One End Insulated, One End Fixed TemperatureIn this model, one end of the wire is maintained at a fixed temperature (say 0°C), while the other end isinsulated. du/dt k d2u/dx2Where k > 0 is a constant (the thermal conductivity of the material).Boundary Conditions and Initial Condition:At both ends of the wire, the temperature is fixed at zero:u (0,t) = 0 and u(L,t) = 0The initial temperature distribution along the wire can be some function f(x), where:u(x,0) f(x), for 0≤x≤L, u(x, 0) = f (x), foro≤x≤L0temperature uSeparation of variablesXinsulation

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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

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d) Find the time constant associated with this transient analysis. e) Find the time it takes for the temperature of the wire surface to reach a temperature that is within 2∘C of the steady-state temperature of the wire.
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Use FEM to calculate the temperature at nodes 2 and 3, and the heat at nodes 1 and 4. Assume A is one unit area.
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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.
An unmanned submarine is equipped with temperature and depth measuring instruments and hasradio equipment that can transmit the output readings of these instruments back to the surface.The submarine is initially floating on the surface of the sea with the instrument output readingsin steady state. The depth measuring instrument is approximately zero order and the temperaturetransducer first order with a time constant of 50 seconds. The water temperature on the seasurface, T0, is 20C and the temperature Tx at a depth of x metres is given by the relation:Tx = T0- 0.01x(a) If the submarine starts diving at time zero, and thereafter goes down at a velocity of 0.5metres/second, draw a table showing the temperature and depth measurements reported atintervals of 100 seconds over the first 500 seconds of travel. Show also in the table the error ineach temperature reading(b) What temperature does the submarine report at a depth of 1000 metres?
Q 1b
The steady-state temperature distribution in a one-dimensional wall of thermal conductivity k=83 (W/m) °C) and thickness 300 mm is observed to be T(°C) = ax2+bx+c, where a = -2500 °C/m2 , b = 500 °C/m, c = 250 °C and x is in meters. a) What is the heat generation rate ?̇ (W/m3 ) in the wall ? b) Find the maximum and minimum temperatures in the wall. c) Find the amount of heat transferred to the right side of the wall (for 1 m2 surface area.)
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Question 2 The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, ka = 20 W/m•K and kc = 50 W/m•K, and known thickness, LA = 0.30 m and Lc = 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB = 0.15 m, but unknown thermal conductivity ke. Under steady-state operating conditions, measurements reveal an outer surface temperature of T0= 20°C, an inner surface temperature of T; = 600° C, and an oven air temperature of T= 800C. The inside convection coefficient h is known to be 25 W/m2 •K. a) Sketch the equivalent thermal resistance of the circuit b) What is the value of kg? Ts0 Ts, i S,0 kA kc kB Air To h LA LB Lc
An unmanned submarine is equipped with temperature and depth measuring instruments and has radio equipment that can transmit the output readings of these instruments back to the surface. The submarine is initially floating on the surface of the sea with the instrument output readings in steady state. The depth measuring instrument is approximately zero order and the temperature transducer first order with a time constant of 50 seconds. The water temperature on the sea surface, , is 20 °C and the temperature at a depth of x meters is given by the relation: If the submarine starts diving at time zero, and thereafter goes down at a velocity of 0.5 meters / second, draw a table showing the temperature and depth measurements reported at intervals of 100 seconds over the first 500 seconds of travel. Show also in the table the error in each temperature reading.What temperature does the submarine report at a depth of 1000 meters?
The following figure shows a coffee thermos as a lumped thermal system. Derive the symbolic expression using the given parameters for the temperature change rate of the coffee dT/dt (10 Ambient Temperature Ta Thermos Thickness L Surface area A Conductivity k Connectivity with air h₂ Coffee Temperature T Thermal capacitance C Connectivity with the thermos h₁

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