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### sm5_12

Course: MAE Heat Trans, Spring 2010
School: Seoul National
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Word Count: 361

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5.12 KNOWN: PROBLEM Diameter, density, specific heat and thermal conductivity of aluminum spheres used in packed bed thermal energy storage system. Convection coefficient and inlet gas temperature. FIND: Time required for sphere to acquire 90% of maximum possible thermal energy and the corresponding center temperature. Potential advantage of using copper in lieu of aluminum. SCHEMATIC: ASSUMPTIONS: (1) Negligible...

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5.12 KNOWN: PROBLEM Diameter, density, specific heat and thermal conductivity of aluminum spheres used in packed bed thermal energy storage system. Convection coefficient and inlet gas temperature. FIND: Time required for sphere to acquire 90% of maximum possible thermal energy and the corresponding center temperature. Potential advantage of using copper in lieu of aluminum. SCHEMATIC: ASSUMPTIONS: (1) Negligible heat transfer to or from a sphere by radiation or conduction due to contact with other spheres, (2) Constant properties. ANALYSIS: To determine whether a lumped capacitance analysis can be used, first compute Bi = 2 h(ro/3)/k = 75 W/m K (0.025m)/150 W/mK = 0.013 < 0.1. Hence, the lumped capacitance approximation may be made, and a uniform temperature may be assumed to exist in the sphere at any time. From Eq. 5.8a, achievement of 90% of the maximum possible thermal energy storage corresponds to Q = 0.90 = 1 exp ( t / t ) cV i where t = Vc / hA s = Dc / 6h = 2700 kg / m 3 0.075m 950 J / kg K / 6 75 W / m 2 K = 427s. Hence, t = t ln ( 0.1) = 427s 2.30 = 984s From Eq. (5.6), the corresponding temperature at any location the in sphere is < T ( 984s ) = Tg,i + Ti Tg,i exp ( 6ht / Dc ) T ( 984s ) = 300C 275C exp 6 75 W / m K 984s / 2700 kg / m 0.075m 950 J / kg K 2 3 ( ) ( ) < 3 T ( 984 ) s = 272.5C Obtaining the density and specific heat of copper from Table A-1, we see that (c)Cu 8900 kg/m 3 6 3 6 400 J/kgK = 3.56 10 J/m K > (c)Al = 2.57 10 J/m K. Hence, for an equivalent sphere diameter, the copper can store approximately 38% more thermal energy than the aluminum. COMMENTS: Before the packed bed becomes fully charged, the temperature of the gas decreases as it passes through the bed. Hence, the time required for a sphere to reach a prescribed state of thermal energy storage increases with increasing distance from the bed inlet. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
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Seoul National - MAE - Heat Trans
PROBLEM 5.16 KNOWN: Thickness and properties of furnace wall. Thermal resistance of film on surface of wall exposed to furnace gases. Initial wall temperature. FIND: (a) Time required for surface of wall to reach a prescribed temperature, (b) Correspondin
Seoul National - MAE - Heat Trans
PROBLEM 5.18KNOWN: Diameter, resistance and current flow for a wire. Convection coefficient and temperature of surrounding oil. FIND: Steady-state temperature of the wire. Time for the wire temperature to come within 1C of its steady-state value. SCHEMAT
Seoul National - MAE - Heat Trans
PROBLEM 5.22KNOWN: Metal sphere, initially at a uniform temperature Ti, is suddenly removed from a furnace and suspended in a large room and subjected to a convection process (T, h) and to radiation exchange with surroundings, Tsur. FIND: (a) Time it tak
Seoul National - MAE - Heat Trans
PROBLEM 5.23 KNOWN: Droplet properties, diameter, velocity and initial and final temperatures. FIND: Travel distance and rejected thermal energy. SCHEMATIC:ASSUMPTIONS: (1) Constant properties, (2) Negligible radiation from space. PROPERTIES: Droplet (gi
Seoul National - MAE - Heat Trans
PROBLEM 5.24KNOWN: Initial and final temperatures of a niobium sphere. Diameter and properties of the sphere. Temperature of surroundings and/or gas flow, and convection coefficient associated with the flow. FIND: (a) Time required to cool the sphere exc
Seoul National - MAE - Heat Trans
PROBLEM 5.25KNOWN: Diameter and thermophysical properties of alumina particles. Convection conditions associated with a two-step heating process. FIND: (a) Time-in-flight (ti-f) required for complete melting, (b) Validity of assuming negligible radiation
Seoul National - MAE - Heat Trans
PROBLEM 5.34 KNOWN: Series solution, Eq. 5.39, for transient conduction in a plane wall with convection. FIND: Midplane (x*=0) and surface (x*=1) temperatures * for Fo=0.1 and 1, using Bi=0.1, 1 and 10 with only the first four eigenvalues. Based upon thes
Seoul National - MAE - Heat Trans
PROBLEM 5.35 KNOWN: One-dimensional wall, initially at a uniform temperature, Ti, is suddenly exposed to a convection process (T, h). For wall #1, the time (t1 = 100s) required to reach a specified temperature at x = L is prescribed, T(L1, t1) = 315C. FIN
Seoul National - MAE - Heat Trans
PROBLEM 5.37KNOWN: Thickness, properties and initial temperature of steel slab. Convection conditions. FIND: Heating time required to achieve a minimum temperature of 550C in the slab. SCHEMATIC:ASSUMPTIONS: (1) One-dimensional conduction, (2) Negligibl
Seoul National - MAE - Heat Trans
PROBLEM 5.39KNOWN: Thickness, initial temperature and properties of furnace wall. Convection conditions at inner surface. FIND: Time required for outer surface to reach a prescribed temperature. Corresponding temperature distribution in wall and at inter
Seoul National - MAE - Heat Trans
PROBLEM 5.46KNOWN: Stack of circuit board-pressing plates, initially at a uniform temperature, is subjected by upper/lower platens to a higher temperature. FIND: (a) Elapsed time, te, required for the mid-plane to reach cure temperature when platens are
Seoul National - MAE - Heat Trans
PROBLEM 5.57KNOWN: A ball bearing is suddenly immersed in a molten salt bath; heat treatment to harden occurs at locations with T &gt; 1000 K. FIND: Time required to harden outer layer of 1mm. SCHEMATIC:ASSUMPTIONS: (1) One-dimensional radial conduction, (
Seoul National - MAE - Heat Trans
PROBLEM 5.59KNOWN: Diameter and initial temperature of ball bearings to be quenched in an oil bath. FIND: (a) Time required for surface to cool to 100C and the corresponding center temperature, (b) Oil bath cooling requirements. SCHEMATIC:ASSUMPTIONS: (
Seoul National - MAE - Heat Trans
PROBLEM 5.60KNOWN: Sphere quenching in a constant temperature bath. FIND: (a) Plot T(0,t) and T(ro,t) as function of time, (b) Time required for surface to reach 415 K, t , (c) Heat flux when T(ro, t ) = 415 K, (d) Energy lost by sphere in cooling to T(r
Seoul National - MAE - Heat Trans
PROBLEM 5.66 KNOWN: Two large blocks of different materials like copper and concrete at room temperature, 23C. FIND: Which block will feel cooler to the touch? SCHEMATIC:ASSUMPTIONS: (1) Blocks can be treated as semi-infinite solid, (2) Hand or finger te
Seoul National - MAE - Heat Trans
PROBLEM 5.71KNOWN: Tile-iron, 254 mm to a side, at 150C is suddenly brought into contact with tile over a subflooring material initially at Ti = 25C with prescribed thermophysical properties. Tile adhesive softens in 2 minutes at 50C, but deteriorates ab
Seoul National - MAE - Heat Trans
PROBLEM 5.73 KNOWN: Procedure for measuring convection heat transfer coefficient, which involves melting of a surface coating. FIND: Melting point of coating for prescribed conditions. SCHEMATIC:ASSUMPTIONS: (1) One-dimensional conduction in solid rod (n
Seoul National - MAE - Heat Trans
PROBLEM 5.74KNOWN: Irreversible thermal injury (cell damage) occurs in living tissue maintained at T 48C for a duration t 10s. FIND: (a) Extent of damage for 10 seconds of contact with machinery in the temperature range 50 to 100C, (b) Temperature histor
Seoul National - MAE - Heat Trans
PROBLEM 5.80 KNOWN: Initial temperature of copper and glass plates. Initial temperature and properties of finger. FIND: Whether copper or glass feels cooler to touch. SCHEMATIC:ASSUMPTIONS: (1) The finger and the plate behave as semi-infinite solids, (2)
Seoul National - MAE - Heat Trans
PROBLEM 5.99KNOWN: A 0.12 m thick wall, with thermal diffusivity 1.5 10-6 m2/s, initially at a uniform temperature of 85C, has one face suddenly lowered to 20C while the other face is perfectly insulated. FIND: (a) Using the explicit finite-difference me
Seoul National - MAE - Heat Trans
PROBLEM 6.3 KNOWN: Boundary layer temperature distribution. FIND: Surface heat flux. SCHEMATIC:PROPERTIES: Table A-4, Air (Ts = 300K): k = 0.0263 W/mK. ANALYSIS: Applying Fourier's law at y = 0, the heat flux is q = -k s u y u = - k ( T - Ts ) Pr exp - P
Seoul National - MAE - Heat Trans
PROBLEM 6.6 KNOWN: Expression for the local heat transfer coefficient of a circular, hot gas jet at T directed normal to a circular plate at Ts of radius ro. FIND: Heat transfer rate to the plate by convection. SCHEMATIC:ASSUMPTIONS: (1) Steady-state con
Seoul National - MAE - Heat Trans
PROBLEM 6.20 KNOWN: Experimental measurements of the heat transfer coefficient for a square bar in cross flow. FIND: (a) h for the condition when L = 1m and V = 15m/s, (b) h for the condition when L = 1m and V = 30m/s, (c) Effect of defining a side as the
Seoul National - MAE - Heat Trans
PROBLEM 6.23 KNOWN: Variation of hx with x for flow over a flat plate. FIND: Ratio of average Nusselt number for the entire plate to the local Nusselt number at x = L. SCHEMATIC:ANALYSIS: The expressions for the local and average Nusselt numbers areNu L
Seoul National - MAE - Heat Trans
PROBLEM 6.24 KNOWN: Laminar boundary layer flow of air at 20C and 1 atm having t = 1.13 . FIND: Ratio / t when fluid is ethylene glycol for same conditions. SCHEMATIC:ASSUMPTIONS: (1) Laminar flow. PROPERTIES: Table A-4, Air (293K, 1 atm): Pr = 0.709; Ta
Seoul National - MAE - Heat Trans
PROBLEM 6.29KNOWN: Form of Nusselt number for flow of air or a dielectric liquid over components of a circuit card. FIND: Ratios of time constants associated with intermittent heating and cooling. Fluid that provides faster thermal response. PROPERTIES:
Seoul National - MAE - Heat Trans
PROBLEM 6.35 KNOWN: Air flow conditions and drag force associated with a heater of prescribed surface temperature and area. FIND: Required heater power. SCHEMATIC:ASSUMPTIONS: (1) Steady-state conditions, (2) Reynolds analogy is applicable, (3) Bottom su
Seoul National - MAE - Heat Trans
PROBLEM 6.36 KNOWN: Heat transfer correlation associated with parallel flow over a rough flat plate. Velocity and temperature of air flow over the plate. FIND: Surface shear stress l m from the leading edge. SCHEMATIC:ASSUMPTIONS: (1) Modified Reynolds a
Seoul National - MAE - Heat Trans
PROBLEM 6.44 KNOWN: Species concentration profile, CA(y), in a boundary layer at a particular location for flow over a surface. FIND: Expression for the mass transfer coefficient, hm, in terms of the profile constants, CA, and DAB. Expression for the mola
Seoul National - MAE - Heat Trans
PROBLEM 6.50KNOWN: Convection heat transfer correlation for flow over a contoured surface. FIND: (a) Evaporation rate from a water film on the surface, (b) Steady-state film temperature. SCHEMATIC:ASSUMPTIONS: (1) Steady-state conditions, (b) Constant p
Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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Seoul National - MAE - Heat Trans
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