phy You are given a 0.5 m square aluminum plate that is 0.3 m thick. The top and

Question

phy You are given a 0.5 m square aluminum plate that is 0.3 m thick. The top and bottom and one side are insulated. The opposite side is exposed to a radiant heat surface at 500 K. The remaining two sides are exposed to a fluid with h = 250 W/m2 K and T-infinity = 400 K. At I = 0 seconds, the radiant heat surface is tuned off and becomes a black body and the fluid on one of the surfaces changes instantly to 300 K. Assuming the plate is divided into m by a mesh nodes (where m = n), write the explicit, time dependent temperature distribution equations for generic interior, surface and comer nodes. What would be an appropriate value for the size of (or distance between) node points? Explain how you would determine the initial (i.e., 1 = 0 sec.), temperature distribution. What would be an appropriate time step to determine the time dependent temperature of each node? Explain how you would determine the final (i.e., t right arrow infinity) temperature distribution.

Explanation / Answer

(Eq1)    

(Eq2)    T(x) = C1x + C2

To obtain the constants of integration, C1 and C2, boundary conditions must be introduced. Boundary conditions are chosen at x = 0 and x = L, in which case:
T(0) = Ts,1

and

T(L) = Ts,2

Applying the condition at x = 0 to the general solution, it follows that:

Ts,1 = C2

Similarly, at x = L:

Ts,2 = C1L + C2 = C1L + Ts,1

in which case:

= C1

Substituting into the general solution, the temperature distribution is then:

+ Ts,1

Note that A is the area of the wall normal to the direction of heat transfer and, for the plane wall, it is a constant independent of x. The heat flux is then:

(Ts,1 Ts,2)

A=.5sqrm and l=.3m

T=

d dx ( k dT dx ) = 0

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.