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C17
Heat and Mass Transfer
23
Science
Undergraduate 3
05/31/2011

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Cards

Term
Heat transfer
Definition

energy transfer due to a temperature difference (the driving force is always the temperature difference)

 

Q=hA(T1-T2)

Q=-kL/A(T1-T2)

Term
Newtonian heating and cooling
Definition
when a Biot number is small (<0.1) temperature gradients in the solid are negligible and as a result the whole plateau decreases/increases with time
Term
Boundary Layer
Definition
the region effected by viscous force and these viscous forces are based on velocity, dynamic viscosity
Term
Viscous Force
Definition
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Term
Black body
Definition

a hypothetical ideal surface that is a perfect emitter or absorber. Radiation emitted by a black body varies continuously with wavelength and increases with temperature

  • ρ=0, τ=0, α=1, ε=1 (black bodies are perfect admitter and absorbers of radiation)
  • At thermal equilibrium, q=0 and ε=α
  • Black bodies can be approximated by having an insulated cavity with a small aperture as the absorptivity goes to zero due to repeated absorption and reflection

carbon black has an emissivity very near 1

Term
Radiation
Definition

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  • As radiation has a 4th power dependence on temperature, at high temperature it can dominate but more often radiation and convection must be considered

Term
Conduction
Definition

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  • Fourier’s first law: temperature profile does not change with time
  • The general heat conduction equation: a mathematical expression of the principle of energy conservation in a solid substance
    • Relevant boundary conditions include – the temperature, heat flux, heat transfer by convection
  • For a composite system: Q is the same throughout

Term
Convection
Definition
  • heat transfer due to motion of fluid past surface.  We really want to understand h and how it varies with fluid properties.  Geometry is also very important and buoyancy effects lead to complex velocity fields
  • Heat conduction in a solid is influenced by the amount of heat transferred by convection at the surface
Term
Natural Convection
Definition
  • density difference between air near the hot surface caused also by buoyancy effect [q=0.53]
  • When heat is applied to a body of fluid volume changes lead to differential velocities and therefore convection
Term
Mass Transfer
Definition
  • If a fluid is moving, flux will contain two componenets: diffusion from a stationary concentration layer plus a bulk flow

 

Term
Stoke's Law
Definition
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Term

Dimensionless Parameters

-Conduction

Definition
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  • Biot Number: ratio of convective heat transfer and conductive heat transfer at the surface of a solid (as this number goes to zero there is no temperature gradient in the solid)
Term

Dimensionless Parameters

-Convection

Definition
  • The relative magnitude of ν/α determines the magnitude of convective heat transfer (Reynolds, Prandtl, and Nusselt) all can be used to estimate the value of heat transfer coefficient.  All fluid properties are evaluated at a mean boundary layer temperature (known as Tfilm which is the average of surface and environment temperatures)
  • Forced convection:
  • Reynolds number: parameter to determine laminar v. turbulent flow
  • Natural convection:
  • Grashof number: a parameter used to evaluate h in free convection
Term
what is the driving force for heat transfer
Definition
temperature difference
Term

boundary conditions for general heat conduction equation

"Fourier's Second Law"

Definition

Convective heat transfer into a fluid at fixed temperature (therefore heat balance at boundary is achieved by q=h(Ts-T∞)=-k(T1-T2)/L at surface edge)

dT/dt=0 (steady state)

surface is maintained at a constant temperature

fixed value of heat flux at a boundAry (ie q is constant)

if q=0: system is adiabatic and also known as a homogeneous boundary condition

 

Term
How can you find the thermal resistance of a hollow cylinder
Definition
using the 1D heat conduction equation, derive a general equation for T(r) then plug into q=-kdT/dr>Q=Aq>R cylinder
Term
Features of black bodies
Definition
  1. At low T, mostly IR; at high T, mostly UV
  2. with increasing T, max emission is higher and occurs at shorter wavelength
  3. The total rate of emission (emissive power of a black body at T) is the integral if E v. wavelength graphs
  4. E and e are always less than Eb and eb.  The proportionality constant is known as emissivity of the material, ε
Term
Grey surface
Definition

one in which the emissivity does not vary with

wavelength (but in real materials it does)

Term
Total irradiation of a material
Definition

G=Gα+Gρ+Gτ

α+ρ+τ=1

α-absorptivity

ρ-reflectivity

τ-transmittivity

 

α=1, ρ=0, τ=0, for BB

τ=0 for opaque materials

Term
What is the significance of a system being in thermal equilibrium
Definition

q=0

ε=α (consider a real body in an atmosphere of black bodies)

Term
What is the closest approximation to a black body?
Definition

a cavity with a small aperture since radiation entering the cavity is subject to repeated partial absorption and reflection the effective absorptivity is 1

 

ehole=εeb(1/1-ρ)

α+ρ+τ=1, τ=0, therefore α=1-ρ, α=ε (thermal eq)

therefore ehole=eb

Term
significance of moving fluid in mass transfer
Definition

the flux will contain two components: diffusion from a staitionary concentration layer of width S plus a bulk flow

 

J=-DdC/dx+uC

Term
why might heat transfer coefficient change for different temperature ranges
Definition
at high temperatures just below the melting point, there may be many airpockets preventing heat flow from occuring because of the small surface area contact of fluid with material whereas heat flow is more efficient at lower T with less airpockets and more surface area
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