Thermodynamics- Conduction Flashcards
In what direction is heat transfer in relation to isotherms?
Perpendicular to the isotherms in the direction of decreasing temperature.
General energy balance for heat transfer through an object
Energy in plus energy generated equals energy out plus energy stored
Formula for energy stored
Est=mCpdT/dt
Conduction equation for incompressible substance in any direction
dρCpT/dt + Δ(-kΔT)=qgen
Where d is curly and Δ is nabla upside down
Conduction equation in one dimension
ρCpdT/dt = d/dx(kdT/dx)+qgen If conductivity is constant: dT/dt = αd^2T/dx^2+qgen Where α is thermal diffusivity k/ρCp All ds are curly This is called the heat equation
What can be said about rate of change in temperature for a steady state system?
Equals 0
dT/dt=0
Means heat equation is d^2T/dx^2=-qgen/k
What boundary conditions can be used with the second order heat equation?
The temperature at x=0 (surface temperature).
The applied flux at x=0, -kdT/dx(0,t)=q”
d is curly
What is the heat flux if a surface is ideally insulated?
0 at that surface
Formula for applied heat flux boundary condition when one surface is in contact with flowing fluid
-kdT/dx(0,t)=h(Ts-Tinf)
Temperature against x position for wall exposed to convection heating and insulated on the opposite side (x=0)
At t=0: straight line at initial temperature.
At t=inf: straight line at Tinf
Heat flux equation with boundary conditions for constant k
q”=-kdT/dx=k/L(Ts1-Ts2)
What is thermal resistance equal to?
L/kA
Symbol R
How do thermal resistances combine in series?
Like electrical resistors.
What is total thermal resistance related to overall heat transfer coefficient?
Rt=1/UA
How do thermal resistances combine in parallel
Like electrical resistors
