Q1: Find expression for nondimensionalized one-dimensional transient conduction problem. (25 pt)
- pes The one dimensional transient conduction can be expressed as: 22T 1 OT Oxzat a. Rewrite this equation with finite differences using forward differencing in time and central differencing in space. b. Since you are using forward time differencing, the resulting algebraic equation will be explicit. What is the condition for stability in explicit finite differences? c. To solve the resulting algebraic equation, you need two boundary conditions. What else do you need?
Two-Dimensional Steady and Transient Conduction - Cooling a very
large scale microelectronic chip,
A simplified
representation for cooling in very large-scale integration (VLSI)
of microelectronics is shown in the sketch below. A silicon chip is
mounted in a dielectric substrate, and one surface of the system is
convectively cooled, while the reminding surfaces are well
insulated from the surrounding. The problem is rendered two
dimensional by assuming the system to be very large in the
direction perpendicular to the paper....
4. Which one of the following is the correct expression for one-dimensional constant properties, heat conduction equation for a cylinder with heat eady-e generation r dr qun 5. A 10 cm diameter sphere maintained at 30°C is buried in the earth at a place where the ·K. The depth to the centerline is 24 cm, and the thermal conductivity, k = 1.2 W/m earth surface temperature is 0°C. Calculate the heat loss from the sphere. (A) 25.3W (D)42.4W (E)20.0 w...
Use k=320 W/mK for your calculation Two-Dimensional Steady and transient Conduction - Heat Sink Aluminum fins with triangle profiles (k = 370 .p=2800 900 ke), shown in the accompanying figure, are used to remove heat from a surface whose temperature is T, = 150°C. The temperature of the surrounding air is 20°C. The natural heat transfer coefficient associated with the surrounding air is h = 190 Determine the temperature distribution along a fin. 20 mm 150°C
Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 50 W/m·K and thickness L = 0.35 m, with no internal heat generation Determine the heat flux and the unknown quantity for each case and sketch the temperature distribution, indicating the direction of the heat flux.
W kg m-K m3 Two-Dimensional Steady and transient Conduction - Heat Sink Aluminum fins with triangle profiles (k = 290 p = 2800 ,C= 900 shown in the accompanying figure, are used to remove heat from a surface kg-K whose temperature is T, = 150°C. The temperature of the surrounding air is 20°C. The natural heat transfer coefficient associated with the surrounding air is h = 190, Determine the temperature distribution along a fin. w m-K Air To, h 20...
7. Find the solution of the heat conduction problem 100uzz = ut, 0 < x < 1, t > 0; u(0,t) 0, u1,t 0, t>0; In Problem 10, consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all t0. Find an expression for the temperature u(,t) if the initial temperature distribution in the rod is the given function. Suppose that a
Problem 2 (8 pt) : Find the expression of voltage drop on 2Ω resistor in figure 2. 1s10 A 4Ω 8Ω 10Ω 2Ω 3Ω 3010 v + 6Ω Figure 2
Problem 2 (8 pt) : Find the expression of voltage drop on 2Ω resistor in figure 2. 1s10 A 4Ω 8Ω 10Ω 2Ω 3Ω 3010 v + 6Ω Figure 2
- Multiple Choice Circle one or more 10. In the transient 1-0 heat conduction solution, will a large h result in a large tempenture variation on - a small temperature variation within solid? (A) a large temperature variation B) a small temperature variation 11. In the transient I-D heat conduction solution, will a large h result in a large or small temperature difference betn the solid surface and surrounding fluid? Al a large temperature difference (B) a small temperature difference...
Use k=320 W/mK for your calculation
w m-K Two-Dimensional Steady and transient Conduction - Heat Sink Aluminum fins with triangle profiles (k = 370- p=2800 kg 900 shown in the accompanying figure, are used to remove heat from a surface whose temperature is Tg = 150°C. The temperature of the surrounding air is 20°C. The natural heat transfer coefficient associated with the surrounding air is h = 190- Determine the temperature distribution along a fin. w m- T., 20 mm...