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# Heat Transfer Principles of Coffee Cups

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by

## Lauren Sepp

on 16 October 2013

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#### Transcript of Heat Transfer Principles of Coffee Cups

Thermal Circuitry and Coffee Mugs
Which Coffee Cup is the Best?
Thermal Circuit Analysis
Not Considering Cup Design
Uniform Material
Solving for Heat Flux
Assumptions and Heat Transfer Calculations
Based on Ohm's Law
Calculations
V= iR
ΔT = qR
Heat Transfer
T = Change in temperature
Finding Total Thermal Resistance
Equivalent resistance in series
R = R + R + R
coffee
mug
air
eq
Conductive resistance = L/kA
Convective resistance = 1/hA
k = thermal conductivity, h = convection coefficient, L = length, A = area
q'' denotes the heat flux which is a measure of heat transfer per unit area
Ceramic (Earthenware) Mug
Rmug = L/kA
Glass Mug
Rmug = L/kA
Paper Cup
Which mug is the best choice?
(heat transfer rate per unit area)
Use the principles of thermal circuitry to determine which mug is best to keep your coffee warm based on the rate of heat transfer.
Earthenware
Glass
Paper Cup
total
R = Equivalent thermal resistance
q = Heat transfer rate
total
Other Considerations
Treat handle as a fin
Heat loss in second direction through open top and bottom neglected for simplicity

Analyzing heat loss through the walls of the vessel defined as a simple cylinder
L = Thickness of mug wall
k = Thermal Conductivity
k = 0.9 W/mK
Using the heat flux equation
q'' = 668 W/m
T = T - T
coffee
air
L = 1/16"
coffee
mug
air
L = 1/8"
h = 750 W/mK
h = 10 W/mK
coffee
air
T = 90 C
coffee
T = 20 C
air
2
L = Thickness of mug wall
k = Thermal Conductivity
k = 1.0 W/mK
Using the heat flux equation
q'' = 680 W/m
2
Rmug = L/kA
L = thickness of mug wall
L = 1/40"
k = Thermal Conductivity
k = 0.18 W/mK
Using the heat flux equation
q'' = 680 W/m
2
Conclusions are based on many assumptions
Earthenware will be the best choice
Coffee Joulies
Full transcript