EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3 Mechanical Engineering Department FAMU/FSU College of Engineering

Mechanical Engineering Department FAMU/FSU College of Engineering Outline Purpose of the lab Testing Equipment The types of equipment setup Units 3 and 4 Units 1 and 2 Additional components Heat sinks Drain tubes Calculations Needed for Experiment

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. Mechanical Engineering Department FAMU/FSU College of Engineering

Testing Equipment For Experiments Mechanical Engineering Department FAMU/FSU College of Engineering

Mechanical Engineering Department FAMU/FSU College of Engineering Adjusting knobs Temperature Recorder Units 1-4 Drain tube

Mechanical Engineering Department FAMU/FSU College of Engineering Thermocouple Selector 1-10 Unit Selector 1-4 On/Off Switches for Units 1-4

Mechanical Engineering Department FAMU/FSU College of Engineering Temperature adjustor for Units 3-4

Mechanical Engineering Department FAMU/FSU College of Engineering Digital Temperature Indicator (ºF)

Equipment for Thermal Conduction Test Units #3 and #4 Mechanical Engineering Department FAMU/FSU College of Engineering

Mechanical Engineering Department FAMU/FSU College of Engineering Heat flow for units 3 and 4

Mechanical Engineering Department FAMU/FSU College of Engineering Heat flow for units 3 and 4 Notes: Do NOT adjust the flow valves.

UNIT #3 x2x2 x1x1 T1T1 T2T2 Q=KA*ΔT/Δx K = coeff. of therm. conductivity NOTE: K is unknown and must be determined Mechanical Engineering Department FAMU/FSU College of Engineering

UNIT #4 x2x2 x1x1 T1T1 T 10 Q=KA*ΔT/Δx K = coeff. of therm. conductivity NOTE: K is unknown and must be determined Mechanical Engineering Department FAMU/FSU College of Engineering

Equipment Thermal Resistance and Contact Resistance Test Units #1 and #2 Mechanical Engineering Department FAMU/FSU College of Engineering

Mechanical Engineering Department FAMU/FSU College of Engineering Heat flow for units 1 and 2

Mechanical Engineering Department FAMU/FSU College of Engineering 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. Heat flow for units 1 and 2

Units #1 and #2 Cu (Al) Contact Resistance T1T1 T 10 x1x1 x2x2 Stainless Steel Steel (Mg) Mechanical Engineering Department FAMU/FSU College of Engineering

Heat Sinks One water cooled heat sink is located on each unit Units #1 and #2 they are located at extreme end of the assembly away from the heat source Units #3 and #4 are located on the top of each unit The heat sinks will be used to determine heat lost by each unit. Q=m w C p (ΔT) Mechanical Engineering Department FAMU/FSU College of Engineering

Drain Tube Flow Rate Calculations Mechanical Engineering Department FAMU/FSU College of Engineering

Mechanical Engineering Department FAMU/FSU College of Engineering Drain tubes leading from heat sinks

Mechanical Engineering Department FAMU/FSU College of Engineering Graduated cylinder to measure flow rate Drain tube Also will need a stopwatch to time fluid flow

Calculations Mechanical Engineering Department FAMU/FSU College of Engineering

Mechanical Engineering Department FAMU/FSU College of Engineering Conservation of Energy (in a perfect world) q in = q out Calculations Conservation of Energy (in our world) q in = Cq out Where C is a constant which represents any losses not accounted for.

Units #1 and #2 Stainless Steel Cu (Al) Steel (Mg) Heat In Heat Sink Q=m w C p (ΔT) Q out =Q in R t,c = ΔT/Q Mechanical Engineering Department FAMU/FSU College of Engineering

Mechanical Engineering Department FAMU/FSU College of Engineering Calculations Thermal Contact Resistance R t,c = Thermal contact resistance  T = Temperature change q = Heat flux

UNIT #3 x2x2 x1x1 Q out Q in Q=m w C p (ΔT) Q out =Q in Q=KA ΔT/Δx Mechanical Engineering Department FAMU/FSU College of Engineering

Mechanical Engineering Department FAMU/FSU College of Engineering (1) – Rate of heat flow at the sink m w = mass of cooling water displaced in time  t C p = Specific heat of water at constant pressure  T = (T out - T in ) of cooling water  t = time required to displace a volume V w of water (2) – Relationship between heat flow and temperature difference K = proportionality constant A = cross-sectional area  T = temperature difference of the material  x = distance (1)(2) Calculations

Q=KA ΔT/Δx Q=-KA dT/dx dT/dx = temperature gradient x T dT/dx Mechanical Engineering Department FAMU/FSU College of Engineering

Errors Time Flow rate Steady State Heat Losses Not perfectly insulated Mechanical Engineering Department FAMU/FSU College of Engineering