Question

One-dimensional, steady-state conduction with uniform internal energy generation occurs in a plane wall with a thickness of 50 mm and a constant thermal conductivity of 5 W/mK . For these conditions, the temperature distribution has the form T(x)= a + bx + cx2. The surface at
x =0 has a temperature of T(0) = To = 120C and experiences
convection with a fluid for which T =20C and h= 500 W/m2 *K. The surface at x =L is well insulated.

(a) Applying an overall energy balance to the wall, calculate
the volumetric energy generation rate.

b) Determine the coefficients a, b, and c by applying

the boundary conditions to the prescribed temperature
distribution. Use the results to calculate and
plot the temperature distribution.
(c) Consider conditions for which the convection coefficient
is halved, but the volumetric energy generation
rate remains unchanged. Determine the new
values of a, b, and c, and use the results to plot the
temperature distribution. Hint: recognize that T(0)
is no longer 120C.
(d) Under conditions for which the volumetric energy
generation rate is doubled, and the convection coefficient
remains unchanged (h =500 W/m2 K),
determine the new values of a, b, and c and plot the
corresponding temperature distribution. Referring
to the results of parts (b), (c), and (d) as Cases 1, 2,
and 3, respectively, compare the temperature distributions
for the three cases and discuss the effects of
h and on the distributions.

Answer 1

Answer:

answers in the attachment

Explanation:

The detailed steps an appropriate derivation is shown in the attachment.