient of h = 45 W/m2·K. Using the explicit finite difference method with a mesh size of Δx = Δy = 10 cm, the centerline temperature after 20 minutes is desired. (a) Obtain the finite-difference nodal equations required to solve this problem and (b) Determine the upper limit of the time step that can be used to ensure numerical stability of the explicit finite-difference solution.
Do not solve fo the temperatures. Only construct the nodal equations and determine the limit on ∆t.

Solutions

Expert Solution


Related Solutions

1. A thick metal plate (alpha = 3.5 x 10-6 m2/s and k = 0.7 W/m-K),...
1. A thick metal plate (alpha = 3.5 x 10-6 m2/s and k = 0.7 W/m-K), initially at a uniform temperature of 100oC, is suddenly exposed to a convection environment of water at 20oC, giving a very large convection coefficient. a. Sketch the surface heat flux, q", as a function of time b. Using an explicit numerical scheme with a time step of 60 s, calculate the time required for the temperature to change 80 mm from the surface.
A long, cylindrical, electrical heating element of diameter D= 10 mm, thermal conductivity k= 240 W/m·K,...
A long, cylindrical, electrical heating element of diameter D= 10 mm, thermal conductivity k= 240 W/m·K, density ρ= 2700 kg/m3, and specific heat cp= 900 J/kg·K is installed in a duct for which air moves in cross flow over the heater at a temperature and velocity of 27°C and 15 m/s, respectively. (a) Neglecting radiation, estimate the steady-state surface temperature when, per unit length of the heater, electrical energy is being dissipated at a rate of 1500 W/m. (b) If...
A nuclear fuel element is in the form of long solid cylindrical rod (k=0.85 W/mK) of...
A nuclear fuel element is in the form of long solid cylindrical rod (k=0.85 W/mK) of diameter 14 mm is generating heat at an uniform rate of 0.45×108 W/m3 because of nuclear fission. Heat is transfer to pressurized cooling water at 300 0C and surface heat transfer coefficient is 4500 W/m2k. calculate the maximum temperature in the fuel rod in the system. What is the change in Tmax if the fuel element is encapsulated in a thin metal cladding of...
A steam generator consists of a bank of stainless stell (k=15 W/m·K) tubes habing the core...
A steam generator consists of a bank of stainless stell (k=15 W/m·K) tubes habing the core configuration of CF7.0-5/8J and an inner diameter of 13.8 mm. The tubes are installed in a plenum whose square cross section is 0.6 m on a side, thereby providing a frontal area of 0.36 m2. Combustion gases whose propertires may be aproximated as those of atmospheric air, enter the plenum at 900 k and pass in cross flow over the tubes at 3 kg/s....
A wall is constructed of two layers of 2-cm-thick sheetrock (k = 0.17 W/m·K) separated by...
A wall is constructed of two layers of 2-cm-thick sheetrock (k = 0.17 W/m·K) separated by 16 cm by wood studs (k = 0.11 W/m·K) whose width is 5 cm. The studs are placed vertically 55 cm apart, and the space between them is filled with stagnant air (16 by 55 cm) as insulation (k = 0.026 W/m·K). Pay attention to the measurements! The house is maintained at 20°C and the ambient temperature outside is ?9°C. Taking the heat transfer...
A steam generator consists of a bank of stainless stell (k=15 W/m·K) tubes habing the core...
A steam generator consists of a bank of stainless stell (k=15 W/m·K) tubes habing the core configuration of CF7.0-5 and an inner diameter of 13.8 mm. The tubes are installed in a plenum whose square cross section is 0.6 m on a side, thereby providing a frontal area of 0.36 m2. Combustion gases whose propertires may be aproximated as those of atmospheric air, enter the plenum at 900 k and pass in cross flow over the tubes at 3 kg/s....
Let W be a discrete random variable and Pr(W = k) = 1/6, k = 1,...
Let W be a discrete random variable and Pr(W = k) = 1/6, k = 1, 2 ,....., 6. Define X = { W,  if W <= 3; 1,  if W >= 4; } and Y = { 3,  if W <= 3; 7 -W,  if W >= 4; } (a) Find the joint probability mass function of (X, Y ) and compute Pr(X +Y = 4). (b) Find the correlation Cor(X, Y ). Are X and Y independent? Explain.
USE EXCEL TO SOLVE After heat treatment, the 2-cm thick metal plates (k = 180 W/m·K,...
USE EXCEL TO SOLVE After heat treatment, the 2-cm thick metal plates (k = 180 W/m·K, ρ = 2800 kg/m3, and cp = 880 J/kg·K) are conveyed through a cooling chamber with a length of 10 m. The plates enter the cooling chamber at an initial temperature of 500°C. The cooling chamber maintains a temperature of 10°C, and the convection heat transfer coefficient is given as a function of the air velocity blowing over the plates h = 33V0.8, where...
1. If n=28, x¯ (x-bar)=50, and s=6, find the margin of error at a 95% confidence...
1. If n=28, x¯ (x-bar)=50, and s=6, find the margin of error at a 95% confidence level (use at least two decimal places) 2. What is the margin of error for a poll with a sample size of 2400 people? Round your answer to the nearest hundredth of a percent. % 3. If you want a poll to have a margin of error of 3.24%, how large will your sample have to be? Round your answer to the nearest whole...
The average weather conditions are net radiation = 40 W/m2; air temperature = 28 .5° C;...
The average weather conditions are net radiation = 40 W/m2; air temperature = 28 .5° C; relative humidity = 55 percent; and wind speed = 2.7 m/s at a height of 2 m. Calculate the open water evaporation rate in millimeters per day using the energy method, the aerodynamic method, the combination method, and the Priestley-Taylor method. Assume standard atmospheric pressure is 101 kPa and Z0 is 0.03 cm.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT