2. Determine k, thermal conductivity of a wall if q = 1000 kcal/m? -hr at thickness, k= 33 m 206
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- Determine k, thermal conductivity of a wall if q = 1000 kcal/m2 -hr at thickness, k = 33 mm and ∆t = 30°C.
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- The figure shows the cross section of a wall made of three layers. The thicknesses of the layers are L₁, L2=0.750 L₁, and L3 = 0.350 L₁. The thermal conductivities are k₁, k₂ = 0.840 k₁, and k3 = 0.780 k₁. The temperatures at the left and right sides of the wall are TH = 23 °C and Tc = -10 °C, respectively. Thermal conduction is steady. (a) What is the temperature difference AT2 across layer 2 (between the left and right sides of the layer)? If k2 were, instead, equal to 1.160 k₁, (b) would the rate at which energy is conducted through the wall be greater than, less than, or the same as previously, and (c) what would be the value of AT2? TH k₁ L₁ kg|kz kq L₂ L3 TcQuestion # 3: Design a heat equation model to determine the solution. The physical data needed to model for copper includes: density p= 5.82g/cm', thermal conductivity K = 0.095cal / cm sec C, %3D specific heat O =0.097cal / g C. The initial temperature is 70 sin(T x/100) C and the ends %3D are kept at 0 C of a laterally insulated copper bar of 120 cm long. Determine the time its goint to take for the maximum temperature in the bar to drop to 100 C ?= 73,0 GPa As = 1500 mm ² ) rod and a brass (Eg = 100 G+Pa t are stress-free and and AB = 2000mm²) rod. At 25°C, The rods of 1.00mm exosts between them. дар expansion If the coefficrear of thermal as of = 14 [106 m/m'c] that of brass a f = 11 [10° ⁰ m/m²c], A Temperature increased to 350°C.. a A Stech | E₁ kuhat is intermidate Temperature (umt°C) that system must be taken to in order to clase the of 1.00mm? A it Steel 1.00mm → K B Brass 1.50000m. for steal is taken as and 1.0 ME the gap 15
- As shown in the sketh below, a steam pipe of 0.12-m inside diameter is insulated with a layer of calcium silicate. 1. Ts. 1} Steam 12. T8.2} Insulation (a) If the insulation is 27.5 mm thick and its inner and outer surfaces are maintained at T1 = 800 K and T2 = 490 K, respectively. what is the rate of heat loss per unit length (q') of the pipe, in W/m? (b) Determine the rate of heat loss per unit length (q'), in W/m, and outer surface temperature T2, in K, for the steam pipe with the inner surface temperature fixed at T₁ = 800 K, inner radius r₁ = 0.06 m, and outer radius r₂ = 0.14 m. The outer surface is exposed to an airflow (To = 25°C) that maintains a convection coefficient of h = 25 W/m²-K and to large surroundings for which Tsur = To = 25°C. The surface emissivity of calcium silicate is approximately 0.8.Problem 1. 67 pts bar shown below, determine the temperatures at Nodes 2 and 3. Assume 1-D heat transfer that only occurs in the x-direction as the upper and lower 1-D Heat Transfer with Conduction. For the 1-D composite boundaries of the elements are insulated. Assume the cross-sectional area is the same for all elements, A=0.01 m?. For Element 1, let the thermal conductivity be 100 W/(m °C). For Element 2, let the thermal conductivity be 110 W/(m °C). For Element 3, let the thermal conductivity be 120 W/(m °C). The left end of the bar has a constant temperature of 120 °C (at Node 1) and the right end has a constant temperature of 276 °C (at Node 4). Insulated, 1-d heat transfer in x-dir Node 1 Node 2 Node 3 Node 4 +x 120°C E1 E2 ЕЗ 276°C 1 mm 2 mm 0.5mm InsulatedA boiler furnace wall must have a heat loss no greater than 700 Btu/hr~ft2 and is madeof a material with a thermal conductivity of 0.60 Btu/hr~ft~F. The inner wall surfacetemperature is '2000°F, and the outer surface temperature is 800°F. What wall thick~ness is required?
- As shown in the sketh below, a steam pipe of 0.12-m inside diameter is insulated with a layer of calcium silicate. "2. Ta2} 1. Ta,1} Steam Insulation (a) If the insulation is 10 mm thick and its inner and outer surfaces are maintained at T, = 800 K and Ta = 490 K. respectively,. what is the rate of heat loss per unit length (q) of the pipe, in W/m? (b) Determine the rate of heat loss per unit length (d), in W/m, and outer surface temperature T,2, in K, for the steam pipe with the Inner surface temperature fixed at T = 800 K, inner radius = 0.06 m, and outer radius n = 0.18 m. The outer surface is exposed to an airflow (T 25°C) that maintains a convection coefficient of h = 25 W/m2-K and to large surroundings for which Tur = T, = 25°C. The surface emissivity of calcium silicate is approximately 0.8.A slab of thickness L = 0.1 m and of thermal conductivity k = 1 W/mK has the temperature distribution as T(x) = ax2 + bx + c. The boundary conditions; insulation at at x = L and a 100 W/m2 constant heat flux at x = 0. What is the temperature at the insulated surface if c = 5 °C?A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 300 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant O degrees C. Let u(x, t) be the temperature in the bar at x at timet, with t measured in seconds. Find u(x, t) and then u7 (2, 0.1). Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.
- Find the thermal resistance r (in hr - °F/BTU) and the equivalent R-value (in hr ft?. °F/BTU) of a typical frame 20' x 7.5" wall consisting of a 0.5" plaster board on the inside of the room, nominai 2 x 4 studs, and a 0.5" sheathing on the outside. The spaces between the studs are filled with an R-15 insulating foam. What is the heat loss (in BTU) through this wall in four hours if the inside temperature is 72°F and the outside temperature is 32°F? (Assume that the 15% of the wall's area are studs and the remaining 85% is filled with the insulating foam. Assume that the air is moving outside the wall.) r= 0.0805 x hr: OF/BTU R=0.09 x hr ft2. F/BTU AQ = BTU(C) The composite wall of a refrigerator consists of three different materials; A, B, and C. Two of the used materials have known thermal conductivity, ka = 30 W/m. K and kc=45 W/m. K, and known thickness, LA=0.20 m and Lc = 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB = 0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,0 = 20°C, an inner surface temperature of Ts,i = 600°C, and a refrigerator air temperature of To∞ = 800°C. The inside convection coefficient h is known to be 25 W/m?.K. What is the value of thermal conductivity for material B? T -T kg kc s, o kA Air T, h LA Figure 2: Composite wall configuration described in part C.A solid bar of length L = 4 m and diameter 200 mm is heated from 20 to 320 degrees celsius and restrained between two solid immovable walls. Young's modulus of the material is 90 GPa and the coefficient of thermal expansion is 22 x 10-6/°C. →Calculate the thermal strain, e, in micro-strain correct to two decimal places. micro-strain. Calculate the thermal stress, o, in megapascals (MPa) correct to two decimal places. E: σ: MPa. Hence calculate the force exerted by the bar in meganewtons (MN) correct to two decimal places: F MN. L
