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2. (16pts) Consider the following heat equation for a rod of length L=1 with constant thermal...
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<
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...
The ends of a metal rod of length L = 100 cm and thermal diffusivity a...
The ends of a metal rod of length L = 100 cm and thermal diffusivity a = 1 are subjected to temperatures of 0 °C, that is to say T (0, t) = T (L, t) = 0 °C. Knowing that the temperature distribution at t = 0, is T(x,0) = 100 sin (2 x) – 50(34x). Note that the maximum temperature of the rod is in the center of the rod and it is equal to 150 °C. a)...
heat transfer Consider a long solid rod of constant thermal conductivity k whose cross section is...
heat transfer
Consider a long solid rod of constant thermal conductivity k whose cross section is a sector of a circle of radius ro and the angle a as shown in the figure. A peripheral heat flux 9":falls onto the peripheral surface. The plane surface at - O is kept isothermal at the ambient temperature T.. The other plane surface at = a loses heat by convection to the ambient. The steady temperature distribution is a function of r and...
Determinc the equilibrium temperature distribution for a one-dimensional rod with constant thermal properties with the following...
Determinc the equilibrium temperature distribution for a one-dimensional rod with constant thermal properties with the following sources and bound- ary conditions: 1.4.1. * (a) Q=0, f) Ko 0
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg.K, and p=400 kg/m3. (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m?. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m².K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q'"...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg.K, and p=400 kg/m3. (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m?. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m².K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q'"...
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...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg-K, and p=400 kg/m² (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m2K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q"'...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg-K, and p=400 kg/m² (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m2K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q"'...
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<
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...
The ends of a metal rod of length L = 100 cm and thermal diffusivity a = 1 are subjected to temperatures of 0 °C, that is to say T (0, t) = T (L, t) = 0 °C. Knowing that the temperature distribution at t = 0, is T(x,0) = 100 sin (2 x) – 50(34x). Note that the maximum temperature of the rod is in the center of the rod and it is equal to 150 °C. a)...
heat transfer
Consider a long solid rod of constant thermal conductivity k whose cross section is a sector of a circle of radius ro and the angle a as shown in the figure. A peripheral heat flux 9":falls onto the peripheral surface. The plane surface at - O is kept isothermal at the ambient temperature T.. The other plane surface at = a loses heat by convection to the ambient. The steady temperature distribution is a function of r and...
Determinc the equilibrium temperature distribution for a one-dimensional rod with constant thermal properties with the following sources and bound- ary conditions: 1.4.1. * (a) Q=0, f) Ko 0
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg.K, and p=400 kg/m3. (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m?. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m².K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q'"...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg.K, and p=400 kg/m3. (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m?. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m².K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q'"...
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...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg-K, and p=400 kg/m² (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m2K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q"'...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg-K, and p=400 kg/m² (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m2K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q"'...
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