Summer2022-VM335 Homework 2
Heat Transfer作业代写 The temperature distribution across a wall 0.3 m thick at a certain instant of time is T(x)= a + bx +cx2,
2.5 Assume steady-state, one-dimensional heat conduction through the symmetric shape shown. Heat Transfer作业代写
Assuming that there is no internal heat generation,derive an expression for the thermal conductivity k(x) for these conditions: A(x) = (1 – x)，T(x) = 300 meters, (1-2x-x3),andq=6000W,whereA is in squareT in kelvins, and x in meters.
2.31 The temperature distribution across a wall 0.3 m thick at a certain instant of time is T(x)= a + bx +cx2, where T is in degrees Celsius and x is in meters, a = 200°C,b= – 200°C/m, and c = 30°C/m2. The wall has a ther-mal conductivity of 1 W/m K.
(a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored by the wall.
(b) If the cold surface is exposed to a fuid at 100°C,what is the convection coefficient?
2.54 The one- dimensional system of mass M with constant properties and no internal heat generation shown in the figure is initially at a uniform temperature Ti. Heat Transfer作业代写
The elec-trical heater is suddenly energized, providing a uniform heat flux q”0 at the surface x = 0. The boundaries atx= L and elsewhere are perfectly insulated.
(a) Write the differential equation, and identify the boundary and initial conditions that could be used to determine the temperature as a function of posi-tion and time in the system.
(b) On T- x coordinates, sketch the temperature distri-butions for the initial condition (t≤0) and for several times after the heater is energized. Will a steady-state temperature distribution ever be reached? Heat Transfer作业代写
(c) On q”x- t coordinates, sketch the heat fux q”x(x, t) at the planes x = 0,x= L/2, and x= L as a function of time.
(d) After a period of time te has elapsed, the heater power is switched off. Assuming that the insulation is perfect, the system will eventually reach a final uniform temperatureTf.Derive an expression that can be used to determine Tf as a function of the parameters q”o, te,Ti, and the system characteristics M,cD, andAs(the heater surface area).
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