Chapter 5 Flashcards
Transient Conduction aka
None Steady State. Heat transfer process for which the temperature varies with time, aw well as location within a solid.
Solution techniques for Transient conduction
Lumped Capacitance Method
Exact Solutions
Finite Difference Method
When is transient conduction initiated?
When there is a change in operating conditions such as change in surface convection conditions, surface radiation conditions, surface temperature or heat flux and or internal energy generation.
Lumped Capacitance Method Assumptioms
Mass of body much less then liquid.
Assume Temp of liquid doesn’t change
Solid has constant temperature throughout ie no delta t whithin body
How many dimension is lumped capacitance method and why?
0 Dimension because temperature is constant regardless of position of the body and only changes with time.
Energy Balance Equation for Lumped Capacitance
Ein/Eout= ρVc
Energy from fluid = energy stored or lost from the body
Cp
amount of energy needed heat or cool 1 KG of matter 1 degree celsius
Cp Units
J/Kg degree (celsius/kelvin)
Thermal Time Constant
(1/hAs)(ρVc) or RconvCt
Units of Thermal time Constant
Seconds
Ct meaning and formula
Lumped Thermal Capasitance of a Solid. (ρVc), and ability of the body to accumulate energy
Rt meaning and formula
Resistance to convection heat transfer
Units of hAs/(ρVc)
1/s
Will the time constant be greater or lower for a higher value of Ct?
Higher because tau=RtCt
θ i=
Ti-T∞
Q meaning and formula
Total energy transfer up to some time t, (ρVc) θi[1-exp(-t/ταυ]
Bi number equation all forms , units and meaning
hl/k, Rcond/Rconv, (Ts1-Ts2/Ts2-Tinf), unitless, provides a measure of the temperature drop in the solid relative to the temp drop of the surface and fluid
What will a high number of thermal conductivity do to the Bi number and why?
It will make the Bi number lower because it is in the denominator.
What does a high condcutivity (K) mean for temperature distribution in a wall?
It means heat is transferred easily so it should be flat or linear throughout.
What does a high Bi number do to the Temperature profile.
Make it less linear and less flat.
Bi number formula
Rcond/Rconv=LcH/K
What does the Bi number allow us to do?
Use lumped capasitance method
Bi number formula in terms of characteristic length
h*Lc/k
Fouriers number equation
α*t/(Lc)^2
Characteristic Length
Ratio of Volume to surface area
What does Fouriers number tell us?
Provides a measure of the relative effectiveness with which solid conducts and stores thermal energy.
Thermal Diffusivity equation symbol and meaning
alpha, k/pCp, and is the ratio of conductivity to to heat capacity
Basic formula of characteristic length and meaning
V/As, average length of the body
What does the Bi number physically represent?
Temperature drop in a solid relative to temperature difference between the solid and fluid.
Formula for the Temperature Distribution using Lumped Capacitance Method.
θ/θi=(T-T♾)/(Ti-T♾)=exp(-Bi•Fo)
What does Bi*Fo=
hAst/pVc
Theta
T-Tinf
t*
Unitless Time=FO
X*
x/L
θ*
Dimensionless Temp
