Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 9, Problem 9.86P
To determine
The maximum allowable spacing for conduction across the air.
The effect of temperature on the spacing.
The effect of pressure on the spacing.
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A brass plate has a circular hole whose diameter is slightly smaller than the diameter of an aluminum ball. Ifthe ball and the plate are always kept at the same temperature,(a) should the temperature of the system be increased or decreasedin order for the ball to fit through the hole? (b) Choose the bestexplanation from among the following:I. The aluminum ball changes its diameter more with temperature than the brass plate, and therefore the temperatureshould be decreased.II. Changing the temperature won’t change the fact that the ballis larger than the hole.III. Heating the brass plate makes its hole larger, and that willallow the ball to pass through.
1. A simple cavity wall consists of two brick layers separated by an air gap of 50 mm. If the inside air temperature is 20oC and the ambient outside temperature is 5 oC, calculate the heat flux through the wall. Bricks are 100 mm thick with thermal conductivity kbrick = 0.5 W/m K, hin = 10 W/m2 K, hout = 20 W/m2 K. The internal air cavity can be considered still (no convection) with kair = 0.015 W/m K.
2. On a day in winter, the outside air temperature drops to -5 oC and the outside convective heat transfer changes to hout = (2 x V) + 8.9 W/m2 K. If the outside wind speed gusts at 50 kph, calculate the change in heat flux for the wall in question 3.
Figure (1)
Q2/ A thermopane window consists of two pieces of glass 7 mm thick that enclose an air space 7 mm thick.
The window separates room air at 20°C from outside ambient air at -10°C. The convection coefficient
associated with the inner (room-side) surface is 10 W/m².K. If the convection coefficient associated with the
outer (ambient) air is ho-80 W/mK, what is the heat loss through a window that is 0.8 m long by 0.5 m
wide? Neglect radiation, and assume the air enclosed between the panes to be stagnant. Take glass thermal
conductivity K-1.4 W/m.K, air thermal conductivity K,-0.0245 W/m.K
[33
Chapter 9 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 9 - The one-dimensional plane wall of Figure 3.1 is of...Ch. 9 - Using the values of density for water in Table...Ch. 9 - Consider an object of Characteristic length 0.01 m...Ch. 9 - To assess the efficacy of different liquids for...Ch. 9 - In many cases, we are concerned with free...Ch. 9 - The heat transfer rate due to free convection from...Ch. 9 - Consider a large vertical plate with a uniform...Ch. 9 - For laminar free convection flow on a vertical...Ch. 9 - Consider an array of vertical rectangular tins,...Ch. 9 - A number of thin plates are to be cooled by...
Ch. 9 - Prob. 9.11PCh. 9 - Prob. 9.13PCh. 9 - The plate described in Problem 9.14 has been used...Ch. 9 - Determine the average convection heat transfer...Ch. 9 - Consider a vertical plate of dimension 0.025m0.50m...Ch. 9 - During a winter day, the window of a patio door...Ch. 9 - Prob. 9.20PCh. 9 - A household oven door of 0.5-m height and 0.7-m...Ch. 9 - Consider a vertical, single-pane window of...Ch. 9 - Consider laminar flow about a vertical isothermal...Ch. 9 - Consider the conveyor system described in Problem...Ch. 9 - Prob. 9.25PCh. 9 - Consider an experiment to investigate the...Ch. 9 - The vertical rear window of an automobile is of...Ch. 9 - Prob. 9.28PCh. 9 - Prob. 9.29PCh. 9 - Prob. 9.30PCh. 9 - A refrigerator door has a height and width of...Ch. 9 - In the central receiver concept of a solar power...Ch. 9 - Prob. 9.34PCh. 9 - Airflow through a long, 0.2-m-square air...Ch. 9 - Prob. 9.36PCh. 9 - An electrical heater in the form of a horizontal...Ch. 9 - Consider a horizontal 6-mm-thick, 100-mm-long...Ch. 9 - Prob. 9.39PCh. 9 - Prob. 9.40PCh. 9 - Prob. 9.41PCh. 9 - Many laptop computers are equipped with thermal...Ch. 9 - Prob. 9.43PCh. 9 - At the end of its manufacturing process, a silicon...Ch. 9 - Integrated circuit (IC) boards are stacked within...Ch. 9 - Prob. 9.48PCh. 9 - Prob. 9.50PCh. 9 - Prob. 9.51PCh. 9 - Prob. 9.52PCh. 9 - Prob. 9.53PCh. 9 - Prob. 9.54PCh. 9 - Prob. 9.55PCh. 9 - Prob. 9.56PCh. 9 - Prob. 9.57PCh. 9 - A horizontal tube of 12.5-mm diameter with an...Ch. 9 - Prob. 9.60PCh. 9 - Prob. 9.61PCh. 9 - Prob. 9.63PCh. 9 - Prob. 9.64PCh. 9 - Common practice in chemical processing plants is...Ch. 9 - Consider the electrical heater of Problem 7.49. If...Ch. 9 - Prob. 9.67PCh. 9 - A billet of stainless steel, AISI 316, with a...Ch. 9 - Lone stainless steel rods of 50-mm diameter are...Ch. 9 - Hot air flows from a furnace through a...Ch. 9 - A biological fluid moves at a flow rate of...Ch. 9 - A sphere of 25-mm diameter contains an embedded...Ch. 9 - Prob. 9.79PCh. 9 - A vertical array of circuit boards is immersed in...Ch. 9 - Prob. 9.81PCh. 9 - The front door of a dishwasher of width 580 mm has...Ch. 9 - A natural convection air healer consists of an...Ch. 9 - A bank of drying ovens is mounted on a rack in a...Ch. 9 - Prob. 9.85PCh. 9 - Prob. 9.86PCh. 9 - Prob. 9.87PCh. 9 - To reduce heat losses, a horizontal rectangular...Ch. 9 - Prob. 9.89PCh. 9 - Prob. 9.90PCh. 9 - Prob. 9.91PCh. 9 - Prob. 9.92PCh. 9 - A 50-mm-thick air gap separates two horizontal...Ch. 9 - Prob. 9.94PCh. 9 - A vertical, double-pane window, which is 1 m on a...Ch. 9 - The top surface (0.5m0.5m) of an oven is 60°C for...Ch. 9 - Prob. 9.97PCh. 9 - Prob. 9.98PCh. 9 - Consider the cylindrical. 0.12-m-diamter radiation...Ch. 9 - Prob. 9.100PCh. 9 - A solar collector design consists of an inner tube...Ch. 9 - Prob. 9.104PCh. 9 - Prob. 9.105PCh. 9 - Liquid nitrogen is stored in a thin-walled...Ch. 9 - Prob. 9.108PCh. 9 - Prob. 9.109PCh. 9 - Prob. 9.110PCh. 9 - Prob. 9.111PCh. 9 - Prob. 9.114PCh. 9 - Prob. 9.115PCh. 9 - Prob. 9.116PCh. 9 - Prob. 9.117PCh. 9 - A water bath is used to maintain canisters...Ch. 9 - On a very Still morning, the surface temperature...Ch. 9 - Fuel cells similar to the PEM cell of Example 1.5...
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- 1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.arrow_forward1.4 To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in W/m K. Problem 1.4arrow_forwardFig. 4 illustrates an insulating wall of three homogeneous layers with conductivities k1, k2, and k3 in intimate contact. Under steady state conditions, both right and left surfaces are exposed to a temperature in a steady state condition at ambient temperatures of T and T , respectively, while ß, and BLare the film coefficients respectively. Assume that there is no internal heat generation and that the heat flow is one-dimensional (dT/dy = 0). For the illustrated ambient temperature in Fig. 4, determine the temperature's distribution at each layer. Material 3 Material 1 Material 2 T= 100 T= 35 °C Kı=20 K3=50 (W/m.k) K3=30 (W/m.k) B1= 10 w/m² °K (W/m.k) BR= 15 w/m²°K 50 mm 35 mm 25 cm Fig. 4arrow_forward
- b) A double glazed window, 1.3m high and 2.4m wide consists of two layers of glass each 4mm thick separated by a 23mm air gap. This window is a replacement for a single glazed unit. The double glazed unit is installed in the wall of a room in which the air temperature is maintained at 23 degreesC, the outer surface of the window is exposed to the atmospheric temperature which is 2 degreesC. The surface heat transfer coefficient of the room side glass is 5.7 W/m?K and 9.1 W/m?K on the outer surface of the window. The thermal conductivity of the glass is known to be 0.76 W/mK. i) On the assumption that the air gap between the layers may be regarded as a stationary layer of air of thermal conductivity 0.026 W/mK, calculate the heat transfer rate through the window and the temperature of the room side surface of the glass. ii) Calculate the heat transfer rate for the single glazed unit which has been replaced. The window was of the same dimensions consisting of a single pane of glass. It…arrow_forwardShow detailed step by step solution. Topic: Thermodynamicsarrow_forwardQUESTION 3 A rectangular window in a home has a length of 1.5 m and a height of 0.80 m. If the window allows heat to escape from the home at a rate of 2,000 watts, how thick must the window be if the inside temperature of the home is 220 c and the outside temperature is 3.0°C? (Assume that the coefficient of thermal conduction of glass is 0.80 W/mK.) а. 7.1 mm b. 11 mm C. 9.1 mm d. 124 mm e. 8.1 mmarrow_forward
- Firefighting job requires a special clothing, a protective clothing is typically constructed of three layers separated by air gaps, as shown in the figure below. _Thermal liner (tl) Moisture -Shell (s) barrier (mb) -1 mm- kmb Imb Fire-side mm- Firefighter k, L Air gap -Air gap Figure 1. Firefighting suit protective layers. Representative dimensions and thermal conductivities for the layers are as presented in the table below: Table 1: The thickness and thermal conductivity for different layers in a firefighters suit Layer Thickness (mm) k (W/m · K) Shell (s) Moisture barrier (mb) Thermal liner (tl) 0.8 0.047 0.55 0.012 3.5 0.038 The air gaps between the layers are 1 mm thick, and heat is transferred by conduction and radiation exchange through the stagnant air. The linearized radiation coefficient for a gap may be approximated as hyd =0(T TIT; + 2) (+ ?)040Tm , where Tayg represents the average temperature of the surfaces comprising the gap, and the radiation flux across the gap may be…arrow_forward3.6 Heat losses through windows in buildings are substantial. What would be the percentage reduction in heat loss that would be mitigated by replacing a window containing a single pane of glass with (a) double-pane low-E insulating glass or (b) a 3-inch-thick sheet of expanded polystyrene sheet? The quoted R values for these items are: • single pane of glass: 0.90 ft 2 hr ° F/Btu, • double pane of low-E insulating glass: 2.3 ft 2 hr ° F/Btu, • 1-inch-thick sheet of polystyrene sheet: 4.0 ft 2 hr ° F/Btu.arrow_forwardi. Calculate the heat loss through the furnace wall (all sides) by using conduction shape factor. ii. Calculate the heat loss through the furnace wall by using thermal resistance from each side (6 sides). iii. Determine the percentage difference of heat loss between case (i) and case (ii). iv. Explain why the heat transfer for both cases are different.arrow_forward
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