Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 1, Problem 1.5P
Consider Figure 1.3. The heat flux in the x-direction is
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4. Which of the following expresses thermal diffusivity of a substance in terms of thermal
conductivity(k), density (p) and specific heat (Cp)
A. p.k.Cp
C. 1/ p.k.Cp
В. К/р.Ср
D. p.Cp /k
5. The boundary condition of the end insulated fin are:
dT
В.
- kA) = 0 and T=To at x=0
dT
- kA -0
dx
A.
= 0 and T=Too at x-L
dx
C. T=0 at x=0 and q=0 at x=L
D. None of them
1. Temperatures are measured at the left-hand face and at a point 4 cm from the left-hand
face of the planar wall shown in the figure below. These temperatures are T₁ = 45.3 °C
and T* = 21.2 °C. The heat flow through the planar wall is steady and one dimensional.
What is the value of T2 at the right-hand surface of the wall?
TI
T*
4 cm
10 cm
T2
Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2)
under steady state condition. The density, conductivity and specific heat of the material are p=(1200*32)kg/mº, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux 9" =1000 W/m² is applied to the upper surface. The right and left surfaces are also kept at 0°C. Bottom surface is insulated.
9" (W/m)
T=0°C
T=0°C
W=(10*32)cm
B=(30*32)cm
Chapter 1 Solutions
Fundamentals of Heat and Mass Transfer
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- An electric heater producing 260 W of heat is used to warm up a room containing 7 m3 of air. If we assume the room is perfectly sealed and there is no heat loss through the room boundaries, such that all of the heater output goes into increasing the air temperature, how long will it take to heat up the air in the room from 5.0 °C to 24.1 °C? Give your answer to the nearest minute and assume that the specific volume (v = 0.85 m3/kg) and specific heat capacity at constant volume (cv = 1.005 kJ/(kg K)) remain constant throughout the heating process.arrow_forwardRelationship to Thermodynamics 4. An electrical resistor is connected to a battery, as shown schematically. After a brief transient, the resistor assumes a nearly uniform, steady-state temperature of 95 °C, while the battery and lead wires remain at the ambient temperature of 25 °C. Neglect the electrical resistance of the lead wires Battery V=24 V Resistor dEst dt Air T. = 25C Lead wire (a) Consider the resistor as a system about which a control surface is placed and Equation 1.12c is applied. Determine the corresponding values of Ein(W), Eg(W), Eout (W), and Est(W). If a control surface is placed about the entire system, what are the values of in, Eg, Eout, and Est? (1.12c) Est Ein - Eout + Eg (b) If electrical energy is dissipated uniformly with in the resistor, which is a cylinder of diameter D= 60 mm and length L=250 mm, what is the volumetric heat generation rate, (W/m3)? (c) Neglecting radiation from the resistor, what is the convection coefficient?arrow_forwardFind the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are ρ =1200 kg/m 3, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux q =1000 W/m 2 is applied to the upper surface. The right and left surfaces are also kept at 0oC. Bottom surface is insulated.arrow_forward
- Find the thermal resistance r (in hr - °F/BTU) and the equivalent R-value (in hr ft?. °F/BTU) of a typical frame 20' x 7.5" wall consisting of a 0.5" plaster board on the inside of the room, nominai 2 x 4 studs, and a 0.5" sheathing on the outside. The spaces between the studs are filled with an R-15 insulating foam. What is the heat loss (in BTU) through this wall in four hours if the inside temperature is 72°F and the outside temperature is 32°F? (Assume that the 15% of the wall's area are studs and the remaining 85% is filled with the insulating foam. Assume that the air is moving outside the wall.) r= 0.0805 x hr: OF/BTU R=0.09 x hr ft2. F/BTU AQ = BTUarrow_forward1.19 A square isothermal chip is of width w = front surface is exposed to the flow of a coolant at T = 15°C. From reliability considerations, the chip temperature must not exceed T = 85°C. 5 mm on a side and is mounted in a substrate such that its side and back surfaces are well insulated; the Coolant Chip If the coolant is air and the corresponding convection coefficient is h = 200 W/m² · K, what is the maximum allowable chip power? If the coolant is a dielectric liquid for which h = 3000 W/m² · K, what is the maximum allowable power?arrow_forwardIn a concentrated solar power plant, molten salt tank is used to store the thermal energy from the sun during the day. The tank wall thickness is 3cm containing molten salt at a temperature of 390 degree Celsius. There is atmospheric air outside the tank at a temperature of 30 degree Celsius. Suppose heat is lost as a result of heat transfer from the molten salt to the atmospheric air. What is the mode of heat transfer in this condition? conduction then convection convection then conduction convection then conduction then convection conduction then convection then conductionarrow_forward
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- 3. A cylindrical pipe of negligible thickness holding a hot fluid at 140°C and having an outer diameter of 0.4 m is insulated with three layers of each 50 mm thick insulation of k₁ = 0.02: k2 = 0.06 and k3 = 0.16 W/m-K (starting from inside). The outside surface temperature is 30°C. Solve for the value of T2 (°C). • show conversions, units, and box in your final answersarrow_forwardGive True or False for the following: 1.In liquids and gases, heat transmission is caused by conduction and convection 2.The surface geometry is the important factor in convection heat transfer 3. The heat transfer by conduction from heated surface to the adjacent layer of fluid, 4. The heat transfer is increased in the fin when &> 1 5.The unit of the thermal diffusivity is m²/s 6. Temperature change between the materials interfaces is attributed to the thermal contact resistance 7. A material that has a low heat capacity will have a large thermal diffusivity. 8. Heat conduction flowing from one side to other depends directly on thickness 9.Fin efficiency is the ratio of the fin heat dissipation with that of no fin 10.The critical radius is represented the ratio of the convicted heat transfer to the thermal conductivityarrow_forwardEXAMPLE 2.3 A = 10 m2 -q= 1000 Wm k= 40 W/mk p= 1600 kg/m The temperature distribution across a wall 1m thick at a certain instant of time is given as Tu) = a+ bx+ c- T(x) = a + bx + cr² where T is in degrees Celsius and x is in meters, while a = 900°C, b = -300°C/m, and c= -50°C/m². A uniform heat generation, ġ = 1000 W/m’, is present in the wall of area 10m² having the properties p = 1600 kg/m’, k = 40 W/m • K, and c, = 4 kJ/kg-K. %3D L=1m- %3D 1. Detemine the rate o heat cansler enterig the wall (x=0) and leaing he wl ( = Im). %3D %3D 2. Determine the rate of change of energy storage in the wall. 3. Detemine the lime rate of tmperature change at x = 0,025 ad 05m. AS 1x 56:43arrow_forward
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