iv. Find the time rate of temperature change at r = 1 mm, and x = 4 mm.
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please send handwritten solution Q6 part iv
Transcribed Image Text:6. (a) The temperature distribution across a wall of an aluminium cylin-
der block, 4 mm thick at a certain instant of time is given as;
T(x) = a +bx+cr², where T is in degrees Celsius, and x is in
metres. The coefficents are;
a = 200 °C,
b=-10000 °C/m, and
c=1x106 C/m².
=
The area of the cylinder wall, normal to the direction of heat
conduction is, A 20 mm². The cylinder block has material
properties as follows; density, p = 2700 kg/m³, conductivity,
K = 220W/m, and, specific heat capacity, c, = 900J/kgK.
i. Find the rate of heat transfer entering the wall, (r = 0), and
leaving the wall, (r = 4x10-³ m).
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ii. What boundary conditions are implied at the surfaces of the
wall, (r = 0), and, (x = 4x10-³ m).
iii. Find the rate of change of energy storage in the wall.
iv. Find the time rate of temperature change at r = 1 mm, and
x = 4 mm.
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