mini-project report radiator heat transfer augmentation by...

Mini-project report

Radiator heat transfer augmentation by changes to wall surface roughness and

emissivity

Mr Krys Bangert [email protected]

June – August 2010

Radiator heat transfer augmentation by changes to wall roughness and emissivity 1) Abstract: This mini-project is a part of ongoing work carried out at Sheffield University by Dr Stephen Beck and multiple PhD and MEng students looking into the effects of combined radiation and convection on household radiators. This study looks at how changes to a walls surface finish can affect a radiators heat transfer. A series of tests and computer simulations were run comparing the heat loss from a radiator when the wall roughness and emissivity directly behind it was changed. To gather the empirical data needed for the study an existing radiator test rig built to approximate European Standard EN 442-2 was used. Thermocouples were mounted on the radiator, wall, inlet/outlet pipes and in the air gap behind the radiator, to gather temperature readings for levels of conduction, radiation and convection in the system. Three tests were carried out under steady state conditions, with a 10°C drop across the radiator to comply with the British Standard. The first test used a plain wall as a control, the second and third tests had sandpaper sheets matching the profile of a radiator attached to the wall behind the radiator. The sheets were sprayed in gloss black and silver paint respectively, to modify the surface emissivity. A computer simulation of the setup and tests was also created for comparison using the CFD (computational fluid dynamics) program Fluent. Unfortunately the results from the tests and simulations were inconclusive due to high levels of experimental error and convergence issues in the CFD model. However, the data did show that the overall trends discovered in previous work relating to emissivity are valid. It is hoped that in future work more accurate results can be obtained based on the recommendations of this study. Keywords: E-Futures, CFD, Heating, Radiator, Convection, Radiation, Heat transfer.

2) Introduction: Domestic energy consumption is one of the key areas currently been looked at by environmental researchers. It has been estimated that the domestic sector accounts for over 30% of the current UK national energy demand, the second largest usage behind the transport sector

1.

If the greenhouse gas emission targets set by the UK government are going to be met in the coming decades, the way we use energy in the home is going to have to become more efficient. One of the best ways to achieve this, in the short to medium term is to upgrade the existing housing infrastructure to make it as energy efficient as possible. This will help to offset the transition as new ‘zero carbon’ housing gradually replaces the ageing housing stock. The biggest domestic efficiency gains are to be made in space and water heating, which account for 58% and 24% of the energy use respectively

2. Since the 1970s the rates of overall domestic heat loss have fallen

progressively due to improvements made in the levels of insulation3. However, the single largest contributor

to this heat loss; the heat lost through walls, is still a common problem today3.

The focus of this mini-project is to continue the work carried out in Sheffield University’s department of mechanical engineering, looking into new methods of increasing household thermal efficiency. This study looks into the effect that wall surface roughness and emissivity have on domestic radiator heat output. This work will be building on the findings gathered by former MEng student S.G. Blakey and current PhD student A.K.A Shati. In their previously published work

4-6, it was found that if surfaces with a higher emissivity were

placed behind a radiator at an optimal distance (s/L = 1/12. Where s is the separation and L is the vertical height of the radiator), a larger heat output could be obtained from the radiator

4. It was then subsequently

discovered that if large scale roughness was also added to the surface finish, the heat flow could be increased even more (upto 26% using a high emissivity saw-tooth surface)

6. With further analysis it was

found that these effects were caused by the wall heating up due to its higher emissivity (more infrared radiation was absorbed than a plain/reflective wall). This heating in turn created a convecting surface behind the radiator which increased the air flow. The addition of roughness to the wall further amplified this effect by increasing the surface area for heat transfer and creating more turbulence, which improved the mass transfer and heat flux in the air gap behind the radiator. This mini-project will look into how the heat transfer is affected by using a different geometry on the wall surface with dissimilar emissivities. The experiments and simulations will be carried out in a similar fashion to the previous studies, but the surface finish will be based upon coarse grain sandpaper with different emissive coatings.

3) Experiments/methodology Test setup: To perform the experiments an existing domestic central heating test rig from the previous studies was reused (see appendix 1.0-1.1). This setup was designed and built to approximate European standard EN 442-2

7, this enabled pervious test results to be compared with the performance figures for commercially

produced radiators. The setup consisted of the following apparatus: Amount: Description: 1 Standard 600mm high by 600mm wide single plate radiator with 50mm expanding foam

insulation covering one side 1 3kW immersion heater regulated by a PID temperature controller (accuracy: ±0.1°C). 1 Hot water cylinder with insulation. 1 Water cistern. 4 Control valves to regulate water flow: two control valves on the radiator, one bypass valve to

the water tank and one output valve. 1 Class F mains powered pump operating at 60W – 2000 RPM. 1 Rotormeter to measure the water flow rate. 1 Pico technology TC-08 Serial thermocouple interface. 1 Pico technology TC-08 USB thermocouple interface. 10 Type T thermocouples (accuracy: ±1°C) 6 Type K thermocouples (accuracy: ±1°C) 1 Digital thermistor type anemometer (accuracy: ±0.3°C and ±0.015m/s) - 15mm copper piping with foam lagging (10mm thick). - 20mm thick High density particle board.

For each test the radiator was mounted 150mm above the floor and 50mm away from the wall, to match the previous test setups. These measurements were used again because it was discovered that the maximum values of heat transfer occur at this distance away from the wall in Blakely’s initial study

4. The thermocouples

were arranged on the radiator, front and back of the wall, inlet and outlet pipe and in the air gap behind the radiator (see appendix 1.2-1.3). A thermocouple was also used to take the ambient air temperature readings and the thermocouple linked to the PID controller was attached to the radiator inlet pipe for temperature feedback; it was assumed that the external pipe temperature was the same as the water. The rest of the thermocouples were linked to a PC for data logging using the PicoLog software, the sample rate set to a 1 minute interval for each interface. The anemometer was also linked to a computer for data logging using the manufacturer’s software. The sensor was mounted using a clamp and stand to give readings at the top of the radiator in the middle of the air gap (see appendix 1.1). To comply with the European standards the temperature gradients across the radiator must have a 10°C drop and be maintained with ±0.1°C. To calibrate the setup the heater was set to 80°C using the PID and left over night to achieve steady state conditions. The valves were then adjusted to get a temperature drop required. However, it was subsequently found that this could not be achieved without stopping the water flow completely. So a compromise value of approximately 8°C was used for the tests with a flow rate of 0.2 L/min. Each test surface was constructed of 9 sheets of 40 grit coarse grain sandpaper held together using fabric tape. The surface was then cut to a 600mm x 600mm size to match the profile of the radiator. One of the surfaces was then spray coated with black gloss multi-surface enamel paint and the other with silver radiator and appliance spray paint (see appendix 1.4). The surfaces were attached to the test wall using fabric tape for each of the tests. Holes were made for the air temperature thermocouples to protrude and the wall thermocouple was attached to the surface using a small piece of fabric tape sprayed in the same finish as the relevant test surface.

Test method: Before the tests were carried out the PID controller was set to 80°C and the system was left for a minimum of 6 hours to reach steady state conditions with an appropriate temperature drop. Once this was achieved each test was run for a period of one hour with the thermocouple and anemometer readings taken automatically by the appropriate software and the initial rotometer flow reading taken manually (previous tests had shown it to be consistent in steady state conditions). The first test was run with a plain wall, the second with the black surface and the third with the silver wall. The test data was then collected from the software and complied in Microsoft Excel for analysis (see digital appendix). CFD modelling: To find the full effects of the heat transfer and air flow a series of CFD simulations were carried out using similar geometry to the physical test setup. The software used for this was Gambit version 2.2.30 and Fluent version 6.3.26. A 2D mesh was created in Gambit which featured a 4 by 3 meter room with 0.1m walls (to comply with the European standard), a 0.6m by 0.02m radiator, 0.050 by 0.6m of thermal insulation (which was attached to the radiator) and a 0.6m separate surface attached to the left hand wall (see appendix 1.5). A quadrilateral mesh was used with the highest density elements around the radiator. The model contained 22058 cells, 45440 faces, 23370 nodes and 1 partition. The 2D mesh was imported into fluent and the following properties and boundary conditions were applied: Entity: Property: Room wall material Brick – Density: 1850 (kg/m

3), Cp: 800 (j/kg-k), Thermal conductivity: 0.595 (w/m-k),

Absorption coefficient: 0.9 (1/m), Scattering coefficient: 0 (1/m), Refractive index: 1.

Room fluid Air – Density (Boussinesq): 1.225 (kg/m3), Cp: 1006.43 (j/kg-k), Thermal conductivity: 0.0242

(w/m-k), Viscosity (kg/m-s): 1.7894x10-5

, Absorption coefficient: 0 (1/m), Scattering coefficient: 0 (1/m), Thermal expansion coefficient (1/k): 0.00343, Refractive index: 1.

Radiator insulation material Foam – Density: 320 (kg/m3), Cp: 1455 (j/kg-k), Thermal conductivity: 0.0485 (w/m-k),


Radiator wall material Steel – Density: 8030 (kg/m3), Cp: 502.48 (j/kg-k), Thermal conductivity: 16.27 (w/m-k),


Rough surface material Test surface (black sandpaper) – Density: 0.69 (kg/m3), Cp: 830 (j/kg-k), Thermal

conductivity: 0.2 (w/m-k), Absorption coefficient: 0.97 (1/m), Scattering coefficient: 0 (1/m), Refractive index: 1. Test surface (Silver sandpaper) – Density: 0.69 (kg/m

3), Cp: 830 (j/kg-k), Thermal

conductivity: 0.2 (w/m-k), Absorption coefficient: 0.47 (1/m), Scattering coefficient: 0 (1/m), Refractive index: 1. Wall Roughness (Both surfaces) - Roughness height: 0.000425(m), Roughness constant: 0.5.

Radiator heat source Fixed value - Temperature: 353 (k) [80°C]

External wall boundary Temperature: 293 (k) [20°C], Wall thickness: 0(m), Heat generation rate: 0 (w/m3).

Five simulations were run emulating the physical tests. The first with ordinary plain wall, the second and third with high emissivity rough and smooth surfaces and the fourth and fifth with a low emissivity rough and smooth surfaces (see table above). The emissivity of all the walls except the test surface and radiator was set to 0.93, with the exception of in the plain wall test in which the left wall and the test surface had the same emissivity. The two tests with rough surfaces used the standard wall function with additional wall roughness attributes added to the simulation. The other simulations used the enhanced near wall functions. Due to the test surfaces have a relatively uniform roughness, it was assumed that the roughness height corresponded to the average sand particle diameter (P40 grit sandpaper = 425 Average particle diameter (µm) = 0.000425 m). The roughness constant was left at the default value of 0.5, which is taken from empirical resistance data for pipes roughened with tightly-packed uniform sand-grains (ref: Fluent 6.3 User’s Guide). The standard k- ε turbulent with full buoyancy and thermal effects (when using enhanced wall function) was used; along with the Discrete transfer (DTRM) radiation models. The gravity was set at -9.81(m/s

2), an operating temperature

at 303 (k) with 1 atmosphere pressure. The rough and smooth high and low emissivity surfaces were modelled for comparison purposes due to uncertainty with the simulation of near wall effects.

4) Results/Discussion: To calculate the heat transfer of the radiator the thermodynamics of the system needed to be analysed. In order for the first law of thermodynamics to be obeyed, the energy input to the system must equal the output. Because the radiator itself does not perform work, this energy (in the form of heat) must come from the water passing through it. As the radiator heats up due to the conduction of the water, the heat is then transferred to the air by the process of convection and radiation. This causes the water flowing through the radiator to lose heat energy

5. Because the water is flowing within a closed loop system, if its temperature is measured on the

input and output of the radiator, the net heat loss demonstrates the heat transfer into the surroundings. However, this calculation is only applicable under steady state conditions within the system (hence the setup tests mentioned in the previous section). To calculate what proportion of the heat loss is down to convection, conduction and radiation, the energy flows in and out of the system must be considered (see appendix 1.6). The heat flows can be grouped into the following main categories; convection into the air, radiation to the room and wall (with some reflection back into the radiator) and conduction through the wall. The amount radiated into the room is so small it was disregarded in this study. Taking these flows into consideration the following equations have be derived:

Heat transferred from the wall surface to the air: �� 1

Convection heat transfer from the radiator to the air: �� 2

Total heat transfer to the air: �� 3 By combining equations 1 and 2 into equation 3 the total heat transfer to the air can be calculated. This is done using the equation for water heat flow (eq:5) and wall conductive heat transfer (eq:6):

�� 4

Where �� . �� 5 and �� !"# ��$$% � ��$$&� � 6

These calculations were performed on the averaged data from all three of the tests and compiled in a Microsoft excel spreadsheet (see digital appendix 1). The experimental error due to equipment data logging accuracy (see table 1) was not incorporated into the calculations. Test data analysis: The graphs showing the various heat transfers from the radiator and through the wall are included in appendix 1.9 and the digital appendix. It can be seen that the black sandpaper wall has the highest heat output to air (86.5w), followed by the plain surface (84.6w) and the silver surface with a much lower output (37w). This result seems to validate the prediction that a black surface should aid convection and produce the largest heat output. However, when the heat transfer by conduction and total heat transfer are also compared, some major abnormalities are present. It was predicted that the silver wall covering have the least heat loss via conduction (due to its lower emissivity), followed by the plain wall and then the black. But the results demonstrate the exact opposite, with Silver, Plain and Black having 67.5, 43.5 and 37.3 Watts respectively. The radiator air temperature profiles also show a different correlation of results, after compensating for ambient temperature. The results show that both rough surfaces give higher outputs than just the plain wall alone, but the silver produces the highest temperature overall. This result as also opposed by the total heat transfer reading which shows that during the silver sandpaper experiment the radiator produced a lower heat output compared to the others. It is difficult to see a clear trend with the results because the data sets appear to be contradictory, but after a careful review of the data and inspection of the experimental apparatus there is a possible explanation. Following the silver sandpaper experiment it was discovered that the thermocouple at the back of the wall had become unstuck from the wall surface. This caused an ambient temperature reading which made the heat loss through the wall calculations artificially high for the silver sandpaper experiment. It has also been shown that the temperature drop across the radiator was not uniform for each experiment, especially the silver again. The plain, black and silver experiments had drops of 8.8, 8.5 and 7.2°C

respectively). These main factors along with other smaller experimental errors (discussed later the in the report) are likely to have produced such an unexpected set of correlations. CFD data analysis: Each of the CFD models converged with all residuals to the power of x10

-3 (see digital appendix). The two

simulations with roughness added to the test surface however did show minor oscillations still present in the turbulence residuals. Each of the simulations shows a heat flux error in the region of -25 watts, which indicates the models solutions have a reasonably large error in the predictions (approx 6%). Each of the models also shows similar velocity and thermal flow characteristics (see appendix 1.7-1.8) with a convectional current present around the walls of the room and radiation causing the heating of the wall behind the radiator as expected. However, there is a slightly anomaly in the convection current because it appears to split into two flows on the floor of the model rather than forming a single enclosed flow circuit as expected. Many different meshes were tried to see if this artefact was grid dependant, but each time it was found consistently. The source of this abnormality was not found, but the results varied by a small enough degree to be classed as been converged for the purposes of the mini project. The total energy output of the radiator was shown to be highest for the black smooth wall, followed by the plain wall, rough black wall, plain silver wall and the rough silver wall (see appendix 2.0). This trend seems to support the hypothesis that a higher emissivity surface increases the radiator output, but it does not show that the turbulence generated from the rough finish helps. In fact, the roughness seems to reduce the output of the radiator (especially in the case of the black surface), making it less efficient than the plain wall alone. However, this result could be artificially low due to problems in convergence with the two rough models and it is also uncertain whether the near wall boundary layers are properly represented using this technique. Further simulations would need to be carried to validate these results, but due to time constraints unfortunately this was outside the scope of this project. Comparison: The results from the experiment and model were compared in another spreadsheet (see digital appendix). The total power output of the radiator and the thermocouple readings for the top, middle and bottom of the air gap behind the radiator were compared with the CFD analysis (see appendix 2.0). There is a large difference between the power outputs from the model and the experimental data. It is not known what has caused this discrepancy; it could be due the oversimplification of the model, unconvergence, experimental error and/or many other possible factors. The trends do not match between the two data sets for the reasons mentioned previously. The air gap temperature readings show a good correlation for each of the wall surfaces, will most of the readings within the two error bars. The CFD readings again support the wall emissivity hypothesis and not the roughness, but the difference in temperature increase is very small (less than 1°C between the plain and black walls). The biggest difference in results between the experimental and simulations is the radiator bottom reading. The simulation trend shows a temperature similar to the radiator middle value but the experimental shows a much more linear drop off. This difference could be due to the radiator mounting bracket and weight (see appendix 1.1) disrupting airflow under the radiator. 5) Conclusions and further work. The findings of this mini-project are on the whole inconclusive, with the exception of some simulation results showing that higher emissivity coatings behind a radiator can improve its heat transfer. There have been many avoidable experimental errors made and problems with the method highlighted during the course of the study. If these issues can be addressed by the next group of students following on from this work, significant progress can be made. In particular I think the experimental test setup can be improved by changing the test surface mounting mechanism, securing thermocouples differently, using a more accurate data logger and altering the radiator mounting from to reduce air drag. Other forms of data logging such as using thermal imaging cameras and surface velocity tests could also be beneficial, along with making the setup closer to British standard and making the test samples more uniform. Many other improvements could be made to the test procedure by eliminating further experimental error (see below). In addition to the physical testing the CFD simulations also need to be improved in accuracy. The roughness effects need to be looked into and possibly new equations developed, the mesh also needs to be properly tested to see its affect on the simulation (invariance testing), a 3d model could potential produce more accurate results. If some of these issues can be addressed in the future work, more useful results can be obtained giving a

valuable insight into how radiator and wall design can be improved to make domestic heating more energy efficient in the future. Further sources of experimental error: Thermocouple error +- 5°C, timing between data sets +- 10 secs, flow readings too variable, Existing thermocouple layout not central, CFD materials based on estimates, Lagging not continuous on apparatus pipe work, temperature taken at surface of pipe not in fluid, backing samples non uniform in surface finish, alignment of backing samples not correct, air flow from ventilation system affected air flow readings, thermocouple layout not aligned properly with drilled holes, different to computer model, sand paper backing not fully flush with wall, mounting tape emissivity and test surface is different material. Acknowledgment: Work reported here is supported by the Department of Mechanical Engineering. I would like to thank my supervisor, Dr Stephen Beck for putting this mini-project together and helping to guide me along the way. PhD students Abdulmaged Shati and Richard Collins; for their help explaining various processes and using the Fluent and Gambit software. My friend and fellow DTC classmate Robert Richards, for his help and collaboration in the initial stages for the project. Technician Malcolm Nettleship for his help setting up the test rig and Fluent Europe of the use of their software. References: 1 Change, D. o. E. a. C. (2010). 2 Change., D. o. E. a. C. (2010). 3 Utley, J. I. & Shorrock, L. D. (BRE Housing, 2008). 4 Beck, S. B. M., Blakey, S. G. & Chung, M. C. The effect of wall emissivity on radiator heat output.

Building Services Engineering Research and Technology 22, 185-194, doi:10.1191/014362401701524217 (2001).

5 Beck, S. M. B., Grinsted, S. C., Blakey, S. G. & Worden, K. A novel design for panel radiators. Applied Thermal Engineering 24, 1291-1300, doi:10.1016/j.applthermaleng.2003.11.026 (2004).

6 Shati, A. K. A., Beck, S. B. M. & Blakey, S. G. The effect of surface roughness and emissivity on radiator output (awaiting publishing). (2010).

7 Institute, B. S. in Part 2: Test methods and rating (1997). 8 Badr, H. M., Habib, M. A., Anwar, S., Ben-Mansour, R. & Said, S. A. M. Turbulent natural convection

in vertical parallel-plate channels. Heat and Mass Transfer 43, 73-84, doi:10.1007/s00231-006-0084-z (2006).

Nomenclature:

Symbol: Description: Units: A Heat transferring surface area (m

2)

Cp+ Specific heat capacity (Jkg−1

K−1

)

g Gravitational acceleration (ms−2

)

h Heat transfer coefficient (Wm−2

K−1

)

K Thermal conductivity of the fluid (Wm−1

K−1

)

L Enclosure wall length (m)

m� + Water mass flow rate (kgs−1

)

Q� 1234�+ Convection heat transfer from the wall to the air (W)

Q� 567389 Net radiation heat exchange between the wall the radiator (W)

Q� 1237 Heat loss by Conduction through the wall (W)

Q� 1234�: Convection heat transfer from the radiator to the air (W)

Q� 929 Total heat transfer from the radiator (W)

Q� 6;5 Total heat transfer to the air (W)

T+;3 Water inlet temperature (K)

T+2=9 Water outlet temperature (K)

T+6>>% Wall surface temperature facing radiator (K)

T+6>>& Wall surface temperature facing outside (K)

U Thermal conductivity of the wall (Wm−1

K−1

)

@ Thermal diffusivity (m2s

-1)

� Kinematic Viscosity (m2s

-1)

β Thermal expansion coefficient (K-1

)

∆T Temperature difference (K)

NuC Nusselt number DhCE F (-)

R6 Rayleigh number DHβ∆JCK

�αF (-)

Appendix 1.0 – Schematic of apparatus

Cistern

Tank with immersion

heater Flowmeter

Pump

Flow rate control pipe

Radiator

Valve T1 T2

Appendix 1.1 – Test right setup

Fabric tape

Sandpaper backing layer

Foam insulation

layer

Inlet pipe and insulation

Outlet pipe and insulation

Serial thermocouple

interface

Thermocouple (x15)

Airflow monitor Radiator

Mounting frame and weights

50mm air gap

Clamp and

stand

Regulator valves (x2)

Chipboard wall

Temperature controller/regulator

Hot water tank w/immersion

heater

Cistern

Water pump

Control valve (x2)

Rotormeter

USB Thermocouple

interface

Appendix 1.2 - USB interface thermocouple layout:

Thermocouple Type Name TC 1 T Ambient air temperature TC 2 T Water temp in TC 3 K Radiator air temp bottom TC 4 K Radiator air temp middle TC 5 K Radiator air temp top TC 6 K Wall temp front TC 7 K Wall temp back TC 8 K Water temp out

TC 8

TC 2

TC 1

300mm

TC 5

Left to right: TC 7, TC6, TC4

TC 3

15

0m

m

30

0m

m

75

0m

m

20mm

25mm

50mm

Appendix 1.3 - Serial interface thermocouple layout (un-insulated side):

Appendix 1.4 – Test surfaces

Silver sprayed surface (left), Black sprayed surface (right)

Thermocouple Type TC 1 T TC 2 T TC 3 T TC 4 T TC 5 T TC 6 T TC 7 T

600m

m

55

0m

m

30

0m

m

50m

m

50mm

300mm

550mm

600mm

TC 6

TC 4

TC 2

TC 7

TC 1

TC 3

TC 5

Appendix 1.5 – CFD mesh used.

Appendix 1.6 – Energy flows in and out of the radiator system.

Close-up of mesh around radiator

Room Air

Wall outer surface

Wall inner surface

Radiator insulation

Radiator

Wall

Test surface

Qcond

Air out

Qrad2-1

Radiator (1)

Qrad1-2

Qconv-w

Qconv-R

Air in

Water out

Qtot

Floor

Wall (

2)

Water in

Rad

iato

r in

su

lato

r

Test surface

Appendix 1.7 – CFD Vector flows (plain wall).

Appendix 1.8 –CFD Temperature contours (plain wall).

Appendix 1.9 – Experimental results. Appendix 2.0 – CFD results comparison.

670.90

128.11

676.41652.73

123.83

589.42567.51

104.61

0

100

200

300

400

500

600

700

To

tal E

ne

rgy

ou

tpu

t (W

)

Total heat transfer from radiator

Plain wall CFD Plain wall actual

Black wall CFD (No rough) Black wall CFD (Rough)

Black wall actual Silver wall CFD (No rough)

Silver wall CFD (Rough) Silver wall actual

128.11123.83

104.61

0

20

40

60

80

100

120

140

He

at

En

erg

y (

W)

Total heat transfer from the

radiator

Plain Black sand Silver sand

43.4837.32

67.52

0

10

20

30

40

50

60

70

80

He

at

En

erg

y (

W)

Heat loss by conduction

through the wall


84.63 86.52

37.09

0

10

20

30

40

50

60

70

80

90

100

He

at

En

erg

y (

W)

Total heat transfer to the air


22

24

26

28

30

32

34

36

Radiator top Radiator middle Radiator bottom

Te

mp

era

ture

(°C

)

Plain wall - 50mm air gap temp

Plain wall CFD Plain wall actual

24

25

26

27

28

29

30

31

32

33

34


Te

mp

era

ture

(°C

)

Black sandpaper wall - 50mm air gap temp

Black wall CFD (No rough) Black wall CFD (Rough) Black wall actual

24

25

26

27

28

29

30

31

32

33

34


Te

mp

era

ture

(°C

)

Silver sandpaper wall - 50mm air gap temp

Silver wall CFD (No rough) Silver wall CFD (Rough) Silver wall actual

mini-project report radiator heat transfer augmentation by...

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