Pré-visualização50 páginas

32ºC, and an emissivity of 0.90. If the rates of heat transfer from the person by convection and by radiation are equal, the combined heat transfer coefficient is (a) 0.008 W/m2·ºC (b) 3.0 W/m2·ºC (c) 5.5 W/m2·ºC (d) 8.3 W/m2·ºC (e) 10.9 W/m2·ºC Answer (e) 10.9 W/m2·ºC Solution Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. T_infinity=20 [C] T_surr=20 [C] T_s=32 [C] A=1.5 [m^2] epsilon=0.90 sigma=5.67E-8 [W/m^2-K^4] Q_dot_rad=epsilon*A*sigma*((T_s+273)^4-(T_surr+273)^4) Q_dot_total=2*Q_dot_rad Q_dot_total=h_combined*A*(T_s-T_infinity) "Some Wrong Solutions with Common Mistakes" Q_dot_rad=W1_h_combined*A*(T_s-T_infinity) "Using radiation heat transfer instead of total heat transfer" Q_dot_rad_1=epsilon*A*sigma*(T_s^4-T_surr^4) "Using C unit for temperature in radiation calculation" 2*Q_dot_rad_1=W2_h_combined*A*(T_s-T_infinity) 1-155 While driving down a highway early in the evening, the air flow over an automobile establishes an overall heat transfer coefficient of 25 W/m2\u22c5K. The passenger cabin of this automobile exposes 8 m2 of surface to the moving ambient air. On a day when the ambient temperature is 33oC, how much cooling must the air conditioning system supply to maintain a temperature of 20oC in the passenger cabin? (a) 0.65 MW (b) 1.4 MW (c) 2.6 MW (d) 3.5 MW (e) 0.94 MW Answer (c) 2.6 MW Solution Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. h=25 [W/m^2-C] A=8 [m^2] T_1=33 [C] T_2=20 [C] Q=h*A*(T_2-T_1) PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. 1-71 1-156 On a still clear night, the sky appears to be a blackbody with an equivalent temperature of 250 K. What is the air temperature when a strawberry field cools to 0°C and freezes if the heat transfer coefficient between the plants and the air is 6 W/m2\u22c5oC because of a light breeze and the plants have an emissivity of 0.9? (a) 14oC (b) 7oC (c) 3oC (d) 0oC (e) \u20133°C Answer (a) 14oC Solution Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. e=0.9 h=6 [W/m^2-K] T_1=273 [K] T_2=250 [K] h*(T-T_1)=e*sigma#*(T_1^4-T_2^4) 1-157 Over 90 percent of the energy dissipated by an incandescent light bulb is in the form of heat, not light. What is the temperature of a vacuum-enclosed tungsten filament with an exposed surface area of 2.03 cm2 in a 100 W incandescent light bulb? The emissivity of tungsten at the anticipated high temperatures is about 0.35. Note that the light bulb consumes 100 W of electrical energy, and dissipates all of it by radiation. (a) 1870 K (b) 2230 K (c) 2640 K (d) 3120 K (e) 2980 K Answer (b) 2230 K Solution Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. e =0.35 Q=100 [W] A=2.03E-4 [m^2] Q=e*A*sigma#*T^4 PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. 1-72 1-158 Commercial surface coating processes often use infrared lamps to speed the curing of the coating. A 2-mm-thick, teflon (k = 0.45 W/m\u22c5K) coating is applied to a 4 m × 4 m surface using this process. Once the coating reaches steady-state, the temperature of its two surfaces are 50oC and 45oC. What is the minimum rate at which power must be supplied to the infrared lamps steadily? (a) 18 kW (b) 20 kW (c) 22 kW (d) 24 kW (e) 26 kW Answer (a) 18 kW Solution Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. k=0.45 [W/m-K] A=16 [m^2] t=0.002 [m] dT=5 [C] Q=k*A*dT/t 1-159 . . . 1-161 Design and Essay Problems KJ PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. 2-1 Chapter 2 HEAT CONDUCTION EQUATION Introduction 2-1C Heat transfer is a vector quantity since it has direction as well as magnitude. Therefore, we must specify both direction and magnitude in order to describe heat transfer completely at a point. Temperature, on the other hand, is a scalar quantity. 2-2C The term steady implies no change with time at any point within the medium while transient implies variation with time or time dependence. Therefore, the temperature or heat flux remains unchanged with time during steady heat transfer through a medium at any location although both quantities may vary from one location to another. During transient heat transfer, the temperature and heat flux may vary with time as well as location. Heat transfer is one-dimensional if it occurs primarily in one direction. It is two- dimensional if heat tranfer in the third dimension is negligible. 2-3C Heat transfer to a canned drink can be modeled as two-dimensional since temperature differences (and thus heat transfer) will exist in the radial and axial directions (but there will be symmetry about the center line and no heat transfer in the azimuthal direction. This would be a transient heat transfer process since the temperature at any point within the drink will change with time during heating. Also, we would use the cylindrical coordinate system to solve this problem since a cylinder is best described in cylindrical coordinates. Also, we would place the origin somewhere on the center line, possibly at the center of the bottom surface. 2-4C Heat transfer to a potato in an oven can be modeled as one-dimensional since temperature differences (and thus heat transfer) will exist in the radial direction only because of symmetry about the center point. This would be a transient heat transfer process since the temperature at any point within the potato will change with time during cooking. Also, we would use the spherical coordinate system to solve this problem since the entire outer surface of a spherical body can be described by a constant value of the radius in spherical coordinates. We would place the origin at the center of the potato. 2-5C Assuming the egg to be round, heat transfer to an egg in boiling water can be modeled as one- dimensional since temperature differences (and thus heat transfer) will primarily exist in the radial direction only because of symmetry about the center point. This would be a transient heat transfer process since the temperature at any point within the egg will change with time during cooking. Also, we would use the spherical coordinate system to solve this problem since the entire outer surface of a spherical body can be described by a constant value of the radius in spherical coordinates. We would place the origin at the center of the egg. 2-6C Heat transfer to a hot dog can be modeled as two-dimensional since temperature differences (and thus heat transfer) will exist in the radial and axial directions (but there will be symmetry about the center line and no heat transfer in the azimuthal direction. This would be a transient heat transfer process since the temperature at any point within the hot dog will change with time during cooking. Also, we would use the cylindrical coordinate system to solve this problem since a cylinder is best described in cylindrical coordinates. Also, we would place the origin somewhere on the center line, possibly at the center of the hot dog. Heat transfer in a very long hot dog could be considered to be one-dimensional in preliminary calculations. PROPRIETARY MATERIAL.