Solution: II
A bar with thermal diffusivity 25 and length \pi has both ends at zero temperature. The initial temperature of the bar is f(x) =x. The solution of the corresponding heat equation is given by
'
A.
The initial condition(IC) is given at t=0,
The boundary condition(BC) is given by at x=0 and at x=L;
and
Therefore initial and boundary conditions are given by:
B. We know that
Multiplying both sides by , and integrating from 0 to L, we have
The initial b, and simplify Find the Find the temperature at th emiddle of the rod after w seconds using the first two terms of the A. The initial b, and simplify Find the Find the temperatu...
(10 Points) To find the heat conduction coefficient of Iron: an Iron rod with diameter of 4 cm and length of 50 cm used for the following tests. 1: The rod heated to 650 oC (Uniform Temperature) at first and immersed in water bath at 50 oC and heat transfer coefficient of h=16.3 kW/m2oC. The surface temperature of the rod measured to be 250 oC after 3.45 seconds. 2: Then we removed the rod and immersed into a new water...
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. 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/m3. 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/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'"...
Simplify your answer. 71 Find the first five terms of the Taylor series for f(x) = cost centered at c=
1-find the recurrence relation using power series solutions. 2-find the first four terms in each of two solutions y1 and y2 3-by evaluating wronskian w(y1,y2) show that they from a fundamental solution set. Iy yry 0, zo = 1
Differential equations Find the first four nonzero terms in a power series expansion about xo - 2 for the solution to the given initial value problem Find the first four nonzero terms in a power series expansion about xo - 2 for the solution to the given initial value problem
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)...
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"'...