MEEN 464 LABS 1 - 10
Overall uncertainty is defined as
((bias limit)2+(precision limit)2)0.5
A blackbody is a perfect emitter and absorber of radiation. No surface can emit more energy than a blackbody at a specified temperature and wavelength. What is the emissivity of the blackbody?
1
Given a plastic sphere [k = 2.0 W/(m⋅K)] with a diameter of 2.5 cm. Heat is removed from the surface of the sphere convectively to a fluid with h = 20 W/(m2⋅K). What is the Biot number of the plastic sphere?
Bi = [hfluid * (Volume / area)] / ksphere L = Volume / area = r/3 for sphere Bi = 0.0416
[Sample] Explain the difference between the film wise condensation and drop wise condensation. Which is a more effective heat transfer mechanism?
Dropwise condensation occurs when drops of fluid are formed on the surface of a specimen and occurs mostly on polished surfaces. Film wise occurs when a uniform thin layer of fluid is formed on the surface of a specimen, The heat transfer is larger for dropwise condensation, since drops running down enhance heat transfer by letting new drops generate
Which of the following is not correct statement on emissive power?
Emissive power is proportional to the fourth power of the temperature in degree Celsius.
Convection coefficient of nucleate boiling is smaller than that of film boiling.
False
Determine the heat transfer coefficient in W/m2·K for cooling water inside the tube in question 2.
LMTD = [deltaT1 - deltaT2] / ln[deltaT1 / deltaT2] deltaT1 = 100-20 = 80 deltaT2 = 100-30 = 70 LMTD = 74.88 Qdot = LMTD*A*h h = Qdot / [LMTD * pi*D*L] plug in all values h = 94.926
Rank from largest to smallest magnitude of emissivity of the surfaces in question (black, red, brushed, polished)
Largest emissivity: Black Second Largest Emissivity: red Third lagest emissivity = brushed Smallest emissivity = polished
Which of the following is not the characteristic of implicit finite difference method?
Largest permissible value of time step Δt is limited
Which of the following is least likely to decrease the thermal contact resistance between two media in contact?
Make a vacuum gap at the interface
Which of the following is not a correct statement on thermal conductivity?
Thermal conductivity of a vacuum approaches infinity.
Sample Exam: Explain briefly how the fins enhance the heat transfer from an object.
They increase the heat transfer surface area, which enhance the convective heat transfer between the object surface and the sorrounding fluid.
Which of the following is the role of baffles in Shell and Tube Heat Exchangers?
To direct the shell side fluid to flow across the shell To maintain uniform spacing between the tubes
Boiling happens at the interface of the solid and the liquid.
True
Evaporation happens at the interface of the gas and the liquid.
True
Given two fins of same geometry and material, the one with a larger diameter will dissipate more heat.
True
Determine the number of transfer unit (NTU) in problem 1. Hint: use the effectiveness-NTU relation for the corresponding heat exchanger
e = [1- e^{-NTU(1-c)}] / [1- ce^{-NTU(1-c)}] c = (mc)cold / (mc)hot = 0.5 0.8 = [1- e^{-NTU(0.5)}] / [1- 0.5e^{-NTU(0.5)}] say x = e^{-NTU(0.5)} then is easy to solve for x x = 1/3 = e^{-NTU(0.5)} solve for NTU = 2.1972
Calculate the effectiveness of the heat exchanger in problem 1.
effectiveness e = [mc*cc*(Tc2 - Tc1)] / [mmin*cmin*(Th1 - Tc1) ] mc*cc = mmin*cmin e = [327-303]/[333-303] = 0.8
The maximum possible heat transfer between the fin and the surroundings occurs if the surface temperature of the fin is __________the base temperature of the fin.
equal to
Two stainless steel rods, A and B of equal diameter (10 cm) and length (50 cm) are pressed against each other. The rods are arranged so that the faces are contacting one another with a heat source at one end and a heat sink at the opposite end. The outer surface of the rods is well insulated. The rod is smooth stainless steel grade 316, with a thermal conductivity equal to 16 W/m·K. The thermal contact resistance at the interface of the rods is 0.01 . The left and right surfaces of the rods are maintained at temperatures of 70 and 20 , respectively. Determine the heat transfer rate per unit area in along the rods under steady state.
qdot = (Tleft - Tright)/ [(La/ka) + R + (Lb/kb)] Tleft = temperature on the left Tright = temperature on the right La = length of rod a ka = conductivity of rod a Lb = length of rod b kb = conductivity of rod b R = Thermal resistance qdot = 689.65 W/m^2
Two stainless steel rods, A and B of equal diameter (10 cm) and length (50 cm) are pressed against each other. The rods are arranged so that the faces are contacting one another with a heat source at one end and a heat sink at the opposite end. The outer surface of the rods is well insulated. The rod is smooth stainless steel grade 316, with a thermal conductivity equal to 16 W/m·K. The thermal contact resistance at the interface of the rods is 0.01 . The left and right surfaces of the rods are maintained at temperatures of 70 and 20 , respectively. Determine the temperature drop at the interface, ΔT ( ).
qdot = ΔT / R ΔT = 6.895
The following pictures indicate the temperature distribution within the balls at a given time. Which ball best represents the lumped capacitance system?
sphere with same temperature everywhere
You will determine the time constant of a bi-metallic dial thermometer. The temperature of the room and the coolant in the constant temperature bath to be 25 and 100 ˚C. What is the temperature of the bi-metallic dial thermometer at one time constant?
(0.632)*(100-25)+25 = 72.4
The following figure shows the transient temperature response of a temperature measuring device. What is the time constant of the device in seconds?
(0.632)*(90-10)+10 = 60.56 Then check time it takes to get from 10 to 60.5, it should be about: 1.5 sec
Consider a very long, cylindrical fin. The temperature of the fin at the tip and base are 25 °C and 50 °C, respectively. The diameter of the fin is 3 cm. The thermal conductivity of the fin is 150 W/m·K. The heat transfer coefficient is 123 W/m2·K. Estimate the fin temperature in °C at a distance of 10 cm from the base.
(T - Tinf) / (T0 - Tinf) = e ^ (-sqrt((h*P)/(k*A)) * x) Tinf = 25 T0 = 50 h = 123 k = 150 P = perimeter = pi*D A = area = (pi * D^2)/4 x = 0.1 T = 33.78
[Sample] The emissive power of a blackbody is 'E'. If the absolute temperature of a blackbody is doubled, the emissive power becomes ______ times E.
16 (I think)
Which thermocouple will have the shortest time constant?
30-gage T-type thermocouple with an exposed junction
Consider three thermocouples initially at temperature Ti are placed into a bath at temperature . The three thermocouples include a sheathed 0.1 inch-diameter T-type thermocouple, sheathed 0.2 inch-diameter T-type thermocouple and 30-gage T-type thermocouple with an exposed junction. Match each probe with the curve (A, B, or C) that best represents the transient response of temperature.
30-gauge T-type thermocouple with an exposed junction: fastest to reach steady state sheathed 0.1 inch-diameter T-type thermocouple: second fastest to reach steady state sheathed 0.2 inch-diameter T-type thermocouple: Slowest to reach steady state
The plastic sphere in problem 3 can be considered a lumped capacitance system.
True Bi < 0.1
Which one of the following surface is best for emitting thermal radiation?
dull black
A cylindrical rod at initial temperature Ti is submerged in a constant-temperature bath at temperature Tbath. The rod is 2 cm long and 0.5 cm in diameter. The rod has a thermal diffusivity of 0.0082 cm2/s. The experimental setup and transient temperature response of the rod are shown below. What is the Biot number of the cylindrical rod?
(T - Tbath)/(Ti - Tbath) = e^(-Fo * Bi) Fo = alpha * time/ (Lc^2) alpha = diffusivity Lc = L / [2 + 4L/d] for cylinder Lc = r/3 for sphere at time 1 (T - Tbath)/(Ti - Tbath) = 0.7 Fo = 0.6642 0.7 = e ^ -0.6642Bi solve for Bi = 0.54
Sample Exam: What assumptions were made to determine the rate of heat transfer in the previous question List at least two assumptions.
- Perfect insulation of the rods - Constant properties of the materials such as thermal conductivities -1-Dimensional heat conduction along the axis of the rods
The heat transfer problem to determine the thermal contact resistance at the interface between two solid media in contact can be approximated as
- Perfect insulation of the rods - Constant properties of the materials such as thermal conductivities -1-Dimensional heat conduction along the axis of the rods
As mentioned in the video lecture, the heat transfer problem to find the unknown thermal conductivities of the rods can be approximated as ___________. Select all that apply.
-Perfect insulation of the rods -Constant properties of the material such as thermal conductivities - 1-Dimensional heat conduction along the axis of the rods (or radial direction for a solid disc)
Sample Exam: Describe two methods to decrease the thermal contact resistance.
-Using thermal paste -Increase pressure at interface
Consider a constant cross-sectional area fin. Which fin dissipates the least heat? Assume all fins have the same heat source.
0.5-inch diameter Carbon steel fin
Identify each regime in the boiling curve.
1 curve starts rising: Natural convection 2 curve keeps rising with a bigger slope and reaches a peak: Nucleate boiling 3 Curve drops to a local minimum: Transition boiling 4 curve rises again after local minima and does not stop rising: Fil boiling
Select all required assumptions to establish the nodal equations in lab 6.
1. There is no heat generation in the medium. 2. The outer surface of the PPP or PVC cylinder is perfectly insulated. 3. Thermal conductivity, specific heat, and density of the medium are constant at any time. 4. Radiation heat transfer is negligible. 5. The nodal spacing is constant. 6. The cylinder has a sufficiently large length-to-diameter ratio. 7. The temperature of the coolant remains constant.
A NIST calibrated thermometer shows an air temperature of 24.3˚C. A student also measured the air temperature by means of an alcohol thermometer as depicted below. What is the bias error of this measurement with the alcohol thermometer?
B = abs(X_mean - X_calibrated) + 0.5*resolution 0.8
For steady state one-dimensional heat conduction [that is, T(x) only] along a rod with a constant cross-sectional area as shown below: How does the heat flux (or the rate of heat transfer per unit area) vary along the rod?
Constant
For steady state one-dimensional heat conduction [that is, T(x) only] along a rod with a constant cross-sectional area as shown below: How does the heat transfer rate vary along the rod?
Constant
What are the thermal boundary conditions for polypropylene (PPP) or polyvinyl chloride (PVC) cylinder in Lab 6
Constant temperature at the inner surface, zero temperature gradient at the outer surface
Which of the following has the largest thermal conductivity?
Copper
T-type thermocouples consist of
Copper / Constantan
Two collinear, short, metallic rods of the same diameter are in contact. The top of the upper rod is electrically heated, and the bottom of the lower rod is cooled with a fluid. The exposed surface of the rods are thermally insulated from the surroundings. Which rods have the smallest thermal contact resistance?
Copper rods with thermal paste at the contact surface
Fins are used to enhance the heat transfer from the extended surface to the surroundings. The rate of heat transfer by convection is dependent on the convection heat transfer coefficient. Which of the following is least likely to affect the convection heat transfer coefficient?
Density of the solid body
Sample Exam: Consider two fins (Aluminum and Stainless Steel) with a constant cross-sectional area, heated on one end, and subjected to forced convection on its surface. Plot the dimensionless temperature profiles along the fins. The base temperature of the fin, 𝑇𝑏𝑎𝑠𝑒 and the air flow temperature, 𝑇∞ of the two fins remain the same. Identify each curve by labeling the curves with Al (Aluminum) and SS (Stainless Steel). Assume heat transfer through the fins is steady. Which fin will provide greater enhancement in heat transfer? [12 pts]
Dimensionless temperature (T - Tinf) / (T0 - Tinf) Both plots start at one, but the steel fin reaches 0 faster than the aluminum, steel finishes in almost 0 dimensionless temperature, while aluminum ends a little bit higher The fin that provides a greater enhancement of heat transfer is the aluminum fin.
A cylinder with a 4 cm diameter hole drilled axially through its center. The outer surface is insulated. Initially, the cylinder is at a uniform temperature of 20 °C, and at time t=0, the coolant from constant temperature bath at 100 °C flows through the axial hole at a high flow speed. The radius of cylinder is divided to 4 nodes. The nodal equation for node T1 was derived using an explicit finite difference numerical method. Determine the temperature of node T1 in °C after 10 sec when a time step ( delta T) 10 sec is used. Assume T0 is always 100 °C.
Equation is 180000T1*/delta(t) = 700T0 + 1000T1 + 1500T2 + 180000T1/delta(t) delta t = 10s at t = 0, T1= T2 = T3 = 20C T0 = 100C plugging numbers in and solving for T1* T1* = 26.67C
Any objects made of plastic with low thermal conductivity can never be considered as a lumped capacitance system.
False
Consider heat transfer between two identical hot solid bodies and their environments. The first solid is dropped in a large container filled with water, while the second one is allowed to cool naturally in the air. The lumped system analysis is more likely to be applicable for the solid that is dropped in water container.
False
In natural convection regime, continuous vapor columns are formed and vapor films cover the part of the heating surface.
False
In parallel-flow heat exchangers, the outlet temperature of the cold fluid may exceed the outlet temperature of the hot fluid.
False
In pool boiling, the fluid motion is generated by an external means such as a pump.
False
Sample Exam: Any objects made of copper subjected to sudden heating or cooling may be assumed to be a lumped capacitance system.
False
Saturated pool boiling is a kind of boiling that happens at fluid temperature lower than saturation temperature of the fluid.
False
Vapor bubble formation in the boiling process must be always avoided since vapor bubbles act as an insulation.
False
When designing a fin, carbon steel is typically a better choice than aluminum
False
The cylindrical rod in problem 2 can be considered a lumped capacitance system.
False since B1 > 0.1
Sample exam: RTD (resistance temperature detector) is a temperature sensor that contains ceramic or polymer that changes its electrical resistance when the temperature changes
False (Pure metal, not polymer)
Sample exam: Due to harsh conditions, a sheath may be used to protect a thermocouple. The time constant of the thermocouple will be smaller due to the sheath.
False (Takes more time to reach steady state)
The heat exchanger in problem 1 is a parallel-flow concentric tube heat exchanger. Hint: note the temperature changes of cold and hot fluids
False It is counter since the hot fluid outlet temperature is less than the cold fluid outlet temperature
Consider heat transfer between two identical hotsolid bodies and their environments. The first solid is dropped in a large container filled with water, while the second one is allowed to cool naturally in the air. The lumped system analysis is more likely to be applicable for the solid that is dropped in water container.
False Water has a higher convective heat transfer
Sample Exam: Lumped capacitance analysis is used to study 1-D steady conduction heat transfer
False (2 - D)
Consider a system in which the finite difference equation of an interior node is given in its simplest form as: (Nodal equation used for lab 6) Which of the following is a correct statement about the numerical analysis above?
Heat transfer is one-dimensional.
Two metallic cylinders have the same shape and thermodynamic properties, but different characteristic length. They were submerged into the constant temperature bath with the boiling water. Both cylinders were heated from the room temperature Tinitial to the temperature of the water Tbath. The cylinders may be considered a lumped capacitance system. Compare the characteristic length L1 with L2 based on the transient temperature responses of the cylinders below.
L1 > L2 L1 takes more time to reach steady state L2 reaches faster steady state
For steady state one-dimensional heat conduction [that is, T(x) only] along a rod with a constant cross-sectional area as shown below: How does the temperature vary along the rod?
Linear going down
Determine the Nusselt number for cooling water inside the tube in question 2.
Nu = h *D / k plug in all values Nu = 7.78
Use the given steady state temperature measurements to calculate the precision limit of the device. Use 95% confidence level.
On calc: click stat, then 1 to edit the list. Exit and then click2nd + list and find the stdev. multiply it by given table. Answer: 0.8568 ˚C stdev = sqrt( sum[(x - mean)^2]/ (n - 1))
Match each heat exchanger with the right description.: Parallel-Flow Heat Exchanger Counter-Flow Heat Exchanger Cross-Flow Heat Exchanger Shell-and-Tube Heat Exchanger
Parallel-Flow Heat Exchanger: Both hot and cold fluids enter the heat exchanger at the same end and move in the same direction Counter-Flow Heat Exchanger: Hot and cold fluids enter heat exchanger at the opposite ends and flow in opposite directions Cross-Flow Heat Exchanger: Hot and cold fluis move perpendicular to each other Shell-and-Tube Heat Exchanger: One fluid flows inside the tube and other fluid flows over the tubes through the shell
A is a noncontact thermometers that measure the temperature of a body based on its emitted thermal radiation.
Pyrometer
Consider a cylindrical rod with a constant cross-section area which is in contact with an electrical heater at one end, and a heat sink at the other end. The heater is held at 80 °C. and the rod is well insulated. The rod's steady state temperature distribution and a linear interpolation are given on the plot below. If the thermal conductivity of the rod is 205 W/(m-K), and the diameter of the rod is 3.5cm, find the heat transfer rate (in watt) through the rod.
Q = -k A dt/dx k = Thermal conductivity = 205 dt/dx = -30 A = pi*D^2 / 4 Q = 5.9169 W
Steam at 100 °C condenses on the surface of a 5 cm-diameter and 15 cm-long tube by cooling water that enters the tube at 20 °C and leaves at 30 °C at 0.004 kg/s Determine the rate of heat transfer in Watts from the steam to the cooling water. Assume that the thermal conductivity and specific heat of water are 0.61 W/m·K and 4.187 kJ/kg·K, respectively.
Qdot = m*cp*delta(T) m = 0.004 cp = 4.187 delta T = 30-20 Qdot = 167.48
We want to predict the temperature of the cylinder in question 2 at different condition. Now the initial temperature of the cylinder is 25 °C. Determine the temperature of node T1 in °C after 10 sec when a time step ( ) 10 sec is used. Assume T0 is always 100 °C.
Same as past question but now T1 = T2 = T3 = 25C Plugg in numbers T1* = 32.36
[Sample ]Now assume that the actual temperature of the entire siding is known to be 54.44 °C. The emissivity of the infrared camera has been set to 0.90. Estimate the actual emissivity of the white painted surface and the brown painted surface. [6 pts] Assume* the camera uses a simple Stefan Boltzmann relation to convert the measured radiative flux to a user friendly temperature, q'' ≈ εσT4 .
Same as question above but all temperatures must be averaged and then that would be the measured temperature Tm. Remember converting to K
Which of the following has the lowest thermal conductivity?
Stainless Steel
The following graph shows temperature profiles along the axial direction of four fins with same geometry. According to the following temperature profile, which fin dissipates the most heat between the fin and the surrounding?
Straight line
The following figure shows the axial temperature distributions of two collinear rods of equal diameter. The rods are arranged so that the faces are contacting one another with a heat source at one end and a heat sink at the opposite end. The rod is stainless steel grade 316 whose thermal conductivity is 20 W/m·K. What is the thermal contact resistance in m2K/W?
T1 = 70 (furthest to the left) T2 = 50 (left of drop) T3 = 40 (right of drop) T4 = 20 (furthest to teh right) x = .04 (distance to drop) k = 20 (conductivity) (T1-T2) / (x/k) = (T2 - T3)/R solve for R R = 0.001
For steady one-dimensional heat conduction in a solid medium, the rate of heat transfer is directly proportional to the cross-sectional area for heat transfer. The following figure shows the axial temperature distributions of two collinear rods of equal diameter. The rods are arranged so that the faces are contacting one another with a heat source at one end and a heat sink at the opposite end. The rod is smooth stainless steel grade 316, with a thermal conductivity equal to 17 W/mK. What is the thermal contact resistance?
T1 = 70 (furthest to the left) T2 = 50 (left of drop) T3 = 40 (right of drop) T4 = 20 (furthest to teh right) x = 4 (distance to drop) k = 316 (conductivity) (T1-T2) / (x/k) = (T2 - T3)/R solve for R R = 0.118
Sample Exam: How do the temperature and the rate of heat transfer vary along the rod when kA>kB>kC? Assume no thermal contact resistance at the interface. Plot T(x) and Q(x). [10 pts]
Temperature linearly goes down, with jumps on where the rods end. As k increases, the slope becomes more horizontal. Heat transfer is completey constant
Resistance Temperature Detectors (RTD) measure the temperature by
The change in electrical resistance in pure metals as a function of temperature
Sample Exam: Biot number is defined as the ratio of
The conduction thermal resistance to the convective thermal resistance
In counter-flow heat exchangers, the outlet temperature of the cold fluid may exceed the outlet temperature of the hot fluid.
True
In film boiling regime, the heating surface is completely covered with vapor film. Radiation heat transfer becomes significant through the vapor film.
True
Sample exam: A Bi-metallic Dial Thermometer is a temperature sensor that contains metal strips that change its length when the temperature changes
True
Sample exam: A mercury in glass thermometer measures the temperature by the change in liquid volume as a function of temperature.
True
The fouling on the heat exchanger surfaces causes additional thermal resistance, thus decreases the heat transfer rate.
True
The plate with four different surface finishes (red, black, brushed, polished) was heated in an oven. The Infrared thermal image of the plate was taken as soon as the plate was removed out of the oven. Although the different colors in the thermal image represent different temperatures, the actual temperature of the plate must be uniform. This is attributed to the variation of emissivity with the four different surface finishes.
True
Two forms of condensation are film condensation and dropwise condensation. The dropwise condensation is a more effective mechanism of heat transfer than filmwise condensation.
True
What is the essential step you need to make to avoid spilling the very hot coolant before connecting/disconnecting the hoses from the constant temperature bath to the fittings on the PVC (or PPP) cylinder?
Turn off the constant temperature bath
Which of the following involves the boiling heat transfer?
Two-phase immersion cooling to remove heat from electric equipment at a high rate Two-phase Refrigeration systems to remove heat from a heated surface(space) Steam generator for power plants to convert water into steam
What are the thermal boundary conditions for brass disc in Lab 6?
Uniform heat flux at the inner surface, convected heat transfer at the outer surface
(SAMPLE) A cylinder with a 4 cm diameter-hole drilled axially through its center. The outer surface is insulated. Initially, the cylinder is at a uniform temperature of 25 °C, and at time t=0, the coolant from constant temperature bath at 100 °C flows through the axial hole at a high flow speed. The cylinder has a radius of 42 𝑐𝑚, density of 𝜌 = 2660 𝑘𝑔/𝑚3 , specific heat capacity of 𝑐𝑝 = 871 𝐽/(𝑘𝑔 ∙ 𝐾) and thermal conductivity of 𝑘 = 160 𝑊/(𝑚 ∙ 𝐾). The radius of cylinder is divided to 5 nodes. Please use ∗ superscript for the end of a time step (or new time step) and no superscripts for the beginning of a time step (or previous time step). Use an explicit finite difference numerical method to find nodal equations for the instantaneous temperature distributions of nodes T1 and T4. Note: no need to simplify the nodal equations. [8 pts]
Use formulas of explicit differentiation on Lab 6
Sample Exam: What is the reason for the shape of your distribution? (Justify your response using mathematical reasoning.
dt/dx is inversily proportional to k, that means that as k increase the slope decrease (becomes more horizontal). Since the first slope is smaller, and the heat transfer reate is directly proportional to the slope, then q is constant but it has diffreent values. Since the slopes increase as length increases, then the heat transfer increases as as the length increases.
Consider a concentric tube heat exchanger operating under the following conditions: Hot fluid heat capacity rate: 6 Hot Fluid Inlet temperature: 333 Hot Fluid Outlet temperature: ? Cold fluid heat capacity rate: 3 Cold Fluid Inlet temperature: 303 Cold Fluid Outlet temperature: 327 Determine the outlet temperature of the hot fluid.
mdoth * ch * (Th1 - Th2) = mdotc * cc * (Tc2-Tc1) Where mdoth * ch = 6 Th1 = 333 mdotc * cc = 3 Tc1 = 303 Tc2 =327 Plug in and solve for Th2 = 321K
(SAMPLE) Determine the temperature of T1 at t=10 sec. Use a time step Δt=10 sec. Show all your work.
plug in delta T as 10 T0 as 100c and all other temperatures as 25
Heat is conducted through 3 layers of wall. Assume steady state heat conduction, no heat generation, and 1-dimensional heat transfer. Compare the heat transfer rate, q1, q2, and q3 when k1>k2>k3.
q1=q2=q3
The plate with four different surface finishes (red, black, brushed, polished) was heated in an oven. The Infrared thermal image of the plate was taken as soon as the plate was removed out of the oven. The average temperature on the black painted surface is 86.9oC. The actual surface temperature of the plate is uniformly 100 oC. The camera assumed an emissivity of 0.95 to convert measured IR radiative flux to temperature data. Assume* the camera uses a simple Stefan Boltzmann relation to convert the measured radiative flux to a user friendly temperature, q'' ≈ εσT4. Estimate the emissivity of the black painted surface.
εa * σ * Ta^4 = εm * σ * Tm^4 εa * Ta^4 = εm * Tm^4 where εa = actual emmisivity = ? εm = measured emmisivity = 0.95 (assumed) σ = stefan-boltzman constant Ta = actual temperature = 100C = 373K Tm = measured temperature = 86.9C = 359.9K plug everything in and solve for εa = 0.823
