Understanding Wet-Bulb Temperature thermal lecture 5

Wet-Bulb Temperature

• When air flows by a wet surface, moisture is evaporated if the relative humidity is less than 100%
• As air gains water vapor, its temperature decreases, as the air provides the heat for liquid water evaporation
• Evaporation and cooling continues until the relative humidity hits 100%
• The wet-bulb temperature is then reached

Wet-Bulb Temperature Calculation

• The wet-bulb temperature can be measured using an IR camera
• Latent heat needed is 2453 kJ kg-1 multiplied by 0.004 kg totaling is 9.81 kJ to evaporate 4 grams of moisture into 1 kg of dry air, assuming the dry air is at 20°C
• Temperature adjusts by -9.81°C as moisture increases to 4 g/kg; specific air heat is 1.0 kJ kg-1 K-1

Practical Implications of Wet-Bulb Temperature

• Air passing over a wet exterior cools it through evaporation
• The wet-bulb temperature is the minimum temperature that a wet sleeve-covered thermometer bulb can reach when air passes over
• High relative humidity results in close wet and dry bulb temperatures, whereas low relative humidity results in a larger difference

Example #20-4

• At a moisture content of 13 g/kg-dry-air, you can find the dew point temperature on a psychrometric chart
• If air at 30 °C with 60% relative humidity cools to 10 °C at 100% relative humidity, the condensed moisture can be determined for every kg of dry air from a psychrometric chart
• You cannot get air in a state above the 100% relative humidity line

Answer #20-4

• The dew-point temperature can be found by following the 13 g/kg line until it meets the 100% relative humidity point
• Air moisture content is 16 g/kg at 30°C dry-bulb and 60% relative humidity, that becomes 7.5 g/kg at 10°C, 100%
• 8.5g of moisture is condensed for every kg of dry air
• Air must be very clean for this to occur, otherwise, excess moisture becomes fog

Heat Transfer Processes

• Three processes involved; conduction, convection and radiation
• Conduction occurs in solids, liquids, and gases with molecules exchanging thermal energy without positional changes, and is slow
• Convection takes place liquids, and gases with molecules carrying thermal energy while changing position, and is more rapid
• Radiation requires no medium, and is electromagnetic radiation

Energy Conservation for an Isolated System

• In an insolated system, the total energy is conserved

Thermal Conductivity

• Heat transfers when moving electrons and molecules exchange energy, mostly through collisions
• Materials differ in heat transfer ability
• Excellent electrical conductors, like metals which have loose outer electrons, are good heat conductors
• Good electrical insulators lack loose electrons and are good thermal insulators like wood, glass, gases, and plastics

Heat Conduction Equation

• The heat transfer rate, is defined by AQ/At = kAΔT/d = hcondAΔT
• "k" represents the thermal conductivity of the material
• "ΔT" is the temperature difference across the surfaces
• "hcond" stands for the conduction heat transfer coefficient
• Measured in Watts per meter per Kelvin (W m-1 K-1)

Thermal Conductivity Values

• Thermal conductivity varies by material:
• Silver: 424 W m-1 K-1
• Copper: 393 W m-1 K-1
• Aluminum: 221 W m-1 K-1
• Solid ice (0° C): 2.2 W m-1 K-1
• Brick: 0.7 W m-1 K-1
• Fresh snow (0°C): 0.6 W m-1 K-1
• Body tissue (muscle): 0.4 W m-1 K-1
• Body tissue (fat): 0.2 W m-1 K-1
• Mineral fiber batt (10kg/m3): 0.037 W m-1 K-1
• Extruded polyurethane: 0.029 W m-1 K-1
• Still air: 0.026 W m-1 K-1

Example #21-1 Considerations

• Two sleeping bags, 3 cm thick with conductivity of 0.03 W m-1 K-1 and exposed surface of 1.5m^2
• Interior temperature: -5°C and skin temperature: 35°C
• To determine if one or both bags should be used for comfort the metabolic rate calculation will be needed

Information for #21-1

• The metabolic heat generation rate for humans ranges
• Sleeping: 60-80 W
• Seated quietly: 90-120 W
• Standing relaxed: 105-125 W
• Walking 3 km/h: 170-210 W
• Walking 6 km/h: 330-400 W
• Tennis, cycling: 400-700 W
• Strenuous exercise: Exceeds 1000 W

Heat Transfer by Convection

• Transfer is a conduction-like process where at least one media is a moving fluid
• Continuous replacement of fluid at the interface maintains the transfer

Convection Calculation

• Without fluid motion, the drop in temperature lowers heat transfer
• Heat transfer rate relies on fluid speed and other variables
• Equation for Fluid passing a surface: AQ/At = hconvAΔT

Radiation Heat Transfer

• Any object will emit and absorb electromagnetic energy
• Heat transfer does not require contact or mediums
• The Stefan-Boltzmann equation determines the rate of heat transfer

Emissivity Explained

• Dull black surfaces: 0.9-1.0 emissivity
• Shiny metallic surfaces: <0.1 emissivity
• Radiation is emitted by objects at body temperature in the infrared spectrum
• Most surfaces have emissivity of about 0.90 to 1.00

First Law of Thermodynamics

• The First Law of Thermodynamics describes heat conservation
• In a system undergoing a process, heat is received and work is performed, which can be expressed as ∆U = Q – W
• The internal energy of the system changes, which is represented as 'U
• Input heat is "Q" and system work is "W"

First Law for a Physical System

• The First Law of Thermodynamics is 'U=Q-W for a physical system, where Q marks the system heat transfer, W marks job done by the system

The First Law for a human body

• The energy input from food metabolism ("E") must be accounted to describe the human body system
• So the relationship is 'U=Q-W+E.

Thermodynamics: Food Energy and Energy Balance

• Food energy, ofter calorific, is the heat released upon food oxidization and is adjusted for digestion
• 1000 calories = 1 Calorie = 4.19 kJ
• Main food sources are lipid (37 kJ/g), protein and carbohydrate (17 kJ/g), and alcohol (29 kJ/g)

Recommended Daily Energy Intake

• Young adult males: 10 MJ
• Young adult females: 8 MJ

Metabolic Work Efficiency

• The equation for metabolic efficiency of the human body can be expressed as η = W / (E – ΔU)
• Energy must come from an ingested source or bodily fat
• If the body stored energy doesn't change, AU = 0, and η = W/E

Work Efficiency: Continued

• For efficiency values less than 1: Q = W ×(1-1/η)
• High work output and low energy usage yields an efficiency near, 1
• The efficiency value of the body is low, ranging from 2 to 10%
• Cycling and climbing will yield values around 20 to 25%

The Heat Loss Rate

• Since Q is the metabolic rate, the heat loss of the human body, is relatively the same rate and is near metabolic rate

Example #22-1, Climber

• A 65 kg climber ascends/descends 1800 m in 10 hours
• Works at 18% efficiency at similar going and descending rates
• Diet: 170 g carbohydrate, 90 g fat, 60 g protein daily

Continued example #22-1

• Key aspects to calculate are the total work done over the 10 hours, what the total metabolic energy used is and how much food will be required to achieve energy balance

#22-1 Answer

• To determine the total work done, calculate the potential energy gained during the ascent: mgh = 65 × 9.8 × 1800 = 1.147 MJ, then multiply by 2 for the descent
• Work rate is is 2.294 × 106 J / (10 × 3600 s) equalling 63.72 W
• Find E – ΔU using the efficiency: = 2.294 / 0.18 to get 12.74 MJ

#22-1 cont

• With the previous data, Q can be calculated, Q = W – (E – ∆U) equalling (negative) -10.45 MJ, meaning heat rejection
• The average heat transfer rate found by, ΔQ/Δt = -10.45 x 10^6 J / (10 x 3600) = -290.3W
• 7.24 MJ total food energy value is less than 12.74 MJ her energy loss

#22-1 continued further

• (E=7.24, So her intake less her outgoings
• Her body will have a shortfall near negative 5.50 MJ, meaning she needs a big meal