Difference between revisions of "Heat transfer module - Fluid Dynamics 2019"

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==  HEAT TRANSFER IN A LAVA LAMP ==
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#REDIRECT [[Heat transfer]]
  
When you flip on the light in a lava lamp, heat from the bulb works slowly to warm up the wax (or ‘lava’). This kind of heat transfer is called conduction, or movement of heat from one place to another. Heat energy flows from high heat (light bulb) to low heat (wax), and the gradient is the driver of conductive heat transfer.
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This page has moved [[Heat transfer|here]].
Sketch showing conduction within anatomy of the lava lamp (build this with heat source and arrow appearance), show isotherms
 
Until things start moving, conduction is the dominant heat transfer process in our lava lamp system.
 
Conduction depends on:
 
Thermal diffusivity of the material through which heat is moving
 
thermal gradient 
 
The density of the wax is inversely related to temperature, meaning that at higher temperatures, the wax is less dense. When the density becomes lower than the density of the liquid in the lava lamp, the wax will tend to float upward.
 
Sketch of different stages of wax density changes through time
 
Wax reaches critical density (less than liquid) and tends to float upward. That movement of wax introduces velocity into the system--advection.
 
Advection depends on:
 
Velocity of the fluid
 
Thermal Gradient
 
Introduce Peclet
 
Dimensionless number which indicates whether conduction or advection dominates the system. Drivers of advection are in the numerator and thermal diffusivity, which dominates conduction, is in the denominator.
 
In THIS SYSTEM wax density changes cause velocity, a term in the numerator for the Peclet
 
Introduce heat transfer equation
 
Sketch of advection (first blob moving up), show isotherms and velocity vector
 
With the movement of wax in the upward direction away from the heat source at the bottom of the container and into a cooler material the wax density increases again (more than liquid). This wax density increase causes the wax to sink back down to the bottom of the container towards the heat source. This process is called convection.
 
Convection depends on:
 
Driving forces:
 
Acceleration due to gravity (g)
 
Density (ρ)
 
The temperature difference between the bottom and top of the convection cell (ΔT)
 
The volume coefficient of thermal expansion (α)
 
The height of the convection cell (d)
 
Resisting forces:
 
Viscosity (μ)
 
Thermal diffusivity (κ)
 
Show Rayleigh Number Equation
 
Dimensionless number used to describe whether convection grows or decays--dependent upon the driving and resisting forces
 
When numerator terms are dominant convection grows
 
When denominator terms are dominant convection decays
 
Where at some critical Rayleigh (Racr) number (dependent on the system), the convection regime shifts
 
show this relationship below
 
Sketch of convection (with 2 convection cells within lava lamp),  show isotherms and velocity vectors
 
 
 
Summary: video of the lava lamp annotated with the different steps
 
 
 
EQUATIONS -- make sure we visit each of these throughout
 
Heat Transfer Equation:
 
Describes how heat changes through time
 
Tt=∇2T+v∇T+A
 
 
 
 
 
 
Peclét Number:
 
Dimensionless number which indicates whether conduction or advection dominates the system.
 
where u = flow velocity, L = characteristic length Height of lava lamp, κ = thermal diffusivity
 
Low peclet regime- dominated by heat transport by conduction
 
High peclet regime- dominated by heat transport by advection
 
 
 
Rayleigh Number
 
Dimensionless number used to describe whether convection grows or decays
 
 
 
g = acceleration due to gravity
 
ρ = density
 
κ = thermal diffusivity
 
ΔT = the temperature difference between the bottom and top of the convection cell
 
α = the volume coefficient of thermal expansion
 
d = the height of the convection cell
 
μ = viscosity
 
κ = thermal diffusivity
 
 
 
At some critical Rayleigh (Racr) number (dependent on the system), the convection regime shifts
 
 
 
 
 
 
 
 
 
== HEAT TRANSFER IN ICE STREAM SHUTDOWN AND START (based on Joughin and Alley, 2011) ==
 
Stop and start of ice streams is dependent on:
 
Thinning (steepens basal temperature gradients)
 
Basal freezing (puts on the brakes for a system)
 
Thickening (build up traps geothermal heat)
 
GO & repeat cycle
 
 
 
See video below to walk through the steps of ice stream shut-down and speed-up.  
 
 
 
 
 
==
 

Latest revision as of 18:59, 12 March 2019

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