HEAT+MASS TRANSFER:FUND.+APPL.
6th Edition
ISBN: 9780073398198
Author: CENGEL
Publisher: RENT MCG
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Question
Chapter 3, Problem 16P
To determine
The heat loss through the wall.
Expert Solution & Answer
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 3 Solutions
HEAT+MASS TRANSFER:FUND.+APPL.
Ch. 3 - Consider heat conduction through a wall of...Ch. 3 - Consider heat conduction through a plane wall....Ch. 3 - What does the thermal resistance of a medium...Ch. 3 - Can we defme the convection resistance for a unit...Ch. 3 - Consider steady heat transfer through the wall of...Ch. 3 - How is the combined heat transfer coefficient...Ch. 3 - Why are the convection and the radiation...Ch. 3 - Consider steady one-dimensional heat transfer...Ch. 3 - Someone comments that a microwave oven can be...Ch. 3 - Consider two cold canned drinks, one wrapped in a...
Ch. 3 - The bottom of a pan is made of a 4-mm-thick...Ch. 3 - Consider a surface of area A at which the...Ch. 3 - How does the thermal resistance network associated...Ch. 3 - Consider steady one-dimensional heat transfer...Ch. 3 - Consider a window glass consisting of two...Ch. 3 - Prob. 16PCh. 3 - Consider a person standing in a room at 20C with...Ch. 3 - Consider an electrically heated brick house...Ch. 3 - A12-cm18-cm circuit board houses on its surface...Ch. 3 - Water is boiling in a 25-cm-diameter aluminum pan...Ch. 3 - A cylindrical resistor element on a circuit board...Ch. 3 - Prob. 22PCh. 3 - A1.0m1.5m double-pane window consists of two...Ch. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28EPCh. 3 - To defog the rear window of an automobile, a very...Ch. 3 - A transparent film is to be bonded onto the top...Ch. 3 - To defrost ice accumulated on the outer surface of...Ch. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Heat is to be conducted along a circuit board that...Ch. 3 - Prob. 37EPCh. 3 - Consider a house that has a 10m20-m base and a...Ch. 3 - Prob. 39EPCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - What is thermal contact resistance? How is it...Ch. 3 - Will the thermal contact resistance be greater for...Ch. 3 - Explain how the thermal contact resistance can be...Ch. 3 - A waII consists of two layers of insulation...Ch. 3 - Prob. 48CPCh. 3 - Consider two surfaces pressed against each other....Ch. 3 - Prob. 50PCh. 3 - Two 5-cm-diameter, 15-cm-long aluminum bars...Ch. 3 - Prob. 52PCh. 3 - Two identical aluminum plates with thickness of 30...Ch. 3 - A tvolayer wall is made of two metal plates, with...Ch. 3 - Prob. 55PCh. 3 - An aluminum plate and a stainless steel plate are...Ch. 3 - Prob. 57PCh. 3 - Prob. 58PCh. 3 - Prob. 59PCh. 3 - Prob. 60PCh. 3 - Prob. 61PCh. 3 - What are the two approaches used in the...Ch. 3 - The thermal resistance networks can also be used...Ch. 3 - When plotting the thermal resistance network...Ch. 3 - A 10-cm-thick vall is to be constructed with...Ch. 3 - Prob. 66EPCh. 3 - Prob. 67PCh. 3 - Prob. 68PCh. 3 - Prob. 69PCh. 3 - Prob. 70PCh. 3 - Prob. 71PCh. 3 - Prob. 72PCh. 3 - A 12-m-long and 5-m-high wall is constructed of...Ch. 3 - Prob. 74EPCh. 3 - Prob. 75PCh. 3 - Prob. 76PCh. 3 - Prob. 77PCh. 3 - What is an infinitely long cylinder? When is it...Ch. 3 - Can the thermal resistance concept be used for a...Ch. 3 - Consider a short cylinder whose top and bottom...Ch. 3 - Prob. 81PCh. 3 - Prob. 82PCh. 3 - Prob. 83PCh. 3 - Superheated steam at an average temperature 20C is...Ch. 3 - Prob. 85PCh. 3 - Prob. 86PCh. 3 - Prob. 87EPCh. 3 - Prob. 88EPCh. 3 - Prob. 89EPCh. 3 - Prob. 90PCh. 3 - Prob. 91PCh. 3 - Prob. 92PCh. 3 - Prob. 93EPCh. 3 - Prob. 94PCh. 3 - Prob. 95PCh. 3 - Prob. 96PCh. 3 - Liquid hydrogen is flowing through an insulated...Ch. 3 - Exposure to high concentrations of gaseous ammonia...Ch. 3 - A mixture of chemicals is flowing in a pipe...Ch. 3 - Ice slurry is being transported in a pipe...Ch. 3 - Prob. 101PCh. 3 - Prob. 102PCh. 3 - Prob. 103PCh. 3 - What is the critical radius of insulation? How is...Ch. 3 - Prob. 105CPCh. 3 - Prob. 106CPCh. 3 - Prob. 107CPCh. 3 - A pipe is insulated such that the outer radius of...Ch. 3 - A 0.083-in-diameter electrical wire at 90F is...Ch. 3 - Repeat Prob. 3-109E, assuming a thermal contact...Ch. 3 - Prob. 111PCh. 3 - Prob. 112PCh. 3 - Hot air is to be cooled as it is forced to flow...Ch. 3 - Prob. 114CPCh. 3 - Prob. 115CPCh. 3 - The fins attached to a surface are determined to...Ch. 3 - Explain how the fins enhance heat transfer from a...Ch. 3 - How does the overall effectiveness of a finned...Ch. 3 - Hot water is to be cooled as it flows through the...Ch. 3 - Consider two finned surfaces that are identical...Ch. 3 - The heat transfer surface area of a fin is equal...Ch. 3 - Does the (a) efficiency and (b) effectiveness of a...Ch. 3 - Two pin fins are identical, except that the...Ch. 3 - Two plate fins of constant rectangular cross...Ch. 3 - Two finned surfaces are identical, except that the...Ch. 3 - Obtain a relation for the fin efficiency for a fin...Ch. 3 - Prob. 127PCh. 3 - Consider a very long rectangular fin attached to a...Ch. 3 - Prob. 129PCh. 3 - Prob. 130PCh. 3 - Prob. 131PCh. 3 - Prob. 132PCh. 3 - Prob. 133EPCh. 3 - Prob. 134EPCh. 3 - Prob. 135PCh. 3 - Prob. 136PCh. 3 - Prob. 137PCh. 3 - Prob. 138PCh. 3 - Prob. 139PCh. 3 - Prob. 140PCh. 3 - Prob. 141PCh. 3 - Prob. 142PCh. 3 - Prob. 143PCh. 3 - Prob. 144PCh. 3 - Prob. 145PCh. 3 - Prob. 146PCh. 3 - The human body is adaptable to extreme climatic...Ch. 3 - Consider the conditions of Example 3-14 in the...Ch. 3 - Consider the conditions of Example 3-14 in the...Ch. 3 - Prob. 150PCh. 3 - What is a conduction shape factor? How is it...Ch. 3 - What is the value of conduction shape factors in...Ch. 3 - Prob. 153PCh. 3 - A thin-walled cylindrical container is placed...Ch. 3 - Prob. 155PCh. 3 - Prob. 156PCh. 3 - Prob. 157PCh. 3 - Prob. 158EPCh. 3 - Prob. 159PCh. 3 - Prob. 160PCh. 3 - Prob. 161PCh. 3 - Prob. 162PCh. 3 - Prob. 163PCh. 3 - Prob. 164PCh. 3 - Consider a house with a flat roof whose outer...Ch. 3 - Prob. 166PCh. 3 - Radioactive material, stored in a spherical vessel...Ch. 3 - What is the R-value of a wall? How does it differ...Ch. 3 - What is effective emissivity for a plane-parallel...Ch. 3 - Prob. 170CPCh. 3 - What is a radiant barrier? What kinds of materials...Ch. 3 - Consider a house whose attic space is ventilated...Ch. 3 - Prob. 173PCh. 3 - Prob. 174PCh. 3 - Prob. 175PCh. 3 - Prob. 176PCh. 3 - Prob. 177PCh. 3 - Prob. 178PCh. 3 - Determine the winter R-value and the U-factor of a...Ch. 3 - The overall heat transfer coefficient (the...Ch. 3 - Prob. 181EPCh. 3 - Determine the summer and winter R-values. in m2 ....Ch. 3 - The overall heat transfer coefficient of a wall is...Ch. 3 - Two homes are identical, except that the walls of...Ch. 3 - Prob. 185PCh. 3 - Consider two identical people each generating 60 V...Ch. 3 - Cold conditioned air at 12C is flowing inside a...Ch. 3 - Hot water is flowing at an average velocity of 1.5...Ch. 3 - Prob. 189PCh. 3 - Prob. 190PCh. 3 - Prob. 191PCh. 3 - Prob. 192PCh. 3 - Prob. 193PCh. 3 - Prob. 194PCh. 3 - Prob. 195PCh. 3 - Prob. 196PCh. 3 - Prob. 197PCh. 3 - A total of 10 rectangular aluminum fins...Ch. 3 - Prob. 199PCh. 3 - A plane wall surface at 200C is to be cooled with...Ch. 3 - Prob. 201PCh. 3 - Prob. 202PCh. 3 - Prob. 203PCh. 3 - Prob. 204PCh. 3 - A 0.6-rn-diameter, 1.9-rn-long cylindrical tank...Ch. 3 - Prob. 206PCh. 3 - Prob. 207PCh. 3 - A thin-walled spherical tank is buried in the...Ch. 3 - Heat is lost at a rate of 275 W per m2 area of a 1...Ch. 3 - Prob. 210PCh. 3 - Heat is generated steadily in a 3-cm-diameter...Ch. 3 - Prob. 212PCh. 3 - Prob. 213PCh. 3 - Prob. 214PCh. 3 - Prob. 215PCh. 3 - Prob. 216PCh. 3 - Consider two walls. A and B, with the same surface...Ch. 3 - Prob. 218PCh. 3 - A room at 20C air temperature is losing heat to...Ch. 3 - Prob. 220PCh. 3 - A 1-cm-diameter, 30cm-long fin made of aluminum...Ch. 3 - A hot surface at 80C in air at 20C is to be cooled...Ch. 3 - A cylindrical pin fin of diameter 0.6 cm and...Ch. 3 - A 3-cm-long. 2-nuti x 2-mm rectangular...Ch. 3 - Two finned surfaces with long fins are identical,...Ch. 3 - A 20-cm-diameter hot sphere at 120C is buried in...Ch. 3 - A 25-cm-diameter, 2.4-rn-long vertical cylinder...Ch. 3 - Prob. 228PCh. 3 - The walls of a food storage facility are made of a...Ch. 3 - The equivalent thermal resistance for the thermal...Ch. 3 - Prob. 231PCh. 3 - Prob. 232PCh. 3 - Prob. 233PCh. 3 - The fin efficiency is defined as the ratio of the...Ch. 3 - Prob. 235PCh. 3 - In the United States, building insulation is...Ch. 3 - Prob. 237PCh. 3 - A plane brick wall (k=0.7W/m.K) and is 10 cm...Ch. 3 - The temperature in deep space is close to absolute...Ch. 3 - In the design of electronic components, it is...Ch. 3 - Using cylindrical samples of the same material,...Ch. 3 - Find out about the wall construction of the cabins...Ch. 3 - Prob. 243PCh. 3 - A house with 200-m2 floor space is to be heated...
Knowledge Booster
Similar questions
- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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