EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3 by EJBAH2f

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									  EML 4304L Thermal Fluids Lab

Thermal Conduction
       Experiment # 3




 Mechanical Engineering Department
 FAMU/FSU College of Engineering
                  Outline

•Purpose of the lab
•Fundamental Equations
•Unit 3 and Unit 4 Analysis
•Unit 1 and Unit 2 Analysis
•Error Analysis
                   PURPOSE
• Conduct a series of thermal conduction
  experiments which examines the effects on heat
  transfer with varying cross-sectional area and
  distance.
   – Using this thermal conduction information derive
     Fourier’s law of thermal conduction.
• Analyze the temperature variance in a series of
  metal rods that are in physical contact.
   – From this information determine thermal resistance
     and contact resistance.
  Q coolant=m Cp dT / t




Q conduction=-k A dT / dx




        Heat flow
        for units
         3 and 4
Heat flow
for units
 1 and 2
Fundamental
 Equations
            m w C p T
      q
                 t
Rate of heat flow at the heat sink
mw = mass of cooling water displaced in time t       (kg)
Cp = Specific heat of water at constant pressure       (kJ/kg °C)
T = (Tout - Tin) of cooling water                    (°C)
t = time required to displace a volume Vw of water   (s)

This equation is used to determine the amount of energy that is
being absorbed by the coolant. Once this is determined for each
unit, it is assumed to be the constant rate of conduction through
each material.
  Qcond = KA(ΔT/Δx)

Rate of heat conduction
K = thermal conductivity constant                 (W/m °C)
A = cross-sectional area                          (m2)
T = temperature difference across the material   (°C)
x = distance between temperature readings        (m)




      Used to determine rate of heat conduction through
      a body based on material properties, area,
      temperature difference, and length of material.
  Qcond = -KA dT/dx


     Fourier’s law of heat conduction
     -K = thermal conductivity constant          (W/m °C)
     A = cross-sectional area                    (m2)
     dT = differential element for temperature   (°C)
     dx = differential element for distance      (m)



Used to determine rate of heat conduction through a body
based on material properties, area, and temperature/distance
gradient.
• Q=KA ΔT/Δx             Q=-KA dT/dx
• dT/dx = temperature gradient

    T

        dT/dx


                    x
               Calculations


        Conservation of Energy
              Qin = Q out
         Q conduction = Q coolant

            dT
    k  A     m  C p  T
                 
            dx
This equation assumes there is no heat loss
through the system boundary. Though each
unit is insulated, there will still be some heat
loss.
               T
       Rt ,c 
                q

Thermal Contact Resistance
Rt,c = Thermal contact resistance          (ºC/W)
T = Temperature change                    (ºC)
q = Heat flux                              (W)



     Calculates thermal contact resistance for a
     given temperature discontinuity and a known
     power input.
Heat Conduction
for Units 3 and 4
Thermocouple Placement
   for Units 3 and 4
                         UNIT #3
Q=KA*ΔT/Δx




  Diameter is a function of x:


            D(x)=D0+mx
     D(x)=1”+(x/(11+1/16))
         Unit #3
Area can also be written as
     a function of x:
       A = (p/4) d2
    A(x) = (p/4) d(x)2
       Q=KA*dT/dx
             Unit #3


Q = -k A T/x = -k A(x) dT/dx

                             dT
       Q      k A ( x) 
                             dx
                            
             1
    Q             dx   k  1 dT
          A ( x)            
       
               Unit #3
                   1
              Q        dx
                  A( x )
           k
                T  T0
Once k is solved for, the temperature
can be found for any distance, x.


                   
                 Q           1
   T( x)     T0                  dx
                 k      A ( x)
                   
                           UNIT #4
       Q=KA*ΔT/Δx
       K = coeff. of therm. conductivity         NOTE: K is
                                                 unknown and
                                                 must be
Qout                                       Qin   determined




             x2                       x1
  Thermal Contact
    Resistance
Determination Units
    #1 and #2
Thermal contact resistance(Rc) is a discontinuity in
the temperature gradients between two materials in
contact. The value is determined by projecting the
temperature gradients, calculating the temperature
difference, and dividing the temperature difference
by the power that is transmitted through the
materials.
    Factors affecting thermal contact resistance:
       1 - Surface Roughness
       2 - Type of materials in contact
       3 - Temperature materials are at
       4 - Pressure applied to materials
       5 - Type of fluid trapped at interface
elements are enclosed in the insulating jacket. Figure1 illustrates the schematics of the apparatus. The dimensions of the tapered rod are indicated
in Fig. 2.
               Units #1 and #2
      Steel            Cu          Stainless
      (Mg)            (Al)         Steel


T10                                            T1



      x2                                 x1
              Contact Resistance
Thermocouple placement for
      units 1 and 2
     Ideal Thermal Conduction
         Material 1       Material 2



T1                        T3


                                       T4

           T2



                T2 = T3
     Actual Thermal Conduction
           Material 1       Material 2

               T2
T1




         Temperature
                                         T4
         profile due to
         thermal             T3
         contact
         resistance


                  T2 = T3
       Material 1                     Material 2

     Projected            T2
     Slope T2




                                            ΔT
Temperature profile due
to thermal contact
resistance




                                    Projected
                               T3   Slope T3
                  Temperature vs Distance
                       Material 1
                                Material 2
Temperature(ºF)
                                             Material 3



                     Discontinuities
                     where ΔT must
                     be determined



                         Distance(inches)
  Thermal Contact Resistance
         Calculation

Rt,c = ΔT/Q

       Q = Qwtr

              Qwtr=mwCp(ΔT)


                  ΔT (determined by projection of slope
                  and measuring difference in
                  temperatures)
                  Errors
• Time
     Flow rate
     Steady State
• Heat Losses
     Not perfectly insulated
• Unit #4 Thermocouples #3 and #5
     Inconsistent readings
Heat flow
for units
 3 and 4

								
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