Heisler-Graphics.pdf

cen29305_ch04.qxd 11/30/05 3:00 PM Page 232 232 TRANSIENT HEAT CONDUCTION (Condução Diagramas de Heisler de calor transiente e difusão de massa) T0 – T Ti – T 1.0 0.7 0.5 0.4 0.3 0.2 θ0 = k hL = 1 Bi = 0.7 0. 8 35 7 6 25 30 3 2 1.8 1.6 1.4 1.2 0.05 2.5 16 0.2 2 50 40 20 4 18 5 0.4 0.3 1 45 9 8 0 0 12 10 0.6 0.5 0.1 0.01 0.007 0.005 0.004 0.003 0.002 3 4 6 8 10 14 18 22 26 30 50 τ = α t/L2 70 100 120 T h (a) Midplane temperature (from M. P. Heisler, “Temperature Charts for Induction and Constant Temperature Heating,” Trans. ASME 69, 1947, pp. 227–36. Reprinted by permission of ASME International.) T – T T0 – T x/L = 0.2 1.0 Q Qmax 1.0 0.9 0.9 θ= 0.4 T h x L 2L Bi = hL/k 0.4 0.8 50 20 10 5 2 0.5 0.05 0.1 0.2 0.00 5 0.01 0.02 0.3 0.9 0.1 1.0 0 0.01 0.1 0.00 1 0.00 2 0.5 0.2 0 600 700 Bi = 0.6 0.5 0.3 Initially T = Ti 400 500 0.7 0.6 0.6 0.4 300 0.8 0.8 0.7 150 1 0.001 100 80 90 60 70 14 1.0 0.1 0.07 0.05 0.04 0.03 0.02 Plate 0.2 Plate 1.0 10 100 0.1 0 10–5 Plate 10– 4 10–3 10–2 1 k = Bi hL (b) Temperature distribution (from M. P. Heisler, “Temperature Charts for Induction and Constant Temperature Heating,” Trans. ASME 69, 1947, pp. 227–36. Reprinted by permission of ASME International.) 10–1 1 Bi 2τ = h2α t/k 2 10 102 103 (c) Heat transfer (from H. Gröber et al.) FIGURE 4–15 Transient temperature and heat transfer charts for a plane wall of thickness 2L initially at a uniform temperature Ti subjected to convection from both sides to an environment at temperature T with a convection coefficient of h. 104 7 0.1 0 0.1 0 10–5 Cylinder 10– 4 10–3 10–2 10–1 1 Bi 2τ = h2α t/k 2 10 102 103 104 (c) Heat transfer (from H.4 0. .03 hr 0.002 0.5 0.” Trans.00 1 0. Reprinted by permission of ASME International.9 0.7 0.6 ro r Bi = 0.6 0.0 0.01 0.007 0.02 = 1 Bi = 25 20 12 0.3 Bi = hro /k 0.cen29305_ch04.1 0.0 10 100 1 k = Bi hro (b) Temperature distribution (from M.0 0.00 5 0. ASME 69.5 6 40 0.) 0.2 1.4 0.3 0.4 0.2 0. 16 1 .05 0.6 8 45 35 30 0.4 0.1 k o 4 2.9 350 T Initially T h T = Ti h 0 T – T θ= T0 – T 1.6 0.) 140 150 Q Qmax 1.02 0.01 0. pp.6 70 14 10 0 80 60 50 10 7 0. Heisler.8 0.4 2 1. 3 5 8 1.5 0.4 0. pp.2 0.1 0.01 0.1 1.07 0.5 0.2 0.3 0.2 250 Cylinder 1.7 Cylinder 0. “Temperature Charts for Induction and Constant Temperature Heating.004 0.1 0.5 0.9 0. P. Heisler.) FIGURE 4–16 Transient temperature and heat transfer charts for a long cylinder of radius ro initially at a uniform temperature Ti subjected to convection from all sides to an environment at temperature T with a convection coefficient of h.2 0.8 50 20 10 5 2 1 0.0 0 0. Reprinted by permission of ASME International.05 0. P.0 0.qxd θ0 = 11/30/05 3:00 PM Page 233 233 CHAPTER 4 T0 – T Ti – T 1. 227–36. 1947.3 5 0. 1947.2 0.8 0. ASME 69.04 0. 227–36.0 r/ro = 0.003 90 18 9 1.00 2 0.001 0 1 2 3 4 6 8 10 14 18 22 26 τ = α t/ro2 30 50 70 100 120 (a) Centerline temperature (from M. Gröber et al. “Temperature Charts for Induction and Constant Temperature Heating.005 0.8 0.” Trans. 104 .00 2 0.2 5 0.2 12 14 6 5 4 20 18 16 3.9 0.02 0.0 1.3 0.003 2.” Trans. Gröber et al. “Temperature Charts for Induction and Constant Temperature Heating.0 0.2 0.6 0.00 5 0.” Trans.01 Initially T = Ti 200 0.002 0 0.7 0.5 2 2.2 0.0 0.0 0.01 0.0 2 2 2.5 0 0. 1.9 0.6 0. ASME 69.1 0.001 100 80 90 60 70 Sphere k hr = 1 o Bi = 2 θ0 = 100 (b) Temperature distribution (from M.1 1. 1947.05 0 0.) T – T 1. Heisler.1 0.03 0. 1947.05 0. “Temperature Charts for Induction and Constant Temperature Heating.4 0.4 1.) FIGURE 4–17 Transient temperature and heat transfer charts for a sphere of radius ro initially at a uniform temperature Ti subjected to convection from all sides to an environment at temperature T with a convection coefficient of h.1 0.2 0.5 1.9 0.4 T h 0 ro 250 r Bi = hro /k 0.07 0.6 T h 150 Q Qmax T0 – T r/ro = 0.007 0.02 50 40 45 0 35 3 25 2.1 Sphere 0.4 0.3 0.qxd 11/30/05 3:00 PM Page 234 234 TRANSIENT HEAT CONDUCTION T0 – T Ti – T 1.8 0.4 .2 1. 8 1.05 0. ASME 69.1 0.4 0.0 1 = k Bi hro 10 50 20 10 0.7 0.2 0. 227–36.0 0.004 0.3 0.5 0.04 0. pp. P.7 0.01 0.5 1 0.5 0.8 2.7 0.5 3 4 5 6 7 8 9 10 τ = α t/ro2 20 30 40 (a) Midpoint temperature (from M.6 10 8 9 7 3.00 1 0.8 0. Reprinted by permission of ASME International.0 0. P.005 0. 0 10–5 Sphere 10– 4 10–3 10–2 10–1 1 Bi 2τ = h2α t/k 2 10 102 103 (c) Heat transfer (from H.0 1.35 0.6 1.5 0.cen29305_ch04.5 1.8 100 Bi = θ= 50 5 0. Heisler.