# Thermodynamics & Heat Transfer

This page provides a limited notes on thermodyamics and heat transfer that may be useful to mechanical engineers.

## Definition

Thermodynamics ..From the Greek thermos meaning heat and dynamis meaning power.

Thermodynamics covers the relationship between heat, work, temperature, and energy, including the general behaviour of physical systems in a condition of equilibrium or close to it.    It is a fundamental part of all the physical sciences.

Thermodynamics is an experimental science based on a small number of principles that are derived from experience.   Classical Thermodynamics is concerned only with macroscopic or large-scale properties of matter and does not include the study of small-scale or microscopic structure of matter.  Statistical Thermodynamics ( not covered on this website) includes the study of the thermal relationships of atomic sized particles

## Notation

 Identifier Description Units (typical) c p Specific Heat Capacity at Constant pressure kJ/(kg K) c v Specific Heat Capacity at Constant Volume kJ/(kg K) p Absolute Pressure N / m 2 T Absolute Temperature K v volume per unit mass m 3 W Work Output per unit mass kJ/kg M Molecular Weight - R o Universal Gas Constant = 8,31 kJ /(kg mole.K) Q Heat Quantity kJ R Gas Constant = R o / M kJ /kg.K U Internal energy (thermal) kJ

## Thermodynamic Laws

### Zeroth Law of Thermodynamics

When two objects are separately in thermodynamic equilibrium with a third they are in equilibrium with each other

Objects in thermodynamic equilibrium are at the same temperature

First Law of Thermodynamics...

This law expresses the general law of conservation of energy. and states that heat and work are mutually convertible

Heat In = Work Out over complete cycle
or Sum (d Q ) = sum (d W )

The basic energy equation results from this

dQ = dU + dW

### Second Law of Thermodynamics

This law in its simplest states that heat can only flow from hot to cold and not vice versa.  In terms of thermodynamic engine cycles the law states that the gross heat supplied to a system in a complete cycle must exceed the work done by the system.   Therefore heat must be rejected.  The thermal efficiency of an heat engine must be less than 100%.

## Process Relations

Reversible Polytropic Process

p v n = constant

W = ( p 2 v 2 - p 1 v 1 ) / ( 1 - n ) .. (n not 0 )

For a perfect gas

W = R ( T 2 - T 1 ) / (1 -n )

Q = ( Cv + R /(1 - n) ) ( T 2 -T 1 )

T 2 / T 1 = ( p 2 / p 1 ) ( n-1 ) / n

For Adiabatic processes (Q = 0 ) n = γ = cp / cv

γ = 1.4 for Air,  H 2,  O 2, CO, NO, Hcl

γ = 1.3 for CO 2, SO 2,  H 2O, H 2S, N 2O, NH 3, CL 2,  CH 4, C 2H 2, C 2H 4

## Heat Transfer

Heat Transfer takes place by Conduction, Convection and Radiation

### Heat Transfer by Conduction

• q = Heat Flow Rate W
• t 1 & t 2 = temperature, K (heat flows down (-))
• A = Area, m 2
• k = Coefficient of thermal conductivity, W m -1K -1
• U = Overall Heat Transfer Coefficient,W m -1K -1
• h = Surface Heat Transfer Coefficient, W m -2K -1
• R = Thermal Resistance, W -1.m -1.K
 dq = kA(-dt/dx) q = (k.A /x). (t 1-t 2) U = k/x Therefore q = U.A(t 1-t 2) Thermal resistance R = 1 / U.A

The heat has to pass through the surface layers on both sides of the wall

 q = A.h s1(t s1 - t 1) = k.A(t 1 -t 2) / x = Ah s2(t 2 -t s2) U = 1 / (1/h s1 + x/k + 1/h s2 ) R = 1/A.h s1 + 1/A.h s2 + x/A.k = R s1 + R s2 + R

Table Showing Various values for k at 20 oC
 Metal k=Wm-1K-1 Aluminium 237 Antimony 18.5 Beryllium 218 Brass 110 Cadmium 92 Cobalt 69 Constantan 22 Copper 398 Gold 315 Iridium 147 Cast Iron 55 Pure Iron 80.3 Wr't Iron 59 Lead 35.2 Magnesium 156 Molybdenum 138 Monel 26 Nickel 90.5 Platinum 73 Silver 427 C.Steel 50 St.Steel 25 Tin 67 Zinc 113 Plastics Acrylic 0.2 Nylon 6 0.25; Polythene High Den 0.5 PTFE 0.25 PVC 0.19
 Misc.solids k =Wm-1K-1 Asphalt 1.26 Bitumen 0.17 Br'ze Block 0.15 Brickwork 0.6 Brick-Dense 1.6 Carbon 1.7 Conc-LD 0.2 Conc-MD 0.5 Conc-HD 1.5 Firebrick 1.09 Glass 1.05 Glass -Boro. 1.3 Ice 2.18 Limestone 1.1 Mica 0.75 Cement 1.01 Parafin Wax 0.25 Porcelain 1.05 Sand 0.06 Insulation Balsa 0.048 Straw-Comp 0.09 Cotton Wool 0.029 Polystyrene-Expanded 0.03 Felt 0.04 Glass Wool 0.04 Kapok 0.034 Magnesia 0.07 Plywood 0.13 Rock Wool 0.045 Sawdust 0.06 Slag Wool 0.042 Wood 0.13
 Liquids k= Wm-1K-1 Benzene 0.16 Carb Tet'ide 0.11 Acetone 0.16 Ether 0.14 Glycerol 0.28 Kerosene 0.15 Mercury 8 Methanol 0.21 Machine Oil 0.15 Water 0.58 Sodium 84 Gases k= Wm -1K -1 Air 0.024 Ammonia 0.022 Argon 0.016 Carbon Dio 0.015 Carbon Mon 0.023 Helium 0.142 Hydrogen 0.168 Methane 0.030 Nitrogen 0.024 Oxygen 0.024 Water Vap. 0.016

### Emissivity Values

Refer to link Emissivity Values for better table

Surface Material Emmissity Surface Material Emmissity
Aluminium-Oxidised 0.11 Tile 0.97
Aluminium-Polished 0.05 Water 0.95
Aluminium anodised 0.77 Wood-Oak 0.9
Aluminium rough 0.07 Paint 0.96
Asbestos Board 0.94 Paper 0.93
Black Body -Matt 1.00 Plastics 0.91 Av
Brass -Dull 0.22 Rubber-Nat_Hard 0.91
Brass- Polished 0.03 Rubber _Nat_Soft 0.86
Brick -Dark 0.9 Steel_Oxidised 0.79
Concrete 0.85 Steel Polished 0.07
Copper-Oxidised 0.87 St.Steel-Weathered 0.85
Copper -Polished 0.04 St.Steel-Polished 0.15
Glass 0.92 Steel Galv. Old 0.88
Plaster 0.98 Steel Galv new 0.23

### Heat Transfer by Convection

Convective heat transfer occurs between a moving fluid and a solid surface.The rate of convective heat transfer between a surface and a fluid is given by the Newtonï¿½s Law of Cooling;

It is customary to express the convection coefficient (average or local), in a non-dimensional form called the Nusselt Number.

Natural convection

Nu = C(Gr.Pr) n C and n are tabled below

Note: Convection heat transfer values are very specific to the geometry of the surface and the heat transfer conditions - These example equations are very general in nature and should not be used for serious calcs. The links below provide much safer equations..

 Surface (Gr.Pr) C n Vertical Plates/Cylinders 10 4 to 10 9 0.59 0.25 10 9 to 10 12 0.13 0.33 Horizontal Pipes 10 3 to 10 9 0.53 0.25 Horizontal Plates Heated Face up or Cooled Face Down 10 5 to 2 x 10 7 0.54 0.25 2 x10 7 to 3 x10 10 0.14 0.33 Horizontal Plates Heated Face up or Cooled Face Down 3 x10 5 to 3 x10 10 0.27 0.25

Forced Convection

Laminar flow over Plate    Nu = 0.664(Re) 1/2(Pr) 1/3

Fully Developed pipe flow     Nu = 0.0866(D/L)Re.Pr  /  (1+0.04[D / L(Re.Pr)] 2/3) + 3.66

Turbulent Flow Over Flat Plate    Nu = 0.036Pr 1/3Re 0.8

Turbulent Flow In Pipe     Nu = 0.023Pr 0.4Re 0.8

Typical Values of Heat Transfer Coefficient h = W.m -2K -1

• Free Convection Over Various Shape - Air    2 - 23
• Free Convection Over Various Shape - Water    300 - 1700
• Turbulent Convection Over Various Shape and through tubes - Air    6 - 1400
• Turbulent Convection Over Various Shape and through tubes - Water    1100 - 9000

## Heat Exchangers

Heat exchangers normally transfer energy from a hot fluid to a colder fluid.    The energy in = The energy out.

If the fluids are the same with the same specific heat.   The mass flowrate x the temp drop of the hot fluid = the mass flow rate x the temp rise of the cold fluid.

Typical Values for Overall Heat transfer U are

• Plate Heat Exchanger, liquid to liquid U range 1000 > 4000 W. m.-2K.-1
• Shell and Tube, liquid inside and outside tubes U range150 > 1200 W. m.-2K.-1.
• Spiral Heat Exchanger, liquid to liquid U range 700 > 2500 W. m.-2K.-1