Lecture-Week-3-on - II. Conduction A. Resistance concept 1....

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Unformatted text preview: II. Conduction A. Resistance concept 1. Plane wall (1-D) no heat source Consider T 1 T i = ? specified " q A q = T specified x L 1 L 2 K 1 K 2 If you take any C.V 1 st law of thermo " 1 q " 2 q in steady state " " 2 " 1 q q q = = q = constant Linear temperature profile in each material Fourier law = = dx dT k q 1 " const T: linear 2 2 1 1 1 " ) ( ) ( L T T k L T T k q i i- =- = if 2 1 k k slopes are different but flux is the same so T 1 T 2 1 ) ( ) ( 2 2 1 1 1 T T L Ak T T L Ak q i i- =- = resistence Thermal Difference Potential Thermal R T R T q 2 2 1 1 = = = where 1 1 1 Ak L R = 2 2 2 Ak L R = Thermal resistences d b c a d c b a q + + = = = Algebra . T 1 R 1 T 1 q . T = T 1 T 0 = k k R T q T i Resistances in series R 2 T 2 . T 2 2 1 1 1 Ak L Ak L T T q +- = 2 = R k R A R L Ak L R , , Consider now the situation T fluid @ T q h watt heat transfer coefficient T q = hA (T T ) h is calculated from fluid side (convection) Ah R R T q 1 = = R h R A , 3 So now we can look at: T 1     T Find q = ? fluid R 1 R 2 R 3 R 4 T L 1 , k 1 L 2 , k 2 L 3 , k 3 h T 1 x , Ak L R k k = , K=1,...3 Ah R 1 4 = k k R T T q 4 1 1 = - = = Ah Ak L Ak L Ak L T T 1 3 3 2 2 1 1 1 + + +- 4 It is often convenient to compare convective with conductive resistances, entional Non Biot B k hL Ah Ak L R R i conv cond dim # 1- = = = = resistence convection resistence conduction k hL B i = = If B i << 1 No need to consider the walls only h T 1 T If B i >> 1 Neglect h and only consider the walls T 1 T For comparison: Orders of magnitude of h (W/m C) Natural convection 5 Hot air Air 0(10) rises naturally Water 0(100) Forced convection Air 100 U Water 100 1000 T Boiling 1000 10000 6 Think of convection as conductive resistance T T fluid T w fluid T kA q T k q T T = = " Note T replaces L = = T T con k h kA R Motion decreases ( T ) or reduce its size ) ( h R T 7 Convention: Define an overall heat transfer coefficient by T UA q = T 1 T ) ( 1 - = T T T but R T q = T = (T 1- T ) R A U = 1 (always define which A U is based on) Resistance concept for 1-D steady situations can be used to estimate behavior of move complex systems of composite 2-D walls 8 Conduction of heat 1-D...
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Lecture-Week-3-on - II. Conduction A. Resistance concept 1....

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