Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 4, Problem 4.60P
To determine
The heat transfer rate per unit length.
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Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hz Figure 1: Single-degree-of-freedom system in Problem 1. Please compute the following considering the steady-state response of the SDOF system. Do not consider the transient response unless it is explicitly stated in the question. (a) The natural circular frequency and the natural period of the SDOF. (10 points) (b) The maximum displacement of…
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Chapter 4 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 4 - In the method of separation of variables (Section...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Consider the two-dimensional rectangular plate of...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Using the thermal resistance relations developed...Ch. 4 - Free convection heat transfer is sometimes...Ch. 4 - Consider Problem 4.5 for the case where the plate...Ch. 4 - Prob. 4.9PCh. 4 - Based on the dimensionless conduction heat rates...
Ch. 4 - Determine the heat transfer rate between two...Ch. 4 - A two-dimensional object is subjected to...Ch. 4 - An electrical heater 100 mm long and 5 mm in...Ch. 4 - Two parallel pipelines spaced 0.5 m apart are...Ch. 4 - A small water droplet of diameter D=100m and...Ch. 4 - A tube of diameter 50 mm having a surface...Ch. 4 - Pressurized steam at 450K flows through a long,...Ch. 4 - The temperature distribution in laser-irradiated...Ch. 4 - Hot water at 85°C flows through a thin-walled...Ch. 4 - A furnace of cubical shape, with external...Ch. 4 - Laser beams are used to thermally process...Ch. 4 - A double-glazed window consists of two sheets of...Ch. 4 - A pipeline, used for the transport of crude oil,...Ch. 4 - A long power transmission cable is buried at a...Ch. 4 - A small device is used to measure the surface...Ch. 4 - A cubical glass melting furnace has exterior...Ch. 4 - An aluminum heat sink (k=240W/mK), used to cool an...Ch. 4 - Hot water is transported from a cogeneration power...Ch. 4 - A long constantan wire of 1-mm diameter is butt...Ch. 4 - A hole of diameter D=0.25m is drilled through the...Ch. 4 - In Chapter 3 we that, whenever fins are attached...Ch. 4 - An igloo is built in the shape of a hemisphere,...Ch. 4 - Prob. 4.34PCh. 4 - An electronic device, in the form of a disk 20 mm...Ch. 4 - The elemental unit of an air heater consists of a...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Prob. 4.39PCh. 4 - Prob. 4.40PCh. 4 - One of the strengths of numerical methods is their...Ch. 4 - Determine expressionsfor...Ch. 4 - Consider heat transfer in a one-dimensional...Ch. 4 - In a two-dimensional cylindrical configuration,...Ch. 4 - Upper and lower surfaces of a bus bar are...Ch. 4 - Derive the nodal finite-difference equations for...Ch. 4 - Consider the nodal point 0 located on the boundary...Ch. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Consider the network for a two-dimensional system...Ch. 4 - An ancient myth describes how a wooden ship was...Ch. 4 - Consider the square channel shown in the sketch...Ch. 4 - A long conducting rod of rectangular cross section...Ch. 4 - A flue passing hot exhaust gases has a square...Ch. 4 - Steady-state temperatures (K) at three nodal...Ch. 4 - Functionally graded materials are intentionally...Ch. 4 - Steady-state temperatures at selected nodal points...Ch. 4 - Consider an aluminum heat sink (k=240W/mK), such...Ch. 4 - Conduction within relatively complex geometries...Ch. 4 - Prob. 4.60PCh. 4 - The steady-state temperatures (°C) associated with...Ch. 4 - A steady-state, finite-difference analysis has...Ch. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Consider a two-dimensional. straight triangular...Ch. 4 - A common arrangement for heating a large surface...Ch. 4 - A long, solid cylinder of diameter D=25mm is...Ch. 4 - Consider Problem 4.69. An engineer desires to...Ch. 4 - Prob. 4.71PCh. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Refer to the two-dimensional rectangular plate of...Ch. 4 - The shape factor for conduction through the edge...Ch. 4 - Prob. 4.77PCh. 4 - A simplified representation for cooling in very...Ch. 4 - Prob. 4.84PCh. 4 - A long trapezoidal bar is subjected to uniform...Ch. 4 - Consider the system of Problem 4.54. The interior...Ch. 4 - A long furnace. constructed from refractory brick...Ch. 4 - A hot pipe is embedded eccentrically as shown in a...Ch. 4 - A hot liquid flows along a V-groove in a solid...Ch. 4 - Prob. 4S.5PCh. 4 - Hollow prismatic bars fabricated from plain carbon...
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- The design of the gear-and-shaft system shown requires that steel shafts of the same diameter be used for both AB and CD. It is further required that the angle D through which end D of shaft CD rotates not exceed 1.5°. Knowing that G = 77.2 GPa, determine the required diameter of the shafts. 40 mm 400 mm 100 mm 600 mm T-1000 N-m Darrow_forwardAssume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hzarrow_forward13.44 The end of a cylindrical liquid cryogenic propellant tank in free space is to be protected from external (solar) radiation by placing a thin metallic shield in front of the tank. Assume the view factor Fts between the tank and the shield is unity; all surfaces are diffuse and gray, and the surroundings are at 0 K. Tank T₁ Shield, T T₁ = 100 K E1 Solar irradiation Gs ε₁ = ε₂ = 0.05 ε₁ = 0.10 Gs = 1250 W/m² E2 Find the temperature of the shield T, and the heat flux (W/m²) to the end of the tank.arrow_forward
- question 664 thank youarrow_forward13.38 Consider the attic of a home located in a hot climate. The floor of the attic is characterized by a width of L₁ = 8 m while the roof makes an angle of 0 = 30° from the horizontal direction, as shown in the schematic. The homeowner wishes to reduce the heat load to the home by adhering bright aluminum foil (ε = 0.07) onto the surfaces of the attic space. Prior to installation of the foil, the surfaces are of emissivity & = 0.90. Attic A2, 82, T2 0 = 30° A1, E1, T₁ 土 L₁ = 8 m (a) Consider installation on the bottom of the attic roof only. Determine the ratio of the radiation heat transfer after to before the installation of the foil. (b) Determine the ratio of the radiation heat transfer after to before installation if the foil is installed only on the top of the attic floor. (c) Determine the ratio of the radiation heat transfer if the foil is installed on both the roof bottom and the floor top.arrow_forward13.1 Determine F2 and F2 for the following configura- tions using the reciprocity theorem and other basic shape factor relations. Do not use tables or charts. (a) Small sphere of area A, under a concentric hemi- sphere of area A₂ = 3A₁ A₂ A1 (a) (b) Long duct. Also, what is F₁₂? A₂ Αν (b) (c) Long inclined plates (point B is directly above the center of A₁) B 100 mm A₂ - 220 mm (c) (d) Long cylinder lying on infinite plane + A₁ Az (d) (e) Hemisphere-disk arrangement -A₂, hemisphere, diameter D A₂ A₁, disk, diameter D/2 (e) (f) Long, open channel 1 m AA₂ 2 m (f) (g) Long cylinders with A₁ = 4A₁. Also, what is F₁₂? -D₁ A1 -A₂ -D2 (e) (h) Long, square rod in a long cylinder. Also, what is F22? w=D/5 18 A₁ -A2 (h) -Darrow_forward
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