![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 g](http://img.homeworklib.com/questions/f3e27210-ecaf-11ea-af4c-13cbdeb5b25d.png?x-oss-process=image/resize,w_560)
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5. [8] A bar of length a cm is insulated at both ends. Find the temperature...
Problem 6 Find the temperature in in a laterally insulated bar of length L whose ends...
Problem 6 Find the temperature in in a laterally insulated bar of length L whose ends are also insulated, assuming the same initial temperature profile as in Problem 5. Hint: remember that if the end points are thermally insulated, there is no heat flow. Hence, the temperature gradient must vanish at the endpoints! Problem 5 Find the temperature in a laterally insulated bar of length whose ends are kept at 0° Celsius, assuming that the initial temperature distribution is in...
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 rod of length 1 insulated on both ends, with c2 = 1, so it...
Consider a rod of length 1 insulated on both ends, with c2 = 1, so it follows the heat equation a 22 at 022 If the rod is initially heated with temperature U = U u(x, 0) = f(x) = {1 0 < x < 2 1 < x < 1 1 – 2, what is the temperature of the rod as a function of time?
(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...
please solve 17 for me thanks~~ :) ! temperature f(x) °C, where 5. f(x) = sin 0.1 x 6 f(x) = 4 - 08 |x - 5 7. fix) =x(1...
please solve 17 for me thanks~~ :) !
temperature f(x) °C, where 5. f(x) = sin 0.1 x 6 f(x) = 4 - 08 |x - 5 7. fix) =x(10 - x) 8 Arbitrarytemperatures at ends. If the ends x = 0 and x= Lof the bar in the text are kept at constant 20. CAS PROJECT. Isotherms. Fim solutions (tempe rature s) in the squa with a 2 satisfying the followin tions. Graph isotherms. (a) u80 sin Tx on...
Find the temperature u(x, t) in a rod of length L if the initial temperature is...
Find the temperature u(x, t) in a rod of length L if the initial temperature is f(x) throughout and if the ends x = 0 and x = L are insulated. Solve if L = 2 and f(x) = Jx, 0<x< 1 10, 1<x< 2. ux, t) = + ŠL n = 1
Please provide very detailed steps Find the temperature u(x, t) in a bar of length T...
Please provide very detailed steps
Find the temperature u(x, t) in a bar of length T with thermoconductivity coefficient c2 1 (all the quantities are non-dimensional) under adiabatic boundary conditions (zero heat flux) at ends of the bar if the initial tem- perature u(z, 0) . 130 cos(3x)
Find the temperature u(x, t) in a bar of length T with thermoconductivity coefficient c2 1 (all the quantities are non-dimensional) under adiabatic boundary conditions (zero heat flux) at ends of the...
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)...
Show that for the completely insulated bar (including the ends), ux(0,t) = 0, uz(L,t) 0, and...
Show that for the completely insulated bar (including the ends), ux(0,t) = 0, uz(L,t) 0, and initial condition u(x,0) = f(x), where 1) (use L = 1 and c= 1) f(x) = 1 (5) Can you explain your answer?
* 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
Problem 6 Find the temperature in in a laterally insulated bar of length L whose ends are also insulated, assuming the same initial temperature profile as in Problem 5. Hint: remember that if the end points are thermally insulated, there is no heat flow. Hence, the temperature gradient must vanish at the endpoints! Problem 5 Find the temperature in a laterally insulated bar of length whose ends are kept at 0° Celsius, assuming that the initial temperature distribution is in...
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 rod of length 1 insulated on both ends, with c2 = 1, so it follows the heat equation a 22 at 022 If the rod is initially heated with temperature U = U u(x, 0) = f(x) = {1 0 < x < 2 1 < x < 1 1 – 2, what is the temperature of the rod as a function of time?
(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...
please solve 17 for me thanks~~ :) !
temperature f(x) °C, where 5. f(x) = sin 0.1 x 6 f(x) = 4 - 08 |x - 5 7. fix) =x(10 - x) 8 Arbitrarytemperatures at ends. If the ends x = 0 and x= Lof the bar in the text are kept at constant 20. CAS PROJECT. Isotherms. Fim solutions (tempe rature s) in the squa with a 2 satisfying the followin tions. Graph isotherms. (a) u80 sin Tx on...
Find the temperature u(x, t) in a rod of length L if the initial temperature is f(x) throughout and if the ends x = 0 and x = L are insulated. Solve if L = 2 and f(x) = Jx, 0<x< 1 10, 1<x< 2. ux, t) = + ŠL n = 1
Please provide very detailed steps
Find the temperature u(x, t) in a bar of length T with thermoconductivity coefficient c2 1 (all the quantities are non-dimensional) under adiabatic boundary conditions (zero heat flux) at ends of the bar if the initial tem- perature u(z, 0) . 130 cos(3x)
Find the temperature u(x, t) in a bar of length T with thermoconductivity coefficient c2 1 (all the quantities are non-dimensional) under adiabatic boundary conditions (zero heat flux) at ends of the...
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)...
Show that for the completely insulated bar (including the ends), ux(0,t) = 0, uz(L,t) 0, and initial condition u(x,0) = f(x), where 1) (use L = 1 and c= 1) f(x) = 1 (5) Can you explain your answer?
* 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
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