HEAT TRANSFER NOTES

Shell and Tube heat exchanger

[su_accordion] [su_spoiler title=”Tube side heat transfer coefficient”  open=”no” style=”fancy (Fancy)” icon=”caret (Caret)” anchor=””][/su_spoiler] [su_accordion] [su_spoiler title=”Ligament efficiency”  open=”no” style=”fancy (Fancy)” icon=”caret (Caret)” anchor=””]

When a shell or drum is drilled for tubes in a line parallel to the axis of the shell or drum, the efficiency of ligament between tube holes shall be given as ligament efficiency [/su_spoiler] [/su_accordion]

  • Number of baffles

Number of baffles (NB) on shell side of heat exchanger

shell and tube heat exchanger number of baffles on shell side

  • Shell side cross flow area

Cross flow area of shell side in a shell and tube heat exchanger

shell and tube heat exchanger shell side cross flow area

  • Effectiveness of heat exchanger

h and c denote hot and cold fluid respectively; 1 and 2 denote inlet and outlet fluid respectively

shell and tube heat exchanger effectiveness of heat exchanger

  • Hydraulic diamter

Hydraulic diameter for square pitch shell and tube heat exchanger

shell and tube heat exchanger hydraulic diameter for square pitch

Hydraulic diameter for triangular pitch shell and tube heat exchanger

shell and tube heat exchanger hydraulic diameter for triangular pitch

  • Nusselt number

Nusselt number is defined as

nusselt number

Nusselt number is used in heat transfer, mainly in forced convection.

  • Fluid flowing in a pipe

For fluid flowing in a pipe, Nusselt number is defined as

nusselt number for fluid flow in a pipe

  • Laminar flow over flat plate

Nusselt number (local and average) for heat transfer due to laminar flow over flat plate is given by

nusselt number for laminar flow over flat plate

  • Conduction and convection across wall

Nusselt number for heat transfer across wall of length L involving conduction and convection

nusselt number for heat transfer across wall

  • Natural convection

Nusselt number in case of natural convection is a function of grasshoff number and prandtl number

nusselt number in case of natural convection

  • Biot number

Biot number is defined as

biot number

Biot number gives a simple index of the ratio of the heat transfer resistances inside of and at the surface of a body. Bi = 0 means that temperature within the solid is uniform

Consider a heating rod immersed in water. If biot number is << 1, it means resistance due to conductive heat transfer within the rod is very small compared to the resistance to heat transfer from rod surface to the liquid.

biot number

  • Unsteady state heat transfer model
  • Lump parameter model

Lump parameter model for unsteady state heat conduction / Transient heat conditions

lump parameter model unsteady state heat transfer

  • Time taken for temperature to reach Tf

To calculate time taken for temperature to reach Tf

unsteady state heat transfer time taken to reach temperature T

  • Semi-infinite slab

For transient heat conduction equation for semi-infinite slab, heat flux is inversely proportional to square root of time

transient heat conduction equation for semi-infinite slab

  • Transient 3-D heat conduction

Transient 3-D heat conduction equation

Transient 3-D heat conduction

  • Heat transfer coefficient
  • Steam condensing on vertical plate

Average heat transfer coefficient for steam condensing on vertical plate or falling film on vertical plate

heat transfer coefficient for steam condensing on vertical plate

  • Cylindrical tube

Overall heat transfer coefficient based on outer diameter of cylindrical tube

heat transfer coefficient based on outer diameter of cylindrical tube

  • Resistance to heat transfer

Resistance to heat transfer is given as

resistance to heat transfer

For heat transfer across series of slabs, heat transfer equation correlating total resistance is

resistance to heat transfer for series of slabs

Heat Transfer through composite wall A and wall B in series with the end temperatures TA and TB

resistance for heat transfer through composite wall

Consider two composite slab joined parallel to each other such that one end of both the slabs is at temperature T1 and other end of the slabs are at temperature T2. Let R1 and R2 be the individual resistance to heat transfer offered by slab 1 and 2 respectively. Then total resistance (R) to heat transfer when both the slabs are joined in parallel

resistance for heat transfer through composite wall

  • Critical radius of insulation

critical radius of insulation

Optimum k of insulating material for cylinder

optimum conductivity of insulating material for cylinder

  • Wein’s displacement law

At any given temperature, the maximum monochromatic radiating power is attained at a definite wavelength, denoted by λmax. Wein’s displacement law states that λmax is inversely proportional to the absolute temperature T

wein's displacement law

  • Film wise condensation

Reynolds number for film wise condensation on a vertical plate

Reynolds number for film wise condensation

  • Forced Convection
  • Dittus-Boelter equation

It is used for turbulent flow inside tube, i.e. 10,000 < Re < 120,000, fluid property to be evaluated at bulk temperature.

dittus boelter equation

  • Sieder-Tate equation

It is used when highly viscous oil is used

sieder tate equation

  • Archimedes number

When analyzing mixed convection, a parameter called the Archimedes number (Ar) parameterizes relative strength of free and forced convection. Archimedes number is defined as ratio of Grasshoff number to square of reynolds number.

archimedes number

If Ar is greater than one then natural convection dominates, if Ar is less than one forced convection dominates and if Ar = 1 then both free and forced convection.

  • Lewis number and Psychromatic ratio

Lewis number is defined as ratio of Schmidt number to Prandtl number.

lewis number

Schmidt number is used mainly for diffusion in convective mass transfer calculations.

  • Natural Convection

Nusselt number for heat transfer by natural convection

nusselt number for heat transfer in natural convection

In natural convection heat transfer coefficient is directly proportional to volumetric expansion coefficient

  • Heat transfer balance

Heat balance during heat transfer

heat balance during heat transfer
heat balance during heat transfer

  • Reynolds Analogy

Reynolds analogy is best applicable for gases and turbulent transport, i.e., at Pr =1.

reynolds analogy

  • Chilton-Colburn Analogy

Chilton – colburn analogy used for flow of air over flat plate.

chilton colburn analogy

  • Double pipe heat exchanger

Heat Transfer equation for double pipe heat exchanger

heat equation for double pipe heat exchanger

  • Heat Transfer by Radiation
  • Radiation heat transfer

Equation for heat transfer by radiation

heat transfer by radiation

Heat transfer due to radiation , i.e., difference between rate of heat radiated and absorbed by the surface of insulation

difference between heat radiated and heat absorbed

  • Radiation View Factor(F)

Equations used to calculate view factor for objects exchanging heat via radiation

radiation view factor

View factor matrix is defined as

radiation view factor matrix

  • Emissivity

Emissivity is defined as ratio of heat emitted by a body to heat emitted by a black body

emissivity

Sum of emissivity, transmissivity and reflectivity is equal to one

sum of emissivity, reflectivity and transmissivity

  • Heat Conduction through hollow cylinder

heat conduction through hollow cylinder

  • Fourier law

Fourier second law for transient heat conduction

  • Prandtl number

Prandtl number is defined as

prandlt number

It used in forced and free convective heat transfer calculations.

Prandtl number for liquids ~ 2 * 104Prandtl number for water ~ 7, Prandtl number for gases ~ 0.5 – 1.0

Ratio of hydrodynamic boundary layer thickness to thermal boundary layer thickness is equal to prandtl number raised to power one-third

prandlt number

  • Evaporator economy and capacity

Evaporator capacity = amount of water evaporated

evaporator capacity and economy

  • Energy conversion factors

BTU per cubic feet to kCal per cubic meter to Joule per cubic meter

energy conversion factor

BTU per pound to Joule per kilogram to kCal per kilogram

energy conversion factor

  • Thermal Conductivity

Thermal conductivity is directly proportional to square root of absolute temperature

relationship between thermal conductivity and temperature

  • Bimetallic Strip

Final radius of bimetallic strip when exposed to final temperature T1 for time t

bimetallic strip

  • Peclet number

Peclet number in case of heat transfer is defined as ratio of advective transport rate to diffusive transport rate

peclet number

  • Grasshoff number

Grasshoff number is defined in case of heat transfer via natural convection

grasshoff number

The effect of β is through buoyancy in a gravitational field. The coefficient of thermal expansion β is a property of the fluid, defined as the fractional increase in the volume at constant pressure of the fluid per degree of the temperature change

grasshoff number

In case of ideal gas, coefficient of thermal expansion β is inversely proportional to its absolute temperature

grasshoff number

  • Graetz number

graetz number

Useful in characteristics laminar flow in conduit for determining thermally developing flow entrance length in duct, i.e. transient heat conduction in laminar flow in pipe. Graetz number less than or equal to 100 implies flow would be considered fully developed flow. Graetz number less than 20 implies radial temperature profile fully developed. Time taken by heat to diffuse radially into fluid by conduction is also called relaxation time.

  • Rayleigh number

defined as product of grasshoff number and prandtl number. It is used in case of heat transfer in creeping flow ( slow flow)

rayleigh number

  • Volumetric heat generation

In case of internal heat generation (q*), volumetric heat genration is defined as ratio of total heat generated internally to total volume of substance

volumetric heat generation

  • Wave equation and Heat equation

wave equation and heat equation

  • Equivalent diameter for heat transfer

equivalent diamter for heat transfer

  • Heat Transfer
  • Heat exchangers
      1. At bottom of a countercurrent cooling tower where the water temperature is below the dry bulb temperature of air, the sensible heat flows from air to air/water interface and latent heat flows from water to air/water interface.
      2. If baffle spacing in a shell and tube heat exchanger increases, then shell side Reynolds number decreases.
      3. A process stream is heated in shell and tube heat exchanger with steam condensate at 95oC. The best arrangement is counter flow with process stream on tube side.
      4. Steam is to be condensed in a shell and tube heat exchanger with cooling water. The best arrangement is vertical heat exchanger with steam on the shell side. Vertical heat exchanger with steam on shell side favors drop wise condensation which is associated with higher heat transfer coefficient compared to film wise condensation.
      5. Air is to be heated by condensing steam. The best arrangement is finned tube heat exchanger with air outside and steam inside.
      6. Baffles are used in exchangers to promote cross flow and turbulence in the shell side fluid.
      7. Triangular pitch permits using more number of tubes for a given shell diameter.
      8. Tube side clearance should not be less than one-fourth of tube diameter. The pressure drop on tube side is less than 10 psi.
      9. Baffle spacing should not be greater than diameter of shell or less than one-fifth of shell diameter.
  • Heat transfer coefficient
      1. Heating oils have lower heat transfer coefficient than boiling water.
      2. An insulation is chosen in such a way that its critical insulation thickness is less than pipe radius. In this way any insulation put on pipe will decrease in heat loss.
      3. Object having highest surface area per unit volume undergoes fastest transient heat change. t ∝ 1/(A/V).
      4. Unit of resistance to heat transfer W-1m2K.
      5. 11. A fluid is flowing inside the inner tube of shell and tube heat exchanger. For fixed mass flow rate heat transfer coefficient for turbulent condition ∝ d-1.8 and for fixed velocity heat transfer coefficient for turbulent condition ∝ d-0.2.
  • Evaporation
      1. The advantage of backward feed multi effect evaporator over forward feed units is that “most concentrated liquor is at highest temperature”.
      2. The capacity of multiple effect evaporator is more than a single effect evaporator both operating with significant boiling point rise at the same terminal temperature and surface area in each effect equal to surface area of single effect evaporator.
  • Heat of reaction
      1. Amount of heat generated due to reaction is equal to product of moles reacted per unit time and heat of reaction.
  • Boiling and condensation
    1. In a film type condensation of liquid along a vertical tube, the thickness of the condensate layer increases towards bottom. This implies that the local heat transfer coefficient decreases from top to bottom.