Chapter 9 Natural Convection Flashcards
What is natural convection normally accompanied by
radiation of comparable magnitude except for low emissivity surface
what is a natural convection current and natural convection heat transfer
motion that results from the continual replacement of heated air by cooler air nearby and the heat transfer that is enhanced as a result of this current is called natural convection heat transfer
what is the system of natural convection
nabla temperature drives nabla density, drives change in mass, drives force by newtons second law, drives velocity drives energy change
Describe basic process to find h
Nufree = function of the rayleigh number
Nu = hlc / kfluid = cRa^alpha where alpha, and c depend on geom
Ra = grashof number * Pr
properties evaluated at film temp Tf = Ts + Tinf /2
What is the upward buoyancy force =>
the upward force exterted by a fluid on a body completely or partially immersed in a gravitation field
What is the magnitude of the buoyancy force
= weight of the fluid displaced by the body
F buoyancy =
rho fluid g V body
Net vertical force acting on a body Fnet =
(rho body - rho fluid) g * Vbody
Symbol of the volume expansion coefficient
beta
What is the volume expansion coefficient
variation of the density of a fluid with temperature at constant pressure
measure of the change in volume of a substance with temperature at constant pressure
volume expansion coefficient =
1/specific volume * (pard specific volume/ pardT) = -1/rho*(pard rho / pard T)
units of the volume expansion coefficient
1/K
for gases volume expansion coefficient approx =
-1/rho * DELTArho/DELTA T = -1/rho * ((rho inf - rho)/ (Tinf -T) at constant P
ideal gas volume coefficient
1/T
what happens as temperature difference between the fluid adjacent to a hot surface and the fluid away from it increases for natural convection
bigger the buoyancy force, stronger the natural convection, the higher the heat transfer
What is the flow rate established by in natural convection
dynamic balance of buoyancy and friction
Whats the difference between velocity for natural and force convection
the fluid velocity is zero at the outer edge of the velocity boundary layer as well as at the surface of the plate
how does boundary layer thickness vary with flow direction
it increases
Draw the temperature and velocity profile for natural convection
see book
How do the the shape of temperature and velocity profiles vary with cold surfaces
they are reversed but same shape
Derive the equation of motion that governs natural convection flow in laminar boundary layer
see book
What is the continuity equation
see book
What is the momentum equation
see book
What is the energy equation
see book
What does the grahof number represent
the natural convection effects in momentum equation
is a measure of the relative magnitudes of the buoyancy force and opposing viscous force acting on the fluid
What does the grashof number allow you to
determine whether the fluid flow is laminar or turbulent in natural convection,
critical grashof number is 10^9
If a body is subject to external flow what does the problem involve
both natural and forced convection
When natural and forced convection are involved how do you determine which is dominant
ratio of Gr/Re^2
if Gr/Re^2 «_space;1
natural convection effects are negligible
if Gr/Re^2»_space; 1
free convection dominates and the forced convection effects are negligible
if Gr/Re^2 =1
both effects are significant and must be considered i
mixed convection
What does natural convection depend on
the geom of the surface
the orientation
variation of temp on the surface
thermophyscial properties of the fluid
Heat transfer relation in natural convection are mostly based on
experimental studies
Nu =
hLc/k = C (Gr Pr)^n = C Ra^n where c and n depend on the geom and the flow regime
what is the value of n usually for Nu = C Ra^n
1/4 for laminar and 1/3 for turbulent
If Gr is big what does that mean
high buoyancy less viscous
what is Gr a ratio of
buoyancy and viscous effects
Draw the boundary layer for a hot cylinder
see book
How does the boundary layer develop over a hot horizontal cylinder
develop at the bottom increasing in thickness along the circumference and forming a rising plume at the top
What is the local nusselt number highest for a hot clyinder
at the bottom and lowest at the top of the cylinder when the boundary layer flow remains laminar
How does a hot cylinder compare to a cold cylinder
Everything is reversed, boundary layer develops at the top of the cylinder and ending with a descending plume at the botoom
For two parallel plates (fins or PCBs) where does the boundary layer start to develop
at the lower ends of opposing surfaces and eventually merges at the mid plane if the plates are vertical and sufficiently long will have fully developed channel flow
For two parallel plates what happens if the boundary layers never meet
natural convection flow on a surface is not affected by the presence of the opposing surface, problem anaylsed as two independent plates
How is a fin approximated
isothermal Ts = const
How is a PCB approximated
qs = const isoflux
What happens in a vertical enclosure and why are enclosures used
fluid adjacent to the hotter surface rises and the fluid adjacent to the cooler one falls, setting of rotationary motion within the enclosure that enhances heat transfer through the enclosure
Draw a diagram of an enclosure
see book
What is the equation for RaL
see book
Fluid in an enclosure thermal conductivity =
kNu as a result of the convection currents
keff =
kNu
Nu = 1
the effective thermal conductivity of the enclosure is equal to the conductivity of the fluid, ie pure conduction
What does a nusselt number of 3 for an enclosure indicate
heat transfer through the enclosure but natural convection is three time that by pure conduction
Q. = for enclusre
hAs (T1 - T2) = kNu As (T1 - T2)/ Lc
what does the the convection heat transfer coefficient equal for an enclosure
h = kNu/L
simple power law relations for Nu =
CRa^n where C and n are constants, usually applicable to a narrow range of prandltl and rayleigh numbers and aspect ratios