Answer:
Explanation:
A plane wall of thickness 2L=40 mm and thermal conductivity k=5W/m⋅Kk=5W/m⋅K experiences uniform volumetric heat generation at a rateq
˙
q
q
˙
, while convection heat transfer occurs at both of its surfaces (x=-L, +L), each of which is exposed to a fluid of temperature T∞=20∘CT
∞
=20
∘
C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x)=a+bx+cx2T(x)=a+bx+cx
2
where a=82.0∘C,b=−210∘C/m,c=−2×104C/m2a=82.0
∘
C,b=−210
∘
C/m,c=−2×10
4
C/m
2
, and x is in meters. The origin of the x-coordinate is at the midplane of the wall. (a) Sketch the temperature distribution and identify significant physical features. (b) What is the volumetric rate of heat generation q in the wall? (c) Determine the surface heat fluxes, q
′′
x
(−L)q
x
′′
(−L) and q
′′
x
(+L)q
x
′′
(+L). How are these fluxes related to the heat generation rate? (d) What are the convection coefficients for the surfaces at x=-L and x=+L? (e) Obtain an expression for the heat flux distribution q
′′
x
(x)q
x
′′
(x). Is the heat flux zero at any location? Explain any significant features of the distribution. (f) If the source of the heat generation is suddenly deactivated (q=0), what is the rate of change of energy stored in the wall at this instant? (g) What temperature will the wall eventually reach with q=0? How much energy must be removed by the fluid per unit area of the wall (J/m2)(J/m
2
) to reach this state? The density and specific heat of the wall material are 2600kg/m32600kg/m
3
and 800J/kg⋅K800J/kg⋅K, respectively.
