Explanation Given: Diameter of the hot dog ( D ) is 2 cm . Length of the cylinder ( 2 L ) is 12 cm . Initial temperature of the hot dog ( T i ) is 5 ° C . Temperature of the boiling water ( T ∞ ) is 100 ° C . Center temperature of the hot dog ( T 0 ) is 80 ° C . Convection heat transfer coefficient ( h ) is 600 W / m 2 ⋅ K . Calculation: Write the given properties of the hot dog. ρ = 980 kg / m 3 c p = 3.9 kJ / kg ⋅ K k = 0.76 W / m ⋅ K α = 2 × 10 − 7 m 2 / s Calculate the Biot number of the wall ( Bi wall ) . Bi wall = h L k = ( 600 W / m 2 ⋅ K ) ( 0.06 m ) 0.76 W / m ⋅ K = 47.37 Refer Table 18-2, “Coefficients used in the one-term approximate solution of transient one-dimensional heat conduction in plane walls, cylinders, and spheres”, obtain the constants λ 1 and A 1 corresponding to the Biot number of 47.37 . λ 1 = 1.5380 A 1 = 1.2726 Calculate the Biot number of the cylinder ( Bi cyl ) . Bi cyl = h r 0 k = h ( D 2 ) k = ( 600 W / m 2 ⋅ K ) ( 0.01 m ) 0.76 W / m ⋅ K = 7.895 Refer Table 18-2, “Coefficients used in the one-term approximate solution of transient one-dimensional heat conduction in plane walls, cylinders, and spheres”, obtain the constants λ 1 and A 1 corresponding to the Biot number of 7

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Chapter 18, Problem 107RQ

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Ch. 18 - Prob. 1P Ch. 18 - Prob. 2P Ch. 18 - In what medium is the lumped system analysis more...Ch. 18 - Prob. 4P Ch. 18 - Prob. 5P Ch. 18 - Prob. 6P Ch. 18 - Prob. 7P Ch. 18 - Consider a hot baked potato on a plate. The...Ch. 18 - Prob. 9P Ch. 18 - Prob. 10P

Ch. 18 - Prob. 11P Ch. 18 - Prob. 12P Ch. 18 - Prob. 13P Ch. 18 - Prob. 14P Ch. 18 - Consider a 1000-W iron whose base plate is made of...Ch. 18 - Metal plates (k = 180 W/m·K, ρ = 2800 kg/m3, and...Ch. 18 - A 5-mm-thick stainless steel strip (k = 21 W/m·K,...Ch. 18 - A long copper rod of diameter 2.0 cm is initially...Ch. 18 - Prob. 21P Ch. 18 - Steel rods (ρ = 7832 kg/m3, cp = 434 J/kg·K, and k...Ch. 18 - Prob. 23P Ch. 18 - The temperature of a gas stream is to be measured...Ch. 18 - Prob. 25P Ch. 18 - A thermocouple, with a spherical junction diameter...Ch. 18 - Prob. 27P Ch. 18 - Prob. 28P Ch. 18 - Carbon steel balls (ρ = 7833 kg/m3, k = 54 W/m·K,...Ch. 18 - Prob. 31P Ch. 18 - Prob. 32P Ch. 18 - Prob. 33P Ch. 18 - Prob. 34P Ch. 18 - Prob. 35P Ch. 18 - Prob. 36P Ch. 18 - Prob. 37P Ch. 18 - Prob. 38P Ch. 18 - Prob. 39P Ch. 18 - A body at an initial temperature of Ti is brought...Ch. 18 - In a meat processing plant, 2-cm-thick steaks (k =...Ch. 18 - Prob. 42P Ch. 18 - Prob. 43P Ch. 18 - Prob. 45P Ch. 18 - Prob. 46P Ch. 18 - Prob. 47P Ch. 18 - Prob. 48P Ch. 18 - Prob. 49P Ch. 18 - A long iron rod (ρ = 7870 kg/m3, cp = 447 J/kg·K,...Ch. 18 - Prob. 51P Ch. 18 - A long 35-cm-diameter cylindrical shaft made of...Ch. 18 - Prob. 54P Ch. 18 - Prob. 55P Ch. 18 - Prob. 56P Ch. 18 - A father and son conducted the following simple...Ch. 18 - Prob. 58P Ch. 18 - Prob. 59P Ch. 18 - Citrus fruits are very susceptible to cold...Ch. 18 - Prob. 61P Ch. 18 - Prob. 63P Ch. 18 - Prob. 64P Ch. 18 - Prob. 65P Ch. 18 - White potatoes (k = 0.50 W/m·K and α = 0.13 × 10−6...Ch. 18 - Prob. 67P Ch. 18 - Prob. 68P Ch. 18 - Prob. 69P Ch. 18 - Consider a hot semi-infinite solid at an initial...Ch. 18 - Prob. 71P Ch. 18 - Prob. 72P Ch. 18 - Prob. 73P Ch. 18 - Prob. 74P Ch. 18 - Prob. 75P Ch. 18 - Prob. 76P Ch. 18 - Prob. 77P Ch. 18 - Prob. 78P Ch. 18 - Prob. 79P Ch. 18 - Prob. 81P Ch. 18 - Prob. 82P Ch. 18 - Prob. 83P Ch. 18 - Prob. 84P Ch. 18 - Prob. 85P Ch. 18 - Prob. 86P Ch. 18 - Prob. 88P Ch. 18 - Prob. 89P Ch. 18 - A 2-cm-high cylindrical ice block (k = 2.22 W/m·K...Ch. 18 - Prob. 91P Ch. 18 - Prob. 93P Ch. 18 - Prob. 94RQ Ch. 18 - Large steel plates 1.0-cm in thickness are...Ch. 18 - Prob. 96RQ Ch. 18 - Prob. 97RQ Ch. 18 - Prob. 98RQ Ch. 18 - Prob. 99RQ Ch. 18 - Prob. 100RQ Ch. 18 - Prob. 101RQ Ch. 18 - Prob. 102RQ Ch. 18 - The water main in the cities must be placed at...Ch. 18 - Prob. 104RQ Ch. 18 - Prob. 105RQ Ch. 18 - Prob. 106RQ Ch. 18 - Prob. 107RQ

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Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license