Homework Answers
Problem in this then comment below.i will help you..
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please thumbs up for this solution..thanks..
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you did small mistake .. actually first term is h in place of n in both exponents...
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first box = e^(-ht)
2nd box = e^(-(h+k(n*pi/L)^2)t) cos(n*pi*x/L)
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Suppose heat is lost from the lateral surface of a thin rod of length L into...
Problem #6: A rod of length I coincides with the interval [0, L] on the x-axis....
Problem #6: A rod of length I coincides with the interval [0, L] on the x-axis. Let u(x, t) be the temperature. Consider the following conditions. (A) There is heat transfer from the lateral surface of the rod into the surrounding medium, which is held at temperature 0° (B) There is heat transfer from the left end into the surrounding medium, which is held at a constant temperature of 0° (C) The left end is insulated. (D) The right end...
For (1) – (3), the model is with regards to a rod of length L with...
For (1) – (3), the model is with regards to a rod of length L with thermal diffusivity k coinciding along the interval (0, L) on the z-axis. Set up the boundary-value problem for the temperature u(x,t). (1) The left end is insulated and the right end is held at a temperature of 0°. The initial temperature is 1° throughout. (2) The left end is at a temperature of 50e-t, the right end if held at zero, and there is...
Partial Differential Equations Question: A homogeneous cylindrical rod of length L = 1 is insulated along...
Partial Differential Equations Question: A homogeneous cylindrical rod of length L = 1 is insulated along the cylindrical side. At the end caps, heat exchange obeys Newton’s law of cooling, i.e. the flux is proportional to the difference of the temperature of the rod with that of the surrounding medium, written explicitly as ux(0,t) = u(0,t ) -T1 and ux(1,t) = T2- u(1,t) where T1 = 0 and T2 = 1. Find the steady state distribution of the temperature.
A thin flat plate of length L, thickness t, and width W> L is thermally joined...
A thin flat plate of length L, thickness t, and width W> L is thermally joined to two large heat sinks that are maintained at a temperature T.. The bottom of the plate is well insulated, while the net heat flux to the top surface of the plate is known to have a uniform value of Heat sink T. Heat sink T. a) Derive the differential equation that determines the steady-state temperature distribution T(x) in the plate. b) Solve the...
The conductive heat transfer in a rod of length L is described by the equation au...
The conductive heat transfer in a rod of length L is described by the equation au ди əraat ,0<r<L,+20 where u(x, t) is the local temperature of the rod, t is time, and a is a positive constant describing the thermal conductivity of the rod. The initial and boundary conditions are: T(r, 0) = 0, T(L, t) = 0, and T (0, 1) = 1 for > 0 (1) Find the general solution of this PDE. (11) Find the eigenvalues...
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
2. Consider a thin rod of length L = π (so that 0 x-7) with a...
2. Consider a thin rod of length L = π (so that 0 x-7) with a general internal source of heat, Q(a,t) Ot (10) subject to insulated boundary conditions The initial temperature of the bar is zero a(x, 0) = 0 (12) (a) (3pts) What is k in (10)? (b) (10pts) Assume a separable solution to the homogeneous version of the PDE and boundary conditions (10)-(11) of the form u(r, t)- o(x)G(t). Write down or find the eigenvalues λη and...
The heat that is conducted through a body must frequently be removed by other heat transfer...
The heat that is conducted through a body must frequently be removed by other heat transfer processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature T. The conductivity of the aluminum fin (k) and coefficient of heat convection of...
matlab code Heat Equation ice ice Thin metal rod insulated everywhere except at the edges. At...
matlab code
Heat Equation ice ice Thin metal rod insulated everywhere except at the edges. At t =0 the rod is placed in ice (OT(X.) T(x:1) = 0) T(0,1)=T(1.1)=0- T(4,0) = sin(2x)
2. Consider the 1D heat equation in a rod of length with diffusion constant Suppose the left endp...
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<
Problem #6: A rod of length I coincides with the interval [0, L] on the x-axis. Let u(x, t) be the temperature. Consider the following conditions. (A) There is heat transfer from the lateral surface of the rod into the surrounding medium, which is held at temperature 0° (B) There is heat transfer from the left end into the surrounding medium, which is held at a constant temperature of 0° (C) The left end is insulated. (D) The right end...
For (1) – (3), the model is with regards to a rod of length L with thermal diffusivity k coinciding along the interval (0, L) on the z-axis. Set up the boundary-value problem for the temperature u(x,t). (1) The left end is insulated and the right end is held at a temperature of 0°. The initial temperature is 1° throughout. (2) The left end is at a temperature of 50e-t, the right end if held at zero, and there is...
A thin flat plate of length L, thickness t, and width W> L is thermally joined to two large heat sinks that are maintained at a temperature T.. The bottom of the plate is well insulated, while the net heat flux to the top surface of the plate is known to have a uniform value of Heat sink T. Heat sink T. a) Derive the differential equation that determines the steady-state temperature distribution T(x) in the plate. b) Solve the...
The conductive heat transfer in a rod of length L is described by the equation au ди əraat ,0<r<L,+20 where u(x, t) is the local temperature of the rod, t is time, and a is a positive constant describing the thermal conductivity of the rod. The initial and boundary conditions are: T(r, 0) = 0, T(L, t) = 0, and T (0, 1) = 1 for > 0 (1) Find the general solution of this PDE. (11) Find the eigenvalues...
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
2. Consider a thin rod of length L = π (so that 0 x-7) with a general internal source of heat, Q(a,t) Ot (10) subject to insulated boundary conditions The initial temperature of the bar is zero a(x, 0) = 0 (12) (a) (3pts) What is k in (10)? (b) (10pts) Assume a separable solution to the homogeneous version of the PDE and boundary conditions (10)-(11) of the form u(r, t)- o(x)G(t). Write down or find the eigenvalues λη and...
The heat that is conducted through a body must frequently be removed by other heat transfer processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature T. The conductivity of the aluminum fin (k) and coefficient of heat convection of...
matlab code
Heat Equation ice ice Thin metal rod insulated everywhere except at the edges. At t =0 the rod is placed in ice (OT(X.) T(x:1) = 0) T(0,1)=T(1.1)=0- T(4,0) = sin(2x)
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<
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