How long does it take to heat a vessel?

[Chestermiller]

I think I finally got it, I'll shoot myself if this is wrong:

$$T(t) = \frac{\dot{Q}+kT_a+CT_0}{k}(1-e^{\frac{-kt}{C}}$$

Get your gun out. I get $$T=T_0+\left[\frac{\dot{Q}}{k}+(T_a-T_0)\right](1-e^{-\frac{kt}{C}})$$

 

[Modrisco89]

I think I finally got it, I'll shoot myself if this is wrong:

$$T(t) = \frac{\dot{Q}+kT_a+CT_0}{k}(1-e^{\frac{-kt}{C}}$$

Get your gun out. I get $$T=T_0+\left[\frac{\dot{Q}}{k}+(T_a-T_0)\right](1-e^{-\frac{kt}{C}})$$

Oh man, definitely getting the gun, assuming that the laplace transform method is illegal for that DE? That's what I used perhaps that wasn't good practice

I was told by lecturer that It can solve any DE

 

[Chestermiller]

Oh man, definitely getting the gun, assuming that the laplace transform method is illegal for that DE? That's what I used perhaps that wasn't good practice

I was told by lecturer that It can solve any DE

Certainly Laplae Transform can handle that equation.

 

[Modrisco89]

Certainly Laplae Transform can handle that equation.

Must be my maths is the major issue here, listen thanks so much for your help, I'm coming with realistic values on excel so it's looking good, I took the surface area of the tank and multiplied it by the thermal conductility of air and it's working out alright

 

[Chestermiller]

Must be my maths is the major issue here, listen thanks so much for your help, I'm coming with realistic values on excel so it's looking good, I took the surface area of the tank and multiplied it by the thermal conductility of air and it's working out alright

The surface area times the thermal conductivity of air does not have the proper units.

 

[Modrisco89]

Looks like I'm not out tench yet, so I'm assuming it should be in watts per kelvin for the k value, thermal conductance of air perhaps?

 

[Modrisco89]

I found kA/L

So k = air thermal conductance and A = surface area of tank, what would L be?

 

[Chestermiller]

Looks like I'm not out tench yet, so I'm assuming it should be in watts per kelvin for the k value, thermal conductance of air perhaps?

Start with a value of k equal to the surface area times 10 $\frac{W}{m^2.C}$.

 

[Modrisco89]

Start with a value of k equal to the surface area times 10 $\frac{W}{m^2.C}$.

That's perfect; my values are coming out longer than the original equation I had for time, thank very much for all the help and sorry for my maths

 

[Modrisco89]

Can I ask one question, when you solved that DE, what were your initial conditions? I assumed it to be T(0) would it be something else? like k(Ta-To)?

 

[Chestermiller]

Can I ask one question, when you solved that DE, what were your initial conditions? I assumed it to be T(0) would it be something else? like k(Ta-To)?

The initial condition is $T=T_0$ at time t = 0.

 

[Modrisco89]

Can I ask one question, when you solved that DE, what were your initial conditions? I assumed it to be T(0) would it be something else? like T(0)-Ta?

The initial condition is $T=T_0$ at time t = 0.

Ya I thought that made sense, I'll have to double triple check my maths and find out why the LTM is not working for me, thanks

Marking as solved