A hollow infinite cylinder has internal radius 0.5 and exterior radius 2.0. The external surface is maintained at 0°C and the internal surface at 100°C. Initially the cylinder has a uniform temperature of 15°C and it is required to compute the distribution of temperature across the radius as time progresses. Use an explicit method with a suitable time step to compute the temperature for r = 0.5(0.25)2.0 for the first few time steps.

A hollow infinite cylinder has internal radius 0.5 and exterior radius 2.0. The external surface is maintained at 0°C and the internal surface at 100°C. Initially the cylinder has a uniform temperature of 15°C and it is required to compute the distribution of temperature across the radius as time progresses. Use an explicit method with a suitable time step to compute the temperature for r = 0.5(0.25)2.0 for the first few time steps.

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 5.10P: 5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder...

See similar textbooks

Similar questions

Derive a formula for the thermal resistance, R₁, for a spherical shell assuming one- dimensional heat flux in the radial direction. The inside and outside radii of the spherical shell are r; and r., respectively, and the shell is made of a material having thermal conductivity k. Assume the temperatures at the inside and outside surfaces of the shell are T and T., respectively. The thermal resistance formula assumes the rate of heat transfer through the spherical shell, Q, is constant. The heat flux is in the radial direction for this one-dimensional case, and the dT heat flux is given by Fourier's law: q, = -k The rate of heat transfer through a dr spherical surface is Q =q₁A where A = 4лr². Derive the formula for the thermal 1 ++)) r = resistance for a spherical shell answer: R₁ 1 1 4лk ri
The initial temperature distribution of a 5 cm long stick is given by the following function. The circumference of the rod in question is completely insulated, but both ends are kept at a temperature of 0 °C. Obtain the heat conduction along the rod as a function of time and position ? (x = 1.752 cm²/s for the bar in question) 100 A) T(x1) = 1 Sin ().e(-1,752 (³¹)+(sin().e (-1,752 (²) ₁ + 1 3π TC3 .....) 100 t + ··· ....... 13) T(x,t) = 200 Sin ().e(-1,752 (²t) + (sin (3). e (-1,752 (7) ²) t B) 3/3 t + …............) C) T(x.t) = 200 Sin ().e(-1,752 (²t) (sin().e(-1,752 (7) ²) t – D) T(x,t) = 200 Sin ().e(-1,752 (²)-(sin().e (-1,752 (²7) ²) t E) T(x.t)=(Sin().e(-1,752 (²t)-(sin().e(-1,752 (²) t+ t + ··· .........) t +.... t + ··· .........) …..)
A 1-D conduction heat transfer problem with internal energy generation is governed by the following equation: +-= dx2 =0 W where è = 5E5 and k = 32 If you are given the following node diagram with a spacing of Ax = .02m and know that m-K T = 611K and T, = 600K, write the general equation for these internal nodes in finite difference form and determine the temperature at nodes 3 and 4. Insulated Ar , T For the answer window, enter the temperature at node 4 in Kelvin (K). Your Answer: EN SORN Answer units Pri qu) 232 PM 4/27/2022 99+ 66°F Sunny a . 20 ENLARGED oW TEXTURE PRT SCR IOS DEL F8 F10 F12 BACKSPACE num - %3D LOCK HOME PGUP 170
Write the finite difference form of the two dimensional steady state heat conduction equation with internal heat generation at a constant rate ‘g’ for a region 0.03m X 0.03m by using a mesh size ∆x=∆y= 0.01 m for a material having thermal conductivity 25 W/m.K and heat generation rate, 107 W/m3 . All the boundary surfaces are maintained at 10°C. Express the finite difference equations in matrix form for the unknown node temperatures.
Question 2: Air at the temperature of T1 is being heated with the help of a cylindrical cooling fin shown in the figure below. A hot fluid at temperature To passes through the pipe with radius Rc. a) Derive the mathematical model that gives the variation of the temperature inside the fin at the dynamic conditions. b) Determine the initial and boundary conditions to solve the equation derived in (a). air To Re Assumptions: 1. Temperature is a function of only r direction 2. There is no heat loss from the surface of A 3. Convective heat transfer coefficient is constant
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
Question 2: Air at the temperature of T1 is being heated with the help of a cylindrical cooling fin shown in the figure below. A hot fluid at temperature To passes through the pipe with radius Rc. a) Derive the mathematical model that gives the variation of the temperature inside the fin at the dynamic conditions. b) Determine the initial and boundary conditions to solve the equation derived in (a). air T1 Re Assumptions: 1. Temperature is a function of onlyr direction 2. There is no heat loss from the surface of A 3. Convective heat transfer coefficient is constant
I am able to find the first row and the first column of by hand. However, When I do the 2nd row and 2nd column, my answer doesnt match my matlab code. Would someone be able to help me? Thank you! Use the explicit method to solve by hand the 1D heat equation for the temperature distribution in a laterally insulated wire with a length of 1 cm, whose ends are kept at T(0) = 0 0C and T(1) = 0 0C, for 0 ≤ x ≤ 1 and 0 ≤ t ≤ 0.5. At t = 0, the temperature of the wire is subjected to initial condition T(x) = 100sin(πx). Use the following values of k = 0.15 cm2/s, Δx = 0.25 cm, and Δt = 0.1 s. Calculate by hand the values of temperature at the internal mesh points only for the first time row at t = 0.1 s. Verify the values of temperature at t = 0.1 s calculated by hand. Use Heat1DCN.m M-file to solve the 1D heat equation within the space-time domain 0 ≤ x ≤ 1 and 0 ≤ t ≤ 2 with Δx = 0.05 cm and Δt = 0.1 s. Make the plot of temperature surface.
A thermometer has a time constant of 10 s and behaves as a first-order system. It is initially at a temperature 30°C and then suddenly subjected to a surrounding temperature of 150°C. Calculate the 90 percent rise time and the time to attain 99 percent of the steady-state temperature. Repeat these calculations for a time constant of 5 s and compare the results with that of the previous case
2. Use Separation of variables method to find the heat distribution function u(x, t) of a metal bar of length 30 cm. If it has an initial temperature of f(x) = 2x + 3 °C and its left and right ends are both contacted with ice at 0 °C. (Take a = 1)
5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder (0.1 m diameter, thermal conductivity of 0.2 W/m K) with uniform internal heat generation. By dimensional analysis, determine the relation between the steady-state temperature at the center of the cylinder , the diameter, the thermal conductivity, and the rate of heat generation. Take the temperature at the surface as your datum. What is the equation for the center temperature if the difference between center and surface temperature is when the heat generation is ?
After a thorough derivation by Doraemon to establish an equation for cylindrical fuel rod of a nuclear reactor. Here he was able to come up an equation of heat generated internally as shown below. 96 = 9. where qG is the local rate of heat generation per unit volume at radius r, ro is the outside radius, and qo is the rate of heat generation per unit volume at the centre line. Calculate the temperature drop from the centre line to the surface for a 2.5 cm outer diameter rod having k = 25 W/m K, if the rate of heat removal from the surface is 1650 kW/m2 A 619 °C 719 °C C) 819 °C 919 °C E 1019 °C F None of these