## PicoScope 5000 Series

#### FlexRes® Oscilloscopes

High speed and high resolution. Breakthrough ADC technology switches from 8 to 16 bits in the same oscilloscope.

# Convection heat transfer coefficient on a vertical plate

## Introduction

In this experiment the convection heat transfer coefficient (h) on a metal plate suspended vertically in a room is determined by measuring the ambient temperature of the room and the surface temperature of the plate as it cools from an initial high temperature to a lower temperature undergoing free convection. The methodology used is to compare the experimental cooling trace to a series of theoretical curves for different values of h, then the best match is chosen and the value for h is determined.

The lumped heat capacity method is used in this experiment to determine the convection coefficient. This experiment is well suited for a range of groups ranging from students undertaking a physics subject at high school level (e.g. Year 11 or Year 12) to students undertaking a heat transfer subject at undergraduate level (e.g. Year 2 of a Bachelor of mechanical engineering degree course).

## Equipment required

• TC-08 thermocouple data logger
• PC with PicoLog Data Logging Software installed
• 3 x K-type thermocouples
• Aluminium 356 metal plate (any other metal plate for which bulk heat capacity applies can be used)
• 1 litre container to heat up water used in turn to heat-up sample to initial temperature
• Portable gas burner to heat the water
• U-clamp with sharp-pointed screws (or alternative clamping that minimizes heat loss)
• Base and stand (or alternative rig) for suspending the sample
• A small piece of cloth to clean excess water from plate surface

## Background theory

A solid whose geometry, size and thermal properties are such that the resistance to heat flow is much greater at the external surfaces than internally can be treated as a lump of material cooling at uniform temperature. This is formally known as the lumped heat capacity heat transfer case. The test for the applicability of this method is given by the Biot number criteria as follows:

And the temperature of the solid as a function of time can be described with reasonable accuracy by the following formula:

## Experiment setup

Hold the sample in the clamp by tightening between the sharp-pointed screws and suspend at about 1.5 metres from the ground (or desired height) in the middle of the room or space where the heat transfer coefficient is to be determined. Use the stand as in Figure 1 to suspend the sample or alternative suspension rig.

Connect the TC-08 unit to the PC and plug the three thermocouples to the converter. Place one thermocouple end in the middle of one of the plate faces using some adhesive and place another thermocouple in an appropriate location to measure the room’s ambient temperature. Leave one thermocouple free for measuring the water temperature.

Figure 1. set up rig and sample plate geometry

## Carrying out the experiment

Ignite the burner, place one thermocouple in the water container and heat the water to about 95 degrees Celsius using the burner. Lower the burner flame as needed to maintain this temperature.

Start the computer and run the PicoLog recorder software, set sampling rate to 1 sample per second and make sure the temperature monitor display is on and then start logging data to file.

Use the hot water to heat up the sample by dipping the lower end of the plate into the water. Heat up until the temperature of the sample has reached about 85 degrees Celsius.

When the plate temperature reads about 85 degrees put the water and burner away, quickly wipe off the excess water from the plate end that was submerged in water and let the plate cool for about half an hour. After this time stop the recorder and use the logged data to determine the convection coefficient as described below. The measured temperature range data to use for determining the convection coefficient can be extracted from the recorded data.

Figure 2: water, ambient and plate surface temperature traces (°C vs seconds)

## Determination of convection coefficient using theoretical cooling curves and measured data

An aluminium grade 356 investment-cast sample plate was used in this experiment. The experiment was carried out in a room with minimal air draught and ambient temperature about 18 °C. The sample plate has a rectangular geometry smooth surface finish and rectangular recesses. The setup rig and plate geometry can be seen in Figure 1 above. The overall dimensions, measured area and volume and thermal properties are:

• overall length: 101 mm
• overall width: 62 mm
• overall thickness: 19 mm
• measured surface area: A = 1.848 * 10–2 m2
• measured Volume: V = 1.082 * 10–4 m3
• Density: 2680 kg/m3
• Thermal conductivity: 167.36 W/m·K
• Heat capacity: 963 J/kg K

For the material, geometry and size of sample used, lumped heat capacity applies. When evaluating the criteria for applicability (h*V/A*K) we get 0.0003, which is well below the criteria maximum of 0.1 for reasonable accuracy.

The Figure 2 below shows the three temperature traces for ambient, water and plate surface. The green curve of Figure 2 is the plate surface temperature, the blue curve is the water temperature and the red curve is the ambient temperature.

For the given conditions of the experiment, room temperature 18 °C and no air currents, a typical value of about 10 W/m·K should be expected. Therefore the theoretical curves plotted in Figure 3 below are for values of h around 10.

Figure 3: lumped heat capacity theoretical cooling curves

After overlaying the measured data onto the theoretical curves and refining the range, a close enough value for h is determined around 10 as expected by picking the best match curve as shown in Figure 4 below. The dark black line is the measured temperature.

Figure 4: measured temperature overlayed on theoretical curves for h=9, h=10, and h=11

## Questions and discussion of results

• Why are pointed screws used to clamp the sample?
• How could a closer matching theoretical cooling curve be found?
• What is the radiation effect? Can anything be deducted from the overlay graph of Figure 4? Can the radiation effect be neglected?