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Please show all steps in detail. Thank you!! Find the solution of the following diffusion-related PDE, where C is concentration in a fluid medium and diffusion occurs in only one direction, x, as a f...
Please show all steps and write in a legible way. Thank you beforehand! Fully solve the following PDE. Consider a compre...
Please show all steps and
write in a legible way. Thank you beforehand!
Fully solve the following PDE. Consider a compressed gas container of length L, divided in half by a baffle To the left of the porous baffle is a gas of species A, and to the right of it is a different gas of species B. Suppose they are at the same pressure, so that when the baffle is removed at time t-0 the two gases proceed to...
This is PDE problem. Please show all steps in detail with neat handwriting. Problem . Consider...
This is PDE problem. Please show all steps in detail with neat
handwriting.
Problem . Consider the function a) Find the full Fourier Series of F(x) a(0, y, t) = u(a, y, t) 0 u(z, 0, t ) = u(z, b, l) = 0 u(z,y,0) = f(z,y), u(x, y,0)-g(x,y), 0<y< b,t0 a) b) Solve the initial-boundary value problem for 2D wave equation. What is the physical interpretation of these boundary conditions
PDE. Please show all steps in detail. 2. Consider the 1D heat equation in a rod...
PDE. Please show all steps in detail.
2. Consider the 1D heat equation in a rod of length with diffusion constant Suppose the left endpoint is convecting (in obedience to Newton's Law of Cooling with proportionality constant K-1) with an outside medium which is 5000. while the right endpoint is insulated. The initial temperature distribution in the rod is given by f(a)- 2000 -0.65 300, 0<<t (a) Set up the initial-boundary value problem modeling this scenario. (b) Set up and...
That is u(x,0)-f(x) where f(x) (L-x)/(L-a), a<x<L. (a) State the problem including the PDE and all boundary and i...
That is u(x,0)-f(x) where f(x) (L-x)/(L-a), a<x<L. (a) State the problem including the PDE and all boundary and initial conditions (b) Using separation of variables find the displacement u(z,t) for any 0 < z < L, and t > 0. (c) Using values of L = 65 cm, a 15 cm and c-10 cm/sec, produce a surface plot of your solution over the length of the string and the time interval 0<t<10. Include the first 20 terms of your series...
please answer them in detail. The concentration C(x, t) of a pollutant in a semi-infinite pipe diffuses according to the PDE over 0<<o for > 0, where the diffusivity D is a given positive...
please answer them in detail.
The concentration C(x, t) of a pollutant in a semi-infinite pipe diffuses according to the PDE over 0<<o for > 0, where the diffusivity D is a given positive constant. An experiment is performed in which the initial concentration is zero everywhere, so that C(x, 0)0 for all r 20. Once t > 0 a fixed concentration of C(0, t) Co is imposed at x-0, where Co is a constant, and it is also assumed...
2. Consider the following 1-D wave equation with initial condition u (x, 0)- F (x) where F(x) is a given function. a) Show that u (x, t)-F (x - t) is a solution to the given PDE. b) If the function F...
2. Consider the following 1-D wave equation with initial condition u (x, 0)- F (x) where F(x) is a given function. a) Show that u (x, t)-F (x - t) is a solution to the given PDE. b) If the function F is given as 1; x< 10 x > 10 u(x, 0) = F(x) = use part (a) to write the solution u(x, t) c) Sketch u(x,0) and u(x,1) on the same u-versus-x graph d) Explain in your own...
Please show all steps in detail and as legible as possible. Thank you!!! Consider the two dimensional diffusion of heat in a rectangular section of tissue. Specifically solve for the temperature fiel...
Please show all steps in detail and as legible as possible.
Thank you!!!
Consider the two dimensional diffusion of heat in a rectangular section of tissue. Specifically solve for the temperature field, u(x,y,t), in the rectangular section with dimensions having (0<x < a) and (0<y < b), which is governed by the following initial-value, boundary-value problem, where a is a constant: (0,y,t) = 0 uy (x,0,t) = 0 14. (a,y,t) = 0 u(x,b,t)-0 11 (x, y,0) = f(x, y)
Consider...
please provide me with full working solution. Any help is appreciated. thank you in advance Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing...
please provide me with full working solution. Any help is
appreciated. thank you in advance
Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
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...
Only need the answer to problem 3. Please show all steps. In(a) + ? ln(a) where...
Only need the answer to problem 3. Please show all steps.
In(a) + ? ln(a) where ?, satisfying 0 < ? < 1, determines how patient(? larger) or impatient (? smaller) the consumer is. (a) Set up the Lagraungian for this cousumers problen: choose co and c to imaxinize tihe utility function subject to the lifetime budget constraint. [10 pointsl (b) Usc the first-order conditions to obtain an expression that shows how the consiumers optimal choice of cunsumption growth depends...
Please show all steps and
write in a legible way. Thank you beforehand!
Fully solve the following PDE. Consider a compressed gas container of length L, divided in half by a baffle To the left of the porous baffle is a gas of species A, and to the right of it is a different gas of species B. Suppose they are at the same pressure, so that when the baffle is removed at time t-0 the two gases proceed to...
This is PDE problem. Please show all steps in detail with neat
handwriting.
Problem . Consider the function a) Find the full Fourier Series of F(x) a(0, y, t) = u(a, y, t) 0 u(z, 0, t ) = u(z, b, l) = 0 u(z,y,0) = f(z,y), u(x, y,0)-g(x,y), 0<y< b,t0 a) b) Solve the initial-boundary value problem for 2D wave equation. What is the physical interpretation of these boundary conditions
PDE. Please show all steps in detail.
2. Consider the 1D heat equation in a rod of length with diffusion constant Suppose the left endpoint is convecting (in obedience to Newton's Law of Cooling with proportionality constant K-1) with an outside medium which is 5000. while the right endpoint is insulated. The initial temperature distribution in the rod is given by f(a)- 2000 -0.65 300, 0<<t (a) Set up the initial-boundary value problem modeling this scenario. (b) Set up and...
That is u(x,0)-f(x) where f(x) (L-x)/(L-a), a<x<L. (a) State the problem including the PDE and all boundary and initial conditions (b) Using separation of variables find the displacement u(z,t) for any 0 < z < L, and t > 0. (c) Using values of L = 65 cm, a 15 cm and c-10 cm/sec, produce a surface plot of your solution over the length of the string and the time interval 0<t<10. Include the first 20 terms of your series...
please answer them in detail.
The concentration C(x, t) of a pollutant in a semi-infinite pipe diffuses according to the PDE over 0<<o for > 0, where the diffusivity D is a given positive constant. An experiment is performed in which the initial concentration is zero everywhere, so that C(x, 0)0 for all r 20. Once t > 0 a fixed concentration of C(0, t) Co is imposed at x-0, where Co is a constant, and it is also assumed...
2. Consider the following 1-D wave equation with initial condition u (x, 0)- F (x) where F(x) is a given function. a) Show that u (x, t)-F (x - t) is a solution to the given PDE. b) If the function F is given as 1; x< 10 x > 10 u(x, 0) = F(x) = use part (a) to write the solution u(x, t) c) Sketch u(x,0) and u(x,1) on the same u-versus-x graph d) Explain in your own...
Please show all steps in detail and as legible as possible.
Thank you!!!
Consider the two dimensional diffusion of heat in a rectangular section of tissue. Specifically solve for the temperature field, u(x,y,t), in the rectangular section with dimensions having (0<x < a) and (0<y < b), which is governed by the following initial-value, boundary-value problem, where a is a constant: (0,y,t) = 0 uy (x,0,t) = 0 14. (a,y,t) = 0 u(x,b,t)-0 11 (x, y,0) = f(x, y)
Consider...
please provide me with full working solution. Any help is
appreciated. thank you in advance
Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
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...
Only need the answer to problem 3. Please show all steps.
In(a) + ? ln(a) where ?, satisfying 0 < ? < 1, determines how patient(? larger) or impatient (? smaller) the consumer is. (a) Set up the Lagraungian for this cousumers problen: choose co and c to imaxinize tihe utility function subject to the lifetime budget constraint. [10 pointsl (b) Usc the first-order conditions to obtain an expression that shows how the consiumers optimal choice of cunsumption growth depends...
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