1. Question 1- Laplace Equation: Leibmann's Method The four sides of a square plate of side 12cm, made of homogenous material, are kept at a constant temperature 0°C and 100°C as shown in Figure 1. Using a grid of mesh 4cm and applying Leibmann's method, perform up to four (4) iteration to find the temperature at the various mesh points.
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- 1.4 To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in W/m K. Problem 1.41.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.
- As a designer working for a major electric appliance manufacturer, you are required to estimate the amount of fiberglass insulation packing (k = 0.035 W/m K) that is needed for a kitchen oven shown in the figure below. The fiberglass layer is to be sandwiched between a 2-mm-thick aluminum cladding plate on the outside and a 5-mm-thick stainless steel plate on the inside that forms the core of the oven. The insulation thickness is such that the outside cladding temperature does not exceed 40C when the temperature at the inside surface of the oven is 300C. Also, the air temperature in the kitchen varies from 15Cto33C, and the average heat transfer coefficient between the outer surface of the oven and air is estimated to be 12.0W/m2K. Determine the thickness of the fiberglass insulation that is required for these conditions. What would be the outer surface temperature when the inside surface of the oven is at 475C?The heat conducts through the shape below. The temperature of the right face is 93 °C, while the left face is at 23 °C. If the top and bottom faces are completely insulated, and the thermal conductivity of the material decreases with decreasing temperature. * Assume that the thermal conductivity is 100 at 23, decreased to 10 at 93. A) Sketch the temperature profile inside the plate. B) If both sides of the plate in the above problem is exposed to air: Left side (h = 20 W/m2K, TL = 20 °C) and right side (h = 90 W/m2K). Calculate the temperature of the air on the right side.The walls of the flat furnace are connected by two insulating layers A and B. The temperature of the insulating layer A facing the inside of the Furnace is 800°C and the temperature of the outside air is 60°C. Find the temperature of the interface between the two insulation layers when the thickness of insulation layer A is 150 mm, its thermal conductivity is 0.05 W/m℃, the thickness of insulation layer B is 240 mm, and its thermal conductivity is 0.15 W/m℃
- A 1 in. o.d. (outer diameter) tube reactor is insulated with a 3 inch layer of asbestos. If the temperature of the outer surface of the insulation is 100 °F and the rate of heat loss per foot of reactor length is 50 BTU/hr, what must the temperature of the inside of the reactor be? [for asbestos, k = 0.105 BTU/hr ft °F]Three (3) bricks, specifically A, B, and C were arranged horizontally in such a way that it can be illustrated as a sandwich panel. Consider the system to be in series and in the order of Brick A, Brick B and Brick C. The outside surface temperature of Brick A is 1,500℃ and 150 ℃ for the outside surface of Brick C. The thermal conductivities for Brick A, Brick B and Brick C, are 2 ?/? °? , 0.50 ?/? °? , 60 ?/? °?. The thickness of Brick A and Brick C are 50 cm and 22 cm. The rate of heat transfer per unit area is 1,000 ?/?2 . Determine the following: The thickness of Brick B in the unit of mm. Assume that all the conditions were retain except that the thickness of Brick B was increased to 800 mm, what is the new value for the rate of heat transfer per unit area in ???/ℎ? . ??2 please explain the principles to solve thisTwo bars A and B, each of length 2m and cross sectional area 1m^2, are placed end to end. Their thermal conductivities are kA = 339 W/mK and kB = 837 W/mK . The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K. What is the temperature at the interface between A and B?
- In a glass plant in Cavite, a furnace has fire-brick walls made up of the following two materials in series : Non-corrosive brick as inner layer (material 1) Clay brick as outer layer (material 2) Thickness 4.5 inches 8 inches Thermal conductivity k1 k2 The temperature inside the furnace (inside wall surface of the non-corrosive brick) is found to be 1105 oF while the outside temperature (outside wall surface of clay brick) is 365 oF. This is not the desired temperature inside the furnace so engineers thought of lagging the furnace walls with another material to reduce heat loss. The additional lagging material consists of magnesia layer which is 2 inches thick and has a thermal conductivity of 0.04 Btu /h.ft.oF. During a test run on the furnace with the magnesia lagging material now, new temperature readings were recorded : Point of measurement Temperature reading Inside furnace (inside wall surface of non-corrosive brick 1355 oF Interface between…A coil-shaped cooling pipe is made of SS-304 material. This pipe is 1 ft long, 0.4 inch outside diameter, and inch inside diameter. This coil cooling pipe is used to cool the water in the bath. The temperature of the inner coil pipe is 40oF while the outer coil in contact with water is 80oF. The thermal conductivity of SS-304 is a function of temperature where k(T) = 7.75 + (7.78 x 10-3).T where k is in Btu/h.ft.oF and T is in oF. Calculate the rate of heat dissipation in watts! (1287.7)The compartment below is used as a freezer of refrigerator compartment. Inner wall is at -10 C and outer wall is at 20 C. Insulator with a thermal conductivity of 0.040 W/(mK) is used to prevent the heat losses from the compartment. The shape is in square form with a side of 1.3 m and unit width into the page. Determine the amount of the heat load if the thickness of the insulator is 2 cm? *