Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 31, Problem 3P
Apply the results of Prob. 31.2 to compute the temperature distribution for the entire rod using the finite-element approach.
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Chapter 31 Solutions
Numerical Methods For Engineers, 7 Ed
Ch. 31 - 31.1 Repeat Example 31.1, but for and a uniform...Ch. 31 - Repeat Example 31.2, but for boundary conditions...Ch. 31 - Apply the results of Prob. 31.2 to compute the...Ch. 31 - Use Galerkins method to develop an element...Ch. 31 - Prob. 5PCh. 31 - 31.6 Develop a user-friendly program to model the...Ch. 31 - 31.7 Use Excel to perform the same computation as...Ch. 31 - Use MATLAB or Mathcad to develop a contour plot...Ch. 31 - 31.9 Use Excel to model the temperature...Ch. 31 - 31.10 Use MATLAB or Mathcad to develop a contour...
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- Using finite-element method, solve equation: d'T =-f (x) dx? for a 15-cm rod with boundary conditions of TO, ) = 20 and 15, t) = 100 and a uniform heat source of fAx) = 40. flx) T(0, t) TIL, t) X = 0 x = Larrow_forwardQuestion 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 constantarrow_forwardIt will be solved by the INTRODUCTION TO FINITE ELEMENT METHOD.arrow_forward
- 22. Develop an algorithm, along with the program (preferably in python), to find the temperature distribution in the example below NOTE: Use the explicit finite differences method EXAMPLE 5.9 A fuel element of a nuclear reactor is in the shape of a plane wall of thickness 2L = 20 mm and is convectively cooled at both surfaces, with h = 1100 W/m². K and T=250°C. At normal operating power, heat is generated uniformly within the element at a volumetric rate of q₁ = 107 W/m³. A departure from the steady-state conditions associated with normal operation will occur if there is a change in the generation rate. Consider a sudden change to q₂ = 2 × 107 W/m³, and use the explicit finite-difference method to determine the fuel element temperature distribu- tion after 1.5 s. The fuel element thermal properties are k = 30 W/m . K and a = 5 × 10-6 m²/s.arrow_forwardQ3: 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 dTglass = -0.75Tglass + 0.75TPVT (1) dt - 1.18Tglass – 22TpyT + 237wax (2) dt dTwax 12Tglass + 18TpyT – 19 Twax (3) dt Where, Tptass, 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 sappty In frem water Tank Glass PVT Enpann Nane-PCMPVT Collector Wax Tubes Sterg Tank Mat Nanofluid Heat Exchanger Tepe Contalner Tuek et Pump for drainarrow_forwardI.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.arrow_forward
- 5.8 The heat transfer coefficient for air flowing over a sphere is to be determined by observing the temperature-time history of a sphere fabricated from pure copper. The sphere, which is 12.7 mm in diameter, is at 66°C before it is inserted into an airstream having a temperature of 27°C. A thermocouple on the outer surface of the sphere indicates 55°C 69 s after the sphere is inserted into the airstream. Assume and then justify that the sphere behaves as a spacewise isothermal object and calculate the heat transfer coefficient.arrow_forwardSuppose a point satisfies sufficiency conditions for a local minimum. How do you establish that it is a global minimumarrow_forward16.7 with an inner layer of diatomaceous earth, 40 mm thick, and an outer layer of 85% magnesia, 25 mm thick. The inside surface of the pipe is at the steam temperature, and the heat transfer coefficient for the outside surface of the lagging is 17 W/m² K. The thermal conductivities of diatomaceous earth and 85% magnesia are 0.09, and 0.06 W/m K respectively. Neglecting radiation, and the thermal resistance of the pipe A steam main of 150 mm outside diameter containing wet steam at 28 bar is insulated Problems wall, calculate the rate of heat loss per unit length of the pipe and the temperature of the outside surface of the lagging, when the room temperature is 20°C.arrow_forward
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