Thermal resistance approach
Q = Ti
- Tf / Rtotal.
The flow of energy, for this system, goes to the left
and to the right. The system is analyized in two parts,
the left and the right. Each side will have a different
thermal resistance.
put resistance network
here!!!!!!
The energy required for the system to be in steady state
is 4.9 watts This is for an initial temperature of
27 C. These values will now be substituted into the
next set of calculations to determine the mass flow
rate and ultimatly the pump.
The mass flow rate is varried to incorporate all the
listed pumps above. This will allow the outlet temperture
of the water to be graphed as a function of the mass
flow rate.Mass flow is in SI, kg/s.
Given values: Heat capacity for water and intial inlet
temperture for the supply water. The units are SI
Mass flow rate for six pumps. Given in gallons per hour,
converted to kg per second.
Model # 2
Determine the exit water temperature to verify that
it is not lower than 23 C. Chose a pump that will give
an exit water temperature of approxatmatly 23.5 C.
Given:
Input energy, as determined from Model # 1. Intial
temperature, heat capicity of water, mass flow rate
for six different pumps. (210gph, 250gph, 450gph, 700gph,
750gph, 1200gph)
Assumptions:
No heat loss in pipes, no mechanical energy losses
in pipes.
System Model:
The system model is developed using energy balance.
The system is broken into two separate models. The
first model is used to determine the energy supplied
to the system Q in. The second model is used to determine
the temperature of the the water after it leaves the
water bath and the mass flow rate of the water. The
output temperature of the water should not be less
than the temperature sample, 23 C.
Model # 1
Determine the amount of energy, in watts, needed to
maintain the sample at 23 C. Determine the thickness
of the insulation that will give optimal thermal resistance
for the avalible area.The temperature of the water
will be given an initial value close to that of the
sample. This temperature will be checked for accuracy
in Model # 2.
Given:
The sample must remain at 23 C. The surrounding
temperature is 8 C. The wall thickness is the same
for each cylinder, .3175 cm. Intial trial value for
the water temperature is 30 C. The height of the system
(outter shell) is 25 cm.
Assumptions:
Steady state, one dimentional heat flow, no convetion
on outside wall, the energy into the system is equal
to the energy going to the sample and the outside wall,
Qin
= Qoutside
+ Qsample
.
Given temperatures for the sample, outside temperature,
and the water sample.
Thermal conduction factors for alluminum and the insulation
L is the height of the
system, X1-4
are the wall thicknesses, w's are the thicknesses for
the two insulation layers and the water jacket. The
r's are the values for the the raduii. See figure below.
