Recent content by gmaverick2k

Thank you. Apologies, had a family emergency last week so wasn't able to get back on this

I'm stumped. Tried the T* method but I'm hitting a wall.. where t > 0 T1*(t) = T1(0) - T1(t) = 142.4 - T1(t) T1*(∞) = T1(0) - T1(∞) = 142.4 - 79.3 = 63.1°C T1*(1) = T1(0) - T1(1) = 142.4 - 23.3 = 119.1°C T2*(t) = T2(0) - T2(t) = 94.9 - T2(t) T2*(∞) = T2(0) - T2(∞) = 94.9 - 39.8 = 55.1°C T2*(1)...

I initially used @ t = 0, T2* = 55.1°C as per post #15, which gave T1* = 39.97°C. I thought thats pretty low as the outlet temperature of tank 1 when the water is switched back on shouldn't be that low. So I changed the initial conditions as follows: @ t = 0; T1* = 94.9°C ; T2* = 81.3°C...

I may be wrong. Changed the initial temps

dT1*/dt = 1.489T2* - 3.094T1* dT2*/dt = T1* - 2.991T2* I think this is where eq's. [3] to [7] kick in for simultaneous 1st ODE.

so when T1* is subbed into the differential the terms such as Cw(1-alpha)beta*t3 and CT0 disappear as they are not a function of time

So T1 is T1,i (after cooling water is put back on) and T1 (∞) was T1 at inifinite time by setting differential to zero T1* is T1,i+1 Subbed T1* into the differential term in place of T1 as it will vary with time and T (∞) is constant differential is now dT1*/dt

I get: T1* = 0.01°C T2* = 0.03°C Most likely incorrect because of rounding error

I get: T1 (∞) = 79.3°C T2 (∞) = 39.8°C

I'm most likely wrong here, setting the differentials to 0 in both eq.'s [19] and [20], I get for both eq.'s: 4486.2*T2 - 1500*T1 = 59724 as expected because eq.'s [20] is rearranged form of [19]

Note for XXIII, I got 159.6 for the right hand sided term instead of 309 (see post #2) although the coeffcients remained unchanged

Problem statement below. Final two pages in posts #2 & 3

I was able to get XXV by setting T2 = 94.9 @ t = 0 and putting this into XXIV, but I'm stumped with the other boundary condition result in XXVI