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 largescale properties of matter and does not include the study of smallscale 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 otherObjects 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 )
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} ) ^{( n1 ) / 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 _{2}O, H _{2}S, N _{2}O, NH _{3}, CL _{2}, CH _{4}, C _{2}H _{2}, C _{2}H _{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 ^{1}K ^{1}
 U = Overall Heat Transfer Coefficient,W m ^{1}K ^{1}
 h = Surface Heat Transfer Coefficient, W m ^{2}K ^{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 ^{o}C



Heat Transfer by Radiation
Emissivity Values
Refer to link Emissivity Values for better table
Surface Material  Emmissity  Surface Material  Emmissity 

AluminiumOxidised  0.11  Tile  0.97 
AluminiumPolished  0.05  Water  0.95 
Aluminium anodised  0.77  WoodOak  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  RubberNat_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 
CopperOxidised  0.87  St.SteelWeathered  0.85 
Copper Polished  0.04  St.SteelPolished  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 nondimensional form called the Nusselt Number.
Natural convectionNu = 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 ^{1/3}Re ^{0.8}
Turbulent Flow In Pipe Nu = 0.023Pr ^{0.4}Re ^{0.8}
Typical Values of Heat Transfer Coefficient h = W.m ^{2}K ^{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.^{2}K.^{1}
 Shell and Tube, liquid inside and outside tubes U range150 > 1200 W. m.^{2}K.^{1}.
 Spiral Heat Exchanger, liquid to liquid U range 700 > 2500 W. m.^{2}K.^{1}
In this section
 Thermal Insulation
 Thermal Insulation Tables
 Thermodynamics
 Thermodynamics
 Thermodynamics Air compressors & motors
 Thermodynamics Boilers
 Thermodynamics Carnot Cycle
 Thermodynamics Combustion
 Thermodynamics Condensers & Cooling Towers
 Thermodynamics Entropy
 Thermodynamics First Law Non Flow examples
 Thermodynamics Fundamentals
 Thermodynamics Heat Transfer
 Thermodynamics Laws
 Thermodynamics Properties
 Thermodynamics Rankine cycle Superheated
 Thermodynamics Steam Flow
 Thermodynamics Steam Tables
 Thermodynamics Steam Tables
 Thermodynamics Steam Tables Index
 Thermodynamics Steam Tables Superheated Steam
 Thermodynamics Steam Tables Superheated Steam
 Thermodynamics Steam Tables Superheated Steam
 Thermodynamics Steam Tables Superheated Steam
 Thermodynamics Steam Turbine
 Thermodynamics Two / Four Stroke Engine Notes