Heat_Transfer__Convection examples tmb rev

# Heat_Transfer__Convection examples tmb rev - Heat Transfer...

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Unformatted text preview: Heat Transfer Convection ENES 101 / 101H / 101Y Introductory Engineering Science Modes of Heat Transfer Heat transfer due to convection involves the energy exchange between a surface and an adjacent fluid (gas or liquid). If a solid body is exposed to a moving fluid having a different temperature, energy is carried or convected away from the fluid. Forced convection when a fluid is made to flow past the solid surface by an external agent (pump/fan) Free or natural convection where a warmer or cooler fluid next to the solid boundary causes circulation because of the density difference resulting from the temperature variation throughout a region of the fluid. Newton's Law of Cooling q = h A T = h A(Ts - T ) q rate of heat transfer (W or Btu/hr) A surface area (m2 or ft2) T temperature difference between T surface Ts and the fluid (K or oF) W m 2K h convective heat transfer coefficient Btu hr ft o F Example #3 A tent has a surface area of 30m . Suppose the tent contains a heater that generates 1800 Watts. a) If the outside temperature is 0 C and there is no wind, what will be the interior temperature? We are convecting 1800 W of energy from the air inside the tent to the tent walls, TWi = TWo = TS Then from the tent walls to the outside air. Assume tent wall is thin and it will not TWi=Two=TS Ti provide significant insulation To To o 2 Ti Example #3 (cont.) From Table 6.4 h is between 5 30 W/m K So assume that h = 7 W/m K Q = ho A(TS - To ) 1800W = 10 o TS =6 C o 2 inside air to inside tent surface h = 10 W/m K i 2 W 30m 2 (TS - To ) 2 m 2K ( outside tent surface to outside air on a calm night Q = hi A(Ti - TS ) W 1800W = 7 2 ( 30m 2 )(Ti - TS ) mK Ti = 14.57 o C ) Example #3b a) What is the heat output (W) required in order to maintain an interior temperature of 68 F? How many Btu/hr is this? o Convert 68oF to oC (6832)5/9 = 20 oC Q = hi A(Ti - TS ) W Q = 7 2 30m 2 ( 20 - 6 ) oC mK Btu / hr Btu Q = 2940W 3.412 = 10,031 1 W hr ( ) Example #3c a) Suppose the outside temperature is 0 C and the heat output is 2940W, but the wind velocity is 40 mph. What will be the temperature inside the tent in F? mi 1hr Given h = 5 + 10 v.8 1m -4 40 o o m = 17.9 hr 3600s 6.21x10 mi s W .8 .8 h = 5 + 10v = 5 + 10(17.9 ) = 105.44 2 mK Example #3c (cont) Tent surface temperature: Q = ho A(TS - To ) 2940W = 105.44 TS = 0.93 o C W 30m 2 TS - 0o C m 2K ( )( ) Inside temperature: Q = hi A(Ti - TS ) W 2940W = 7 2 30m 2 Ti - 0.93 o C mK Ti = 14.93 o C ( )( ) Combined Conduction/Convection Heat Transfer Most Heat Transfer problems involve more than one mode of heat transfer. Many involve Convection from fluid to a solid surface Conduction through homogeneous material Convection from solid to fluid Example #4 Wooden cabin with 2cm thick walls kwood = 0.1 W/mK A = 30 m2 Q = 1800 W hi = 5W/m2K ho = 20 W/m2K Example #4a a) Sketch temperature profile A=30m2 T i T si T so T =0C o o Wood Wall x = 2cm k = 0.1W/mK Example #4b a) T = 0 C, what is T ? convection (outside air to outside wood wall) o o i Q = ho A(TSo - To ) TSo = Q 1800W + To = + 0 =3o C W ho A 2 20 2 30m m K ( ) conduction (outside wood wall to inside wood wall) dT kA (TSi - TSo ) = dx x Qx 1800W ( 0.02m ) TSi = + TSo = +3 o C W kA 2 0 .1 30m mK TSi = 15 o C Q = -kA ( ) Example #4b (cont) convection (inside wood wall to inside Q = hi A(Ti - TSi ) Q air) Ti = + TSi = hi A Ti = 27 o C 1800W + 15 o C W 2 5 2 30m m K ( ) T =27 C i o T =15 C si o T =3 C so o T =0C o o 2 cm Example #4c a) What heat output (W) is required to maintain inside temp of ~68 F (20 C)? o kAo (TSi - TSo ) = hi A(Ti - TSi ) - To ) = x Q = ho A(TSo Ti - simplify:To Q= 1 x 1 + + ho A kA hi A 1 20W / m 2K 30m 2 Q = 1333.3W Q= ( )( ) 20 o C 0.02m 1 + + 2 ( 0.1W / mK ) 30m 5W / m 2K 30m 2 ( ) ( )( ) Example #4d a) Suppose Q=1800W, Ti = 72oF(22.2oC), To = 12oF( 11.1oC). What is x? Ti -To T Q= = = 1800W 1 x 1 R + + ho A kA hi A solving for x=0.03m or 3cm Radiation The energy is transferred via electromagnetic wave propagation. No medium is required. Works most efficiently in a vacuum, but also occurs in a medium. StefanBoltzman Law Radiant heat transfer is defined via the StefanBoltzman Law q = A T4 q rate of radiant energy emission (W or Btu/hr) A area of emitting surface (m2 or ft2) T absolute temperature (K or oR) Stefan Boltzman constant W -8 5.676 x10 m 2K 4 Btu 0.1714 x10 -8 hr ft 2 o R 4 Heat Transfer Temperature profile Ti T1 T2 T3 T4 To For steady state heat transfer (1) Q T Ti - To = = 1 t t t 1 A R + + + + hi k 1 k 2 k 3 ho Modes of heat transfer between Ti and T1 T1 and T2 T2 and T3 T3 and T4 T4 and To (2) (3) convection conduction conduction conduction convection h convective heat transfer coeff. t material thickness k material thermal conductivity ...
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