Heat transfer: In a steady state one dimensional conduction with no heat generation, the differential equation is d / dx (k dT / dx) = 0. Prove that T(x) = ax b, where k, a and b are constants. (b) At x = 0, T = c and at x = L, T = d. Prove that T(x) = (d - c) x / L c for boundary conditions.
HEAT TRANSFER - ANSWER 5.2 : When d / dx (k dT / dx) = 0, d (dT) / [ (dx) (dx) ] = 0. Integrate both sides gives dT / dx = a. Second integration gives T(x) = ax + b for both sides (proven). (b) T(0) = a(0) + b = b = c. T(L) = d = aL + c then a = (d - c) / L. Substitute in T(x) = ax + b gives T(x) = (d - c) x / L + c (proven). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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Question 35 – A mixture consists of benzene (B), toluene (T) and xylene (X). At a temperature of 353 K, the data of vapor pressures : B : 754.12, T : 289.71, X : 91.19. Unit is mm Hg. The pressure P is 0.5 atm. The value of k for each substance is k = (vapor pressure) / P. (a) Calculate k for B, T and X. Let L / V = 0.65. (b) By using the equation V = F / [ (L / V) + 1 ], find the value of V when F = 100, then what is the value of L?