Chapter 15 Heat Transfer

Second Law of Thermodynamics Heat flows naturally from hot to cold objects. Heat will not flow spontaneously from cold object to hot object. Heat flows naturally from hot to cold objects. Heat will not flow spontaneously from cold object to hot object.

Methods of Heat Transfer Need to know the rate at which energy is transferred Need to know the rate at which energy is transferred Need to know the mechanisms responsible for the transfer Need to know the mechanisms responsible for the transfer Methods include Methods include ConductionConduction ConvectionConvection RadiationRadiation

Conduction The transfer can be viewed on an atomic scale The transfer can be viewed on an atomic scale It is an exchange of energy between microscopic particles by collisionsIt is an exchange of energy between microscopic particles by collisions Less energetic particles gain energy during collisions with more energetic particlesLess energetic particles gain energy during collisions with more energetic particles Rate of conduction depends upon the characteristics of the substance Rate of conduction depends upon the characteristics of the substance

Conduction example The molecules vibrate about their equilibrium positions The molecules vibrate about their equilibrium positions Particles near the stove coil vibrate with larger amplitudes Particles near the stove coil vibrate with larger amplitudes These collide with adjacent molecules and transfer some energy These collide with adjacent molecules and transfer some energy Eventually, the energy travels entirely through the pan and its handle Eventually, the energy travels entirely through the pan and its handle

Conduction, cont. In general, metals are good conductors In general, metals are good conductors They contain large numbers of electrons that are relatively free to move through the metalThey contain large numbers of electrons that are relatively free to move through the metal They can transport energy from one region to anotherThey can transport energy from one region to another Conduction can occur only if there is a difference in temperature between two parts of the conducting medium Conduction can occur only if there is a difference in temperature between two parts of the conducting medium

Conduction, equation The slab allows energy to transfer from the region of higher temperature to the region of lower temperature The slab allows energy to transfer from the region of higher temperature to the region of lower temperature Rate of heat transfer (L=x) Rate of heat transfer (L=x)

Conduction, equation explanation A is the cross-sectional area A is the cross-sectional area L = Δx is the thickness of the slab or the length of a rod L = Δx is the thickness of the slab or the length of a rod Q is in Joules and t is in seconds Q is in Joules and t is in seconds k is the thermal conductivity of the material k is the thermal conductivity of the material Good conductors have high k values and good insulators have low k valuesGood conductors have high k values and good insulators have low k values Good: copper k=385 W/m·°C Intermediate: concrete k=0.8 W/m ·°C Insulator: air k=0.024 W/m ·°C

Example 3mX15m concrete wall is 30 cm thick. Outside surface –10 C, inside 20 C. What rate does heat transfer through it? ( Outside surface –10 C, inside 20 C. What rate does heat transfer through it? ( k=40x10 -4 cal/cm·s·°C for concrete)

Example What is equivalent thickness of glass wool? ( What is equivalent thickness of glass wool? ( k=9.3x10 -5 cal/cm·s·°C for glass wool) Glass wool is a much better insulator than concrete!!

Example 30 cm concrete house wall with 2.0 cm wood paneling. 10 C outside and 18C inside.What is wood/concrete interface? ( ( k=2.4x10 -4 cal/cm·s·°C for wood)

Home Insulation Substances are rated by their R values Substances are rated by their R values R = L / k; L in inches,R = L / k; L in inches, k in BTU·in/ft 2 ·hour·°Fk in BTU·in/ft 2 ·hour·°F For multiple layers, the total R value is the sum of the R values of each layer For multiple layers, the total R value is the sum of the R values of each layer Wind increases the energy loss by conduction in a home Wind increases the energy loss by conduction in a home Glass wool: k=0.27 BTU in/(ft^2 hour °F) R=(1/k)·thickness = 3.7·thickness

Conduction and Insulation with Multiple Materials Each portion will have a specific thickness and a specific thermal conductivity Each portion will have a specific thickness and a specific thermal conductivity The rate of conduction through each portion is equal The rate of conduction through each portion is equal

Example 7 ft 2 sheet of material allows 80 BTU to flow through it in 40 minutes when temperature difference across it is 35F. What is R-value for the sheet?

Convection Energy transferred by the movement of a substance Energy transferred by the movement of a substance When the movement results from differences in density, it is called natural convectionWhen the movement results from differences in density, it is called natural convection When the movement is forced by a fan or a pump, it is called forced convectionWhen the movement is forced by a fan or a pump, it is called forced convection

Convection example Air directly above the flame is warmed and expands Air directly above the flame is warmed and expands The density of the air decreases, and it rises The density of the air decreases, and it rises The mass of air warms the hand as it moves by The mass of air warms the hand as it moves by

Convection applications Boiling water Boiling water Radiators Radiators Upwelling Upwelling Cooling automobile engines Cooling automobile engines Algal blooms in ponds and lakes Algal blooms in ponds and lakes

Convection Current Example The radiator warms the air in the lower region of the room The radiator warms the air in the lower region of the room The warm air is less dense, so it rises to the ceiling The warm air is less dense, so it rises to the ceiling The denser, cooler air sinks The denser, cooler air sinks A continuous air current pattern is set up as shown A continuous air current pattern is set up as shown

Heat Transfer by Convection T: temperature difference A: area of contact h: convection surface coefficient

Example Heat transfer from glass to outside through convection. Assume window area to be 1 m 2, glass temperature 5 °C and outside temperature –15°C. For air in contact with solid surface h= W/m 2 ·°C. Amount of heat lost in a day?

Radiation Radiation does not require physical contact Radiation does not require physical contact All objects radiate energy continuously in the form of electromagnetic waves due to thermal vibrations of the molecules All objects radiate energy continuously in the form of electromagnetic waves due to thermal vibrations of the molecules Rate of radiation is given by Stefan’s Boltzmann Law Rate of radiation is given by Stefan’s Boltzmann Law

Radiation example The electromagnetic waves carry the energy from the fire to the hands The electromagnetic waves carry the energy from the fire to the hands No physical contact is necessary No physical contact is necessary Cannot be accounted for by conduction or convection Cannot be accounted for by conduction or convection

Radiation equation The power is the rate of energy transfer, in WattsThe power is the rate of energy transfer, in Watts σ = x W/m 2. K 4σ = x W/m 2. K 4 A is the surface area of the objectA is the surface area of the object e is a constant called the emissivitye is a constant called the emissivity e varies from 0 to 1 e varies from 0 to 1 T is the temperature in KelvinsT is the temperature in Kelvins

Example A square steel plate 10 cm on a side at 800 C. Find the rate of heat radiated. In one hour?

Example Temperature of a hot plate is doubled from 100 C to 200 C. How is the rate of heat radiated changed?