Homework Answers
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Problem 6 Find the temperature in in a laterally insulated bar of length L whose ends...
5. [8] A bar of length a cm is insulated at both ends. Find the temperature...
5. [8] A bar of length a cm is insulated at both ends. Find the temperature u(x,t), when 3, and u(x,0) = f(x) = x. Find and give an interpretation of the steady state solution. a =
2. Solve the one-dimensional heat equation problem for a unit length bar with insulated ends with...
2. Solve the one-dimensional heat equation problem for a unit length bar with insulated ends with a prescribed initial linear temperature distribution: c2uxx = 111 , l4 (0,t)-14 (l,t)-0, 0 < x < 1 20-x) , Last Name A-M 3x, Last Name N -Z u(x,0) = The general solution to this problem is given in Example 4, page 563 in the text in terms of a Fourier Cosine Series. Write out the solution steps and evaluate the Fourier coefficients by...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
4.1.1. Suppose the ends of a bar of length l and therrnal diffusivity γ = 1 are held fixed at res...
This is a PDE problem. I need help witb a, b and c
4.1.1. Suppose the ends of a bar of length l and therrnal diffusivity γ = 1 are held fixed at respective temperatures 0° and 10°. (a) Determine the equilibrium temperature profile (b) Determine the rate at which the equilibrium temperature profile is approached (c) What does the temperature profile look like as it nears equilibrium?
4.1.1. Suppose the ends of a bar of length l and therrnal...
(a) The heat flux through the faces at the ends of bar is found to be...
(a) The heat flux through the faces at the ends of bar is found to be proportional to un au/an at the ends. If the bar is perfectly insulated, also at the ends x 0 and x L are adiabatic conditions, Q1 ux(0, t) = 0 0 (2'7)*n prove that the solution of the heat transfer problem above (adiabatic conditions at both ends) gives as, 2 an: nnx u(x, t) Ao t An cos n-1 where Ao and An are...
Homework 5: Problem 9 Next Problem Problem List Previous Problem (1 point) Find the temperature function...
Homework 5: Problem 9 Next Problem Problem List Previous Problem (1 point) Find the temperature function u(r, t) (where is the position along the rod in cm and t is the time) of a 12 cm rod with conducting constant 0,1 whose endpoint are insulated such that no heat is lost, and whose initial temperature distribution is given by: if 6< <8 4 u (,0) 10 otherwise 0.1 To start, we have L 12 Because the rods are insulated, we...
Use the 1D diffusion equation to find T(x,t): 2. A bar of length L has an...
Use the 1D diffusion equation to find T(x,t):
2. A bar of length L has an initial temperature distribution T(x,0) = a + br ( x = L are the ends of the bar). The ends are insulated. Find T(x,t) for t > 0. 0 and си oFlu сх
* Exercise 4: Let k,l 〉 0. The temperature of a rod insulated at the ends...
* Exercise 4: Let k,l 〉 0. The temperature of a rod insulated at the ends with an expo- nentially decreasing heat source in it satisfies the following problem: ux (0, t) u(z,0) 0 = ux (1, t), φ(z) Find the solution to this problem by writing u as a cosine series: Ao(t) u(x, t) An(t) cos and determine limt-Hou(z, t
4) An infinite bar with thermal conductivity of k and thickness L is insulated on the...
4) An infinite bar with thermal conductivity of k and thickness L is insulated on the left surface, whereas air is flowing over the right surface. The bar generates heat at a uniform volumetric rate. State your assumptions clearly. • Derive an expression for temperature profile within the rod in steady state. (20 points) Draw temperature profile for a case, when heat is being generated within the rod. (5 points) Draw temperature profile for the case, when heat is being...
Copper wire coated insulating materials on its surface is assumed perfectly insulated laterally. Thus heat in the w...
Copper wire coated insulating materials on its surface is assumed perfectly insulated laterally. Thus heat in the wire flows in x-direction only. In this case the temperature of the wire can be modeled by 1-D heat equation: =c ends (x-0 and x-L) of the wire are also insuiated for all time and initially temperature distribution of the wire can be modeled by /() Please derive u(x,t) of the copper wire. (15 points) b. If f(x) cos(x). piease tind temperature distribution...
5. [8] A bar of length a cm is insulated at both ends. Find the temperature u(x,t), when 3, and u(x,0) = f(x) = x. Find and give an interpretation of the steady state solution. a =
2. Solve the one-dimensional heat equation problem for a unit length bar with insulated ends with a prescribed initial linear temperature distribution: c2uxx = 111 , l4 (0,t)-14 (l,t)-0, 0 < x < 1 20-x) , Last Name A-M 3x, Last Name N -Z u(x,0) = The general solution to this problem is given in Example 4, page 563 in the text in terms of a Fourier Cosine Series. Write out the solution steps and evaluate the Fourier coefficients by...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
This is a PDE problem. I need help witb a, b and c
4.1.1. Suppose the ends of a bar of length l and therrnal diffusivity γ = 1 are held fixed at respective temperatures 0° and 10°. (a) Determine the equilibrium temperature profile (b) Determine the rate at which the equilibrium temperature profile is approached (c) What does the temperature profile look like as it nears equilibrium?
4.1.1. Suppose the ends of a bar of length l and therrnal...
(a) The heat flux through the faces at the ends of bar is found to be proportional to un au/an at the ends. If the bar is perfectly insulated, also at the ends x 0 and x L are adiabatic conditions, Q1 ux(0, t) = 0 0 (2'7)*n prove that the solution of the heat transfer problem above (adiabatic conditions at both ends) gives as, 2 an: nnx u(x, t) Ao t An cos n-1 where Ao and An are...
Homework 5: Problem 9 Next Problem Problem List Previous Problem (1 point) Find the temperature function u(r, t) (where is the position along the rod in cm and t is the time) of a 12 cm rod with conducting constant 0,1 whose endpoint are insulated such that no heat is lost, and whose initial temperature distribution is given by: if 6< <8 4 u (,0) 10 otherwise 0.1 To start, we have L 12 Because the rods are insulated, we...
Use the 1D diffusion equation to find T(x,t):
2. A bar of length L has an initial temperature distribution T(x,0) = a + br ( x = L are the ends of the bar). The ends are insulated. Find T(x,t) for t > 0. 0 and си oFlu сх
* Exercise 4: Let k,l 〉 0. The temperature of a rod insulated at the ends with an expo- nentially decreasing heat source in it satisfies the following problem: ux (0, t) u(z,0) 0 = ux (1, t), φ(z) Find the solution to this problem by writing u as a cosine series: Ao(t) u(x, t) An(t) cos and determine limt-Hou(z, t
4) An infinite bar with thermal conductivity of k and thickness L is insulated on the left surface, whereas air is flowing over the right surface. The bar generates heat at a uniform volumetric rate. State your assumptions clearly. • Derive an expression for temperature profile within the rod in steady state. (20 points) Draw temperature profile for a case, when heat is being generated within the rod. (5 points) Draw temperature profile for the case, when heat is being...
Copper wire coated insulating materials on its surface is assumed perfectly insulated laterally. Thus heat in the wire flows in x-direction only. In this case the temperature of the wire can be modeled by 1-D heat equation: =c ends (x-0 and x-L) of the wire are also insuiated for all time and initially temperature distribution of the wire can be modeled by /() Please derive u(x,t) of the copper wire. (15 points) b. If f(x) cos(x). piease tind temperature distribution...
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