Solve the heat equation u, = 0.2u on a digital computer usingXXthe Crank-Nicolson scheme.for the initial conditionand boundary conditionsTABLE P4.1Case12345Number ofGrid Points1111161111(x,0) = 100 sinTXL0.250.500.501.002.00L = 1u(0,t) = u(L,t) = 0Compute to t = 0.5 using the parameters in Table P4.1 (if possible) and compare graphicallywith the exact solution.

Answered: Image /qna-images/answer/da2c76dc-cbee-4df9-bb91-ca8834d99972.jpg

Solve the heat equation u, = 0.2u on a digital computer using the Crank-Nicolson scheme. for the initial condition and boundary conditions TABLE P4.1 Case 1 2 3 4 5 Number of Grid Points 11 11 16 11 11 u(x,0)= 100 sin JA L 0.25 0.50 0.50 1.00 2.00 L=1 u(0,1)= u(L,t)=0 Compute to t = 0.5 using the parameters in Table P4.1 (if possible) and compare graphically with the exact solution.

Solve the heat equation u, = 0.2u on a digital computer using the Crank-Nicolson scheme. for the initial condition and boundary conditions TABLE P4.1 Case 1 2 3 4 5 Number of Grid Points 11 11 16 11 11 u(x,0)= 100 sin JA L 0.25 0.50 0.50 1.00 2.00 L=1 u(0,1)= u(L,t)=0 Compute to t = 0.5 using the parameters in Table P4.1 (if possible) and compare graphically with the exact solution.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.12P

See similar textbooks

Similar questions

I.C 02/A/ Use the Crank-Nicolson method to solve for the temperature distribution of a long thin rod with a length of 10 cm and the following values: k = 0.49 cal/(s cm °C), Ax = 2 cm, and At = st 0.1 s. Initially the temperature of the rod is 0°C and the boundary conditions are fixed for all times at 7(0, t) = 100°C and 7(10, t) = 50°C. Note that the rod is aluminum with C = 0.2174 cal/g °C) and p = 2.7 g/cm³. List the tridiagonal system of equations and determined the temperature up to 0.1 s.
A// Use Implicit Method to solve the temperature distribution of a long thin rod with a length of 9 cm and following values: k = 0.49 cal/(s cm °C), Ax = 3 cm, and At = 0.2 s. At t=0 s, the temperature of the rod is 10°C and the boundary conditions are fixed dT (9,t) 1 °C/cm. Note that the rod for alltimes at 7(0,t) = 80°C and derivative condition dx is aluminum with C = 0.2174 cal/g °C) and p = 2.7 g/cm³. Find the temperature values on the inner grid points and the right boundary for t = 0.4 s.
1. A spring mass system serving as a shock absorber under a car's suspension, supports the M=1000kgmass of the car. For this shock absorber,k=1000N/m and c=2000N s/m. The car drives over a corrugated road with force F=2000sin(wt)N. Use your notes to model the second order differential equation suited to thisapplication. Simplify the equation with the coefficient of x'' as one. Solve x (the general solution) interms of using the complimentary and particular solution method. In determining the coefficients ofyour particular solution, it will be required that you assume w2 -1=w or . Do not 1-w2=-wuse Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.You must indicate in your solution:1. The simplified differential equation in terms of the displacement x you will be solving2. The m equation and complimentary solution3. The choice for the particular solution and the actual particular solution xp4. Express the solution x as a piecewise…
(3) For the given boundary value problem, the exact solution is given as = 3x - 7y. (a) Based on the exact solution, find the values on all sides, (b) discretize the domain into 16 elements and 15 evenly spaced nodes. Run poisson.m and check if the finite element approximation and exact solution matches, (c) plot the D values from step (b) using topo.m. y Side 3 Side 1 8.0 (4) The temperature distribution in a flat slab needs to be studied under the conditions shown i the table. The ? in table indicates insulated boundary and Q is the distributed heat source. I all cases assume the upper and lower boundaries are insulated. Assume that the units of length energy, and temperature for the values shown are consistent with a unit value for the coefficier of thermal conductivity. Boundary Temperatures 6 Case A C D. D. 00 LEGION Side 4 z epis
Find the temperature at the interior node given in the following figure 100 °C 75 °C 0 °C 9" %3D 25 °C 6" Using the Lieberman method and relaxation factor of 1.2, the temperature estimated after first iterations is: Select one: а. 60.00 b. 45.19 С. 50.00
Q3: Consider evaluation of different temperatures of solar photovoltaic/thermal system (PVT) as shown in Figure 1(a). The following set of differential equations represent energy balance equations to be solve using matrices and eigenvalues using MATLAB: dTglass = -0.75Tgtass + 0.75TpvT (1) dt - 1.187glass – 22Tpyr + 23Twax (2) dt dTwax 12Tglass + 18TpyT – 19 Twax (3) dt Where, Tgtass , TPVT, and Twax, are temperatures illustrated in Figure 1(b). At time t-0 the initial conditions are Tglass = 35 , Tpyr = 33, and Twax = 31 °C. Cold suppty In frem water Tank Glass PVT Espann Nane-PCMPVT Collector Wax Tubes Sterg Tank Nanofluid Heat Exchanger Contalner Tepe Teek oe Pump for drain
The temperature on a sheet of metal is known to vary according to the following function: T(z,9) – 4z - 2ry We are interested to find the maximum temperature at the intersection of this sheet with a cylindrical pipe of negligible thickness. The equation of the intersection curve can be approximated as: 2+-4 Find the coordinates for the location of maximum temperature, the Lagrangian multiplier and the value of temperature at the optimum point. Wnite your answer with two decimal places of accuracy. HINT: IF there are more than one critical point, you can use substitution in the objective function to select the maximum. Enter your results here: Optimum value of z Optimum value of y Optimum value of A Optimum value of T
The amount of heat conducted through a wall of length r is given by Fourier's Law:. CONDUCTION RATE EQUATION T FOURIER'S LAW q, = -k A dT dx T, >T, where q, is the heat flux, k is a proportionality factor, Ais the wall's cross-sectional area, and 4 is the temperature gradient throughout the wall. Our friend Matt Labb wants to find T2 (temperature of the wall's rightmost edge) given q,, k, and A. Is this possible? If so, briefly explain how to find Tp. If not, briefly explain why.
Let's assume that the outdoor temperature in your region was 1 C on 26.12.2002. Let's assume that you use a 2088 W heater in the room in order to keep the indoor temperature of the room at 20 ° C. In the meantime, a 68 W light bulb for lighting, a computer you use to solve this question and load it into the system (let's assume it consumes 217 W of energy), you and your two friends (three people in total) are in the room to assist you in solving the questions. A person radiates 45 J of heat per second to his environment. When you consider all these conditions, calculate the exergy destruction caused by the heat loss from the exterior wall of your room.
Use Euler's method, with step size, h = 0.1, to approximate the solution at t= 0.3 for the initial value problem dx = =x-t , x(0)=1 dt
In the Fig. 2 below, let Ki = K2 = K and ti = t=t. %3D T -T X Fig. 2 (a) Let T= 0 °C and T= 200 °C. Solve for T: and unknown rates of heat flow in term of k and t. MEC_AMO_TEM_035_02 Page 2 of 11 Finite Element Analysis (MECH 0016.1) – Spring - 2021 -Assignment 2-QP (b) Let T- 400 °C and let fs have the prescribed value f. What are the unknowns? Solve for them in term of K, t, and f.
Q2/A/ Use the Crank-Nicolson method to solve for the temperature distribution of a long thin rod C with a length of 10 cm and the following values: k = 0.49 cal/(s cm °C), Ax = 2 cm, and At = st 0.1 s. Initially the temperature of the rod is 0°C and the boundary conditions are fixed for all times C=0.2174 cal/g °C) at 7(0, t) = 100°C and T(10, t) = 50°C. Note that the rod is aluminum with and = 2.7 g/cm³. List the tridiagonal system of equations and determined the temperature up P to 0.1 s.