Transporte De Calor

Transport Phenomena
Dr Vicente Garza

Final Project • ITESM • November 25, 2011


Table of content
Problem statement 3
1.1 Objective of the analysis 3
2. Energy and materials. 4
2.1 Materials 4
2.2 Power selection 4
3. The system 5
3.1 Case 1: Without insulation. 5
3.1.1 Assumptions of the system: 5
3.1.2Boundary conditions: 5
3.2 Case 2: with insulation 12
3.2.1Assumptions of the system: 12
3.2.2Boundary conditions: 13
3. Units and conversions. 19
Appendixes 21

Problem statement

A tubular minireactor needs to be equipped with a source of energy to heat the reactive stream that will be fed to it. The reactor is cylindrical in shape and is made of steel tubing.
The heating will be done with an electrical resistance that will be wrapped aroundthe reactor wall. Because there is concern that a lot of heat generated by the resistance will be lost to the environment, instead of being directed to the reactor stream, an additional insulation layer around the resistance is being contemplated. As a start, a maximum 10% heat losses will be tolerated.
Your team has been asked to do a preliminary analysis of the heat losses considering thefollowing values:
-Temperature of the reactor stream: 50°F
-Ambient temperature: 70°F
-Local heat transfer coefficient for reactor stream side: 10 BTU/h-ft2-°F
-Local heat transfer coefficient for ambient side: 1 BTU/h-ft2-°F
-Outer radius of reactor wall: ½ in
-Thickness of reactor wall: 0.049 in
-Thickness of resistance layer: ¼ in.
-The resistance layer should be assumed to generateheat uniformly throughout its entire volume.

1.1 Objective of the analysis
a) Selection of insulating material and lookup of its thermal conductivity
b) Selection of a power value for heat generation in Watts.
c) For different insulator thicknesses (including no insulator): heat flow into the reactor vs. heat flow to the environment
d) For one reference scenario (perhaps the one inwhich only 10% is lost): temperature profiles in each layer.
Your report must include:
a. Heat transfer model with appropriate drawings for the geometry.
b. Integration of the model.
c. Description of how the constants were obtained (if applicable submission of an Excel file
by email before the deadline)
c. Values of all parameters used in the analysis
d. Appropriate graphs to performthe analysis mentioned above.
Report everything with units of the international system.
2. Energy and materials.

The objective of this sections is to determine the different materials and power sources for the project... (got no idea)
2.1 Materials

Materials [1] | Thermal conductivity | Unit |
Steel Carbon 1% | 43 | W/(m.K) |
Rock Wool insulation | 0.045 | |
Copper 401 400 | 400 ||


Figure 1 : reference [2]
2.2 Power selection

Power selection 500W
L=2in=2*25.4=50.8mm

3. The system
3.1 Case 1: Without insulation.

english | conversion | SI |
P=100W | | |
L = 2 in | 1in=0.0254m | 0.0508 m |
R0= 0.451in | 1in=0.0254m | 0.011455m |
R1= 1/2 in | 1in=0.0254m | 0.0127m |
R2=3/4 in | 1in=0.0254m | 0.01905m |
ɸ=50.9296js.ft3 | | 3.108x106 js.m3 |1 Btu/(ft.h.oF) | 1Btu/(ft2.h.oF)=5.674 W/(m2.K) | 5.674465897 W/(m2.K) |
10 Btu/(ft.h.oF) | 1Btu/(ft2.h.oF)=5.674 W/(m2.K) | 56.74465897 W/(m2.K) |
50F° | 1.8*°C+32=F° | 10°C |
70F° | 1.8*°C+32=F° | 21.11°C |

Calculation of ɸ:

ɸ=Pr22-r12*π*l= 21.2207js.ft3

3.1.1 Assumptions of the system:
-1-D heat transfer
-Constant K
-Steady State
3.1.2Boundary conditions:
BC1 r=r0qrI=-hi(TI-Ti)
BC2 r=r1 qrI=qrII
BC3 r=r1 TI=TII
BC4 r=r2 qrII=-he(Te-TII)

The general form for heat conduction equation with generation in cylindrical coordinates is:

0=-1r∂rqr∂r+1r∂qθ∂θ+∂qz∂z+Φ

For the expression of the first heat transfer we need 2 GDE because we change of medium during the process.

GDE1
We took the liberty to consider this system at steady state that is why...