Consider a uniform rod of length L with an initial temperature given by u(x,0) = sin(Tx/L), 0 ≤x≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² = 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x.

Consider a uniform rod of length L with an initial temperature given by u(x,0) = sin(Tx/L), 0 ≤x≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² = 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

) Find the steady state temperature, u(r, 0), in the plate shown in the following figure. "="0 atr=2 U=0 y = x insulated at r= 1 u=0 at 0=0 X
4. For a particular thermocouple, if one junction is maintained at 0°C (cold junction) and the other junction is used as a probe to measure the desired Celsius temperature t, the voltage V generated in the circuit related to the temperature t as V = t (a + bt) Further, for this thermocouple, when V is in millivolts, the two constants are a = 0.25 and b = -5.5 x10+. Determine the value of V if the measured temperature is 100°C.
A one-meter long bar has been heated unevenly, with temperature in °C at a distance z meters from one end at time t given by H(2, t) = 110e 0.06t sin(rz) 0 < <1. (a) On a sheet of paper, sketch a graph of H against z for t = 0 and t = 1. Use this graph to select all correct statements below. A. When t = 0, the rod is the same temperature throughout B. The rod is coldest at the r = 0 end, and warmest at the a = 1 and C. The two ends of the rod remain at 0°C D. The rod is coldest in the middle E. The middle of the rod gets colder over time F. The closer you are to the middle of the rod, the greater the temperature change from t = 0 to t = 1 G. None of the above %3D (b) On a sheet of paper, sketch a graph of H against t for a= 1/8, a= 1/4, and a = 1/2. Use this graph, and your observations from the previous graph, to select all correct statements below. JA. As time goes on, all part of the rod approach the same temperature B. The temperature near the middle of the rod changes most quicky…
consider a system that involves a lower critical solution temperature, the components are more miscible at high temperatures because they form a complex (true or false?)
differential equation A metal bar is placed in a room at constant temperature of 0°C. If after 25 mins the temperature of bar drops from 120°C to 55°C, find how many minutes the metal bar will continue to cool from 55°C to 50°C.
5. A platform is suspended by two parallel rods, as shown in the sketch, with each rod being 1.28 cm in diameter. Rod A is manufactured from 4340 steel (Q+T 650 °C) (E= 210 MPa, o.2 = 855 MPa) ; rod B is made from 7075-T6 aluminium alloy (E= 70 GPa, oo.2 = 505 MPa). a) Develop an equation giving the realtionship between the applied force and the elastic strain in the rods up to the point of yielding. Assume full elastic behaviour up to the yield strength given above and that the loading is such that the elastic strain in each rod will be the same.
Q 2: A rod 10cm long, has its ends A and B kept at 50°C and 100°C, respectively, until steady state conditions prevail. The temperature at each end is then suddenly reduced to 0°C and kept so. Find the funetion of distribution temperature along the rod?
Q3) for f(x) = sec2(2x – 1) and g(x) = tan?(2x – 1) show that f'(x) = g'(x).
Constants I Periodic Table A cylindrical pipe has inner radius R1 and outer radius R2 . The interior of the pipe carries hot water at temperature T1. The temperature outside is T, (< T1). Suppose the pipe is steel with R1 of its temperature? = 3.3 cm , R2 = 4.2 cm , and T2 = 18 °C. If the pipe holds still water at Ti = 70 ° C, what will be the initial rate of change Express your answer using two significant figures. Πν ΑΣφ dT °C/s dt Previous Answers Request Answer Submit X Incorrect; Try Again; 8 attempts remaining Part C Suppose water at 70 °C enters the pipe and moves at a speed of 8.4 cm/s . What will be its temperature drop per centimeter of travel? Express your answer using two significant figures. nνα ΑΣφ dT °C/cm dx Request Answer Submit
Given that: P+P = 6.0 kip 0.45x10^6 psi L1 = 20.0 in E = L2 = 15.0 in d1 = 1.25 in d2 = 2.0 in Then the reactions at A and C respectively in kps are: A - d1 L1 В L2 d2 RA = 0.9 kip, RC = 11.1 kip RA = 1.96 kip, RC = 10.04 kip O RA = 1.3 kip, RC = 10.7 kip RA = 2.7 kip, RC = 9.3 kip
A thermometer at a temperature of 90°C is placed in a room at a constant temperature of 25°C. If after 30 minutes the temperature of the bar is 50°C, find: a. the time it will take the bar to reach a temperature same as the room temperature b. the temperature of the bar after 10 minutes
A piece of metal is initially heated to 850°C and is quenched in water which temperature is kept at 50°C. The temperature decay constant of the system is 0.30/min. a.) Determine the temperature of the metal at any time, T(t), using Laplace Transforms. b.) Determine the time needed for the metal to be at 80°C.