Conduction Heat Transfer HANNA ILYANI ZULHAIMI

Transcription

1 + Conduction Heat Transfer HNN ILYNI ZULHIMI

2 + OUTLINE u CONDUCTION: PLNE WLL u CONDUCTION: MULTI LYER PLNE WLL (SERIES) u CONDUCTION: MULTI LYER PLNE WLL (SERIES ND PRLLEL) u MULTIPLE LYERS WITH CONDUCTION ND CONVECTION u CONDUCTION: CYLINDER u CONDUCTION: SHPERE u CRITICL RDIUS OF INSULTION

3 + Conduction: Plane Wall Δx First consider the plane wall where a direct application of Fourier s law may be made. Integration yields: T 1 Q k Δx ( T T1) Q Q heat rate in direction normal to surface T Δx Wall thickness T 1, T the wall face temperature plane wall surface area k thermal conductivity

4 + Conduction: Plane Wall u If k varies with T according linear rela3on :

5 + Heat flow through multilayer plane walls The temperature gradients in the three materials are shown, and the heat flow may be written: Q T T T T k kb kc Δx ΔxB Δxc T T composite wall Note: the heat flow must be the same through all sections. Solving these three equations simultaneously, the heat flow is written Q T1 T4 Δx / k + ΔxB / kb + Δxc / k c

6 + Heat flow through multilayer plane walls R cond Δx k n n Q R T1 T + R + R 4 B C composite wall Note: the heat flow must be the same through all sections. relation quite like Ohm s law in electric-circuit theory ΔT Q R overall R th the thermal resistances of the various materials th

7 + EXMPLE 1

8 + EXMPLE 1

9 + QUIZ 1 composite wall is formed of a.5-cm copper plate, a 3.-mm layer of asbestos, and a 5-cm layer of glass wool. The wall is subjected to an overall temperature difference of 560ºC. Calculate the heat flux through the composite structure. k copper 385 W/m.ºC k asbestos W/m.ºC K glass wool. W/m.ºC

10 THERML RESISTNCE NETWORKS u THE GENERLIZED FORM FOR THE THERML RESISTNCE NETWORK IS BSED ON THE ELECTRICL NLOGY u FOR PRLLEL PTHS, THE DRIVING FORCES RE THE SME FOR THE SME TERMINL TEMPERTURES, S PER FIGURE (3-19)

11 THERML RESISTNCE NETWORKS u TOTL HET TRNSFER u RESISTNCE THROUGH ECH LYER u OVERLL EQUTION u OVERLL RESISTNCE FOR PRLLEL FLOWS:

12 + HET FLOW THROUGH PLNE WLL B q? C D Construct the electrical analog

13 + B C D 1.1 Heat flow through plane wall D C B c B R R R R R R T T Q k x R n n cond Δ k x k x k x k x k x k x T T Q D D C C B B C C B B Δ + Δ + Δ Δ Δ + Δ / / / / 4 1

14 + NEWTON S LW OF COOLING FOR CONVECTION HET TRNSFER RTE Qconv h ( T T ) S S (W) 14 h TS T conv Rconv Q R Convection heat transfer coefficient conv 1 h S ( 0 C / W) R conv Convection resistance of surface Dr. Şaziye Balku

15 MULTIPLE LYERS WITH CONDUCTION ND CONVECTION u FOR SERIES OF LYERS WHERE SYSTEM THE FLUX THROUGH ECH LYER IS CONSTNT

16 MULTIPLE LYERS WITH CONDUCTION ND CONVECTION u THE FLUX THROUGH ECH LYER IS THE SME, SO: u IN TERMS OF RESISTNCE THIS RELTIONSHIP BECOMES:

17 MULTIPLE LYERS WITH CONDUCTION ND CONVECTION u IN OVERLL TERMS, CONSIDER THE DRIVING FORCE TO BE T 1 - T ND THEN EXPRESS THE OVERLL RESISTNCE S u SO THE OVERLL HET TRNSFER CN THEN BE EXPRESSED S

18 + HET CONDUCTION IN CYLINDERS 18 Steady-state heat conduction Heat is lost from a hotwater pipe to the air outside in the radial direction. Heat transfer from a long pipe is one dimensional Dr. Şaziye Balku

19 + LONG CYLINDERICL PIPE STEDY STTE OPERTION Q cond, cyl constant 19 Fourier s law of conduction Q cond, cyl r Q k cond cyl dr r r T 1, T dt dr kdt T 1 Q cond, cyl πlk T 1 ln( r T / r 1 ) Q cond, cyl πrl T 1 T R cyl R cyl ln( r / r1 ) πlk Dr. Şaziye Balku

20 + Heat flow through radial system Multilayer cylinder C B k r r k r r k r r T T L Q ) / ln( ) / ln( ) / ln( ) ( π Note: the heat flow, q must be the same through all layers!

21 + EXMPLE: Combination Conduction and Convection thick walled tube of stainless steel () having k 1.63 W/m.K with dimension of m ID and m OD is covered with a m thick layer of insulation (B), k 0.43 W/m.K. The inside wall temperature of the pipe is 811 K and outside surface of the insulation is at K. For a m length of pipe, calculate the heat loss and also the temperature at the interface between metal and insulation.

22 + NSWER

23 + NSWER

24 + CONDUCTION IN SPHERES 4 FOR SPHERICL SYSTEM (HOLLOW BLL) THE SME METHOD IS USED: Q cond, sph T 1 R T sph 4πr R sph r r 1 4πr 1 r k

25 + CRITICL RDIUS OF INSULTION CYLINDER 5 Q R T 1 ins T + R conv T1 T ln( r / r1 ) 1 + πlk h(πr d Q/ dr 0 L) show r cr, cylinder k h Thermal conductivity External convection heat transfer coefficient Dr. Şaziye Balku

26 + CHOSING INSULTION THICKNESS 6 r < r cr r r cr max r > r cr Before insulation check for critical radius r cr, sphere k h Dr. Şaziye Balku

27 + EXMPLE n electric wire having diameter of 1.5 mm and covered with a plastic insulation (thickness.5 mm) is exposed to air at 300 K and ho 0 W/m. K. The insulation has a k of 0.4 W/m. K. It is assumed that the wire surface temperature is constant at 400 K and it is not affected by the recovering. a) Calculate the value of the critical radius b) Calculate the heat loss per m of wire length with no insulation c) Repeat (b) for insulation being present

28 + NSWER

29 + SUMMRY u Specify appropriate form of the heat equation. u Solve for the temperature distribution. u pply Fourier s Law to determine the heat flux. Simplest Case: One-Dimensional, Steady-State Conduction with u Common Geometries: Ø The Plane Wall: Described in rectangular (x) coordinate. rea perpendicular to direction of heat transfer is constant (independent of x). Ø The Tube Wall: Radial conduction through tube wall. Ø The Spherical Shell: Radial conduction through shell wall

30 + Thank you J