C:An aluminum fin [k=200 W/m C] 3.0 mm thick Z is fin width=20 cm and 7.5 cm long protrudes from a wall, as Figure. The base is maintained at 300°C, and the ambient temperature is 50 C with h=10 W/m2 C. Calculate the heat loss from the fin per unit depth of material. +/dx/+ dqhPds (I)
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- 2-88 A 1.5-mm-diameter stainless-steel rod [k = 19 W/m.°C] protrudes from a wall maintained at 45°C. The rod is 12 mm long, and the convection coefficient is 500 W/m² . °C. The environment temperature is 20°C. Calculate the temperature of the tip of the rod. Repeat the calculation for h = 200 and 1500 W/m² . °C.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 large 100-mm thick steel plate is initially at uniform temperature T = 180°C at time t = 0. Both sides of the plate are exposed to 30°C oil with convection coefficient h = 1500 W/m².K. The thermal conductivity, heat capacity, and density of the steel are k = 38 W/m-K, cp = 485 J/kg-K, and p = 7800 kg/m³. a) Find the temperature at the center of the slab when t = 125 s. b) Find the temperature at the surface of the slab when t=125 s.
- Both ends of a 32 cm long rod are maintained a constant temperature of 100 °C. Dimensions and thermal parameters of the rod are as follows: Diameter D = 2 cm Convection coefficient h = 10 W/m2K Ambient temperature T¥ = 20 °C Thermal conductivity k = 10 W/mK What is the midpoint temperature of the rod?Q2) A straight rectangular fin has a length of 2.5 cm and a thickness of 1.5 mm protrudes from a wall has temperature of 200°C. The thermal conductivity of the fin is 50 W/m.°C, and it is exposed to a convection environment at 20°C and h=500 W/m."C. Calculate the fine effectiveness.1- Fin question {(b) (Accounting the heat transfer at the end)} 2- Derive a nodal equation for analysis of the node(n) in the Figure below 1 n 3- Aluminum plate having a thickness of 4cm and initial temperature is 200 °C. The plate is subjected to a convection with h= 500 w/m².°C and T= 25 °C. Using lumped heat method, calculate the temperature at time of 24.2 sec. Take the density = 2707 kg/m³ , Cp =896 j/kg. °C , k= 204 w/m. °C
- Q1/ A thick wall consists two layers of Gypsum, insulation and brick as shown in figure below. The ambient temperature is 20 °C and heat transfer coefficient is 5 W/m2. K in the left side. The surface temperature of right side is 45 °C. find the heat losses per meter length. What will happen if the insulation's thickness * .increases by 25% Gypsum k = 0.04W/m. K T = 45 °C h=5 W/m'. K T. = 20 °C 5 cm Insulation k = 0.04W/m. K Brick k = 0.69 W/m. KHeat Transfer for Mechanical Engineering Problem 7/4 A 70 mm x 70 mm plate is cooled by convection heat transfer to ambient air having To = 35°C and h = 75 W/m². °C. The temperature of the plate (Tb) is 90°C. In order to increase heat transfer, 49 conical fins are attached to the surface of the chip. The diameter (D) at the fin base 3 mm. The fin length (L) is 25 mm. Assume that the thermal conductivity of the fin is 300 W/m. °C. Find the total heat transfer from the plate to air. ^^^^^^^ Tb To, hQ2: 0.2 m diameter, 4 mm thick, k-120 W/m.ºC disc is welded to 10 cm diameter hot bar at 120 °C (heater). The system is exposed to air at 20 °C, heat transfer coefficient is 12 W/m².°C. Calculate the rate of heat transfer through the disc.
- The fin shown in Figure is insulated on the perimeter. The left end has a constant temperature of 100 °C. A positive heat flux of q = 5000 W/m² acts on the right end. Let Ky = 10 W/(m °C) and cross-sectional area A = 0.1 m2 Determine the temperatures at L/4, L/2, 3L/4, and L, where L = 0.8 m. 4-0.1 m T-100 C 5000 W/mQ2/ A thermopane window consists of two pieces of glass 7 mm thick that enclose an air space 7 mm thick. The window separates room air at 20°C from outside ambient air at -10°C. The convection coefficient associated with the inner (room-side) surface is 10 W/m? K. If the convection coefficient associated with the outer (ambient) air is 80 W/m? K, what is the heat loss through a window that is 0.8 m long by 0.5 m wide? Neglect radiation,[ kglass- 1.4 W/m-K: kair -0.0245 W/m-K] Window, 0.8 m x 0.5 m Glass Air T 20 °C hi = 10 W/m2 K Air L=0.007 m To-10 °C ho = 80 W/m2-K Air#m 3 E D C F3 $ 4 R F Ac = 1m² V Too,1=1 K h₁ = 1 W/m²K (5) Consider a wall (as shown above) of thickness L=1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h = 1 W/m²K and an ambient temperature T.= 1 K. Heat generation inside the wall is q=1W/m³. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). 44 % 5 Q Search F5 T G T₁ B x=0 * A 6 q=1 W/m³ k= 1W/mK L=1m F6 Y H F7 & 7 T₂ x= 1 m U N Top 2 = 1 K h₂=1 W/m²K PrtScn F8 8 Home M F9 ( 9 K End F10 0 L PgUp