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. %3D

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. %3D

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter8: Natural Convection

Section: Chapter Questions

Problem 8.36P

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1.3 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.
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?
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.
1. A beverage cooler is in the shape of a cube, 42 cm on each inside edge. Its 3.0-cm thick wall are made up of plastic (kr = 0.050 W/mK). When the outside temperature is 20°C, how much ice will melt each hour? Tice is 0°C. 2. One of the possible mechanisms of heat transfer in human body is conduction through body fat. Suppose that heat travels through 0.03 m of fat in reaching the skin, which has a total surface area of 1.7 m² and a temperature of 34°C. Find the amount of heat that reaches the skin in half an hour, if the temperature at the body, interior is maintained at the normal value 37°C ? Thermal conductivity of body fat is k = 0.2 J/sm°C. 3. The air in a room is at 25°C and outside temperature is 0°C. The window of the room has an area of 2m² and thickness 2mm. Calculate the rate of loss of heat by conduction through window ? Thermal conductivity for glass is 1 Wm¯'degree!.
Q2: 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.
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?
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.
Determine the temperature distribution (nodal temperatures) of the structure shown in the figure using two equal-length, linear finite elements with the cross-sectional area of 1 m². The thermal conductivity is 10 W/m/°C. The left side is maintained at 300 °C. The right side is subjected to heat loss by convection with h = 1 W/m²/°C and T₁ = 30 °C. All other sides are insulated. T= 300 °C Exercise T₁ Insulated 20 m T₂ T3 T₁= 30 °C 43
#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
Q2/A thermopane window consists of two pieces of glass 7 mm thick that enclose an air space mm thick. The window separates room air at 20°C from outside ambient air at -10°C. The 7 convection coefficient associated with the inner (room-side) surface is 10 W/m2 K. If the convection coefficient associated with the outer (ambient) air is 80 W/m2 K, what is the heat loss through a window that is 0.8 m long by 0.5 m wide? Negleet radiation,[ kglass = 1.4 W/m-K: kair =0.0245 W/m-K] トL十LトL Window, 0.8 m x 0.5 m Glass Air! Ti 20 °C h; = 10 W/m2-K Air L = 0.007 m To.o = -10 °C ho = 80 W/m2-K Air
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.
Temperature distribution along the radius of a long cylindrical shell was found to be -2596.8 W/m2; -1558.1 W/m2; all quantities in SI units. linward T(r) = 365 +21.64 ln(r) Since the temperature is only dependent on radius (r), the heat transfer in this case is radially one- dimensional. The thermal conductivity of cylindrical shell is 36 W/m-K. The shell has inner diameter of 0.5 m and outer diameter of 1 m. Find out the heat flux at r = 0.3 m and at the outer surface of the tube. Justify if the heat transfer is radially outward or radially inward.