.
where x is in meters
is zero 
![\dot{E_{out}}=\rho c_p\int\limits^{x=L}_{x=0} {(T_{x,0}-T_{\infty}) \, dx}\\\dot{E_{out}}=7000 \times 450\int\limits^{x=L}_{x=0} {(300-0.1\times 10^4 x^2-293) \, dx}\\\dot{E_{out}}=3150000[300x-0.1\times 10^4 \frac{x^3}{3}-293x]_0^L\\\dot{E_{out}}=3150000[300(0.08)-0.1\times 10^4 \frac{(0.08)^3}{3}-293(0.08)]\\\dot{E_{out}}=3150000(0.3893)\\\dot{E_{out}}=1.2264 \times 10^7 J/m^2](/tpl/images/0512/2520/3bee3.png)
A plane wall of thickness 8 cm experiences uniform volumetric heat generation ( q ). One
surfa...
A plane wall of thickness 8 cm experiences uniform volumetric heat generation ( q ). One
surface of the wall is insulated, and the other surface is exposed to a fluid at T(infinite) = 20 degree with
convection heat transfer characterized by h=1000W/m2.K. The initial temperature distribution
on the wall is given as: T (x,0) = 300-0.1*10^4*X^2 , where x is in meters. Suddenly, the
volumetric heat generation is deactivated, while convection heat transfer continues to occur at
x=L. If the wall properties are 7000kg/ m^3 ,Cp= 450J/ kg. K, k=108W/ m. K
(a) Determine the magnitude of the volumetric energy generation rate q associated with the
initial condition (t < 0).
(b) Calculate heat flux at the boundary exposed to the convection process at t=0, qx (L,0)
(c) Calculate the amount of energy removed from the wall per unit area (J/m2) by the fluid
stream as the wall cools from its initial steady state condition.
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