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 (N_{B}) on shell side of heat exchanger
 Shell side cross flow area
Cross flow area of shell side in a shell and tube heat exchanger
 Effectiveness of heat exchanger
h and c denote hot and cold fluid respectively; 1 and 2 denote inlet and outlet fluid respectively
 Hydraulic diamter
Hydraulic diameter for square pitch shell and tube heat exchanger
Hydraulic diameter for triangular pitch shell and tube heat exchanger
 Nusselt number
Nusselt number is defined as
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
 Laminar flow over flat plate
Nusselt number (local and average) for heat transfer due to laminar flow over flat plate is given by
 Conduction and convection across wall
Nusselt number for heat transfer across wall of length L involving conduction and convection
 Natural convection
Nusselt number in case of natural convection is a function of grasshoff number and prandtl number
 Biot number
Biot number is defined as
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.
 Unsteady state heat transfer model
 Lump parameter model
Lump parameter model for unsteady state heat conduction / Transient heat conditions
 Time taken for temperature to reach T_{f}
To calculate time taken for temperature to reach T_{f}
 Semiinfinite slab
For transient heat conduction equation for semiinfinite slab, heat flux is inversely proportional to square root of time
 Transient 3D heat conduction
Transient 3D heat conduction equation
 Heat transfer coefficient
 Steam condensing on vertical plate
Average heat transfer coefficient for steam condensing on vertical plate or falling film on vertical plate
 Cylindrical tube
Overall heat transfer coefficient based on outer diameter of cylindrical tube
 Resistance to heat transfer
Resistance to heat transfer is given as
For heat transfer across series of slabs, heat transfer equation correlating total resistance is
Heat Transfer through composite wall A and wall B in series with the end temperatures T_{A} and T_{B}
Consider two composite slab joined parallel to each other such that one end of both the slabs is at temperature T_{1} and other end of the slabs are at temperature T_{2}. Let R_{1} and R_{2} 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
 Critical radius of insulation
Optimum k 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 λ_{max}. Wein’s displacement law states that λ_{max} is inversely proportional to the absolute temperature T
 Film wise condensation
Reynolds number for film wise condensation on a vertical plate
 Forced Convection
 DittusBoelter equation
It is used for turbulent flow inside tube, i.e. 10,000 < Re < 120,000, fluid property to be evaluated at bulk temperature.
 SiederTate equation
It is used when highly viscous oil is used
 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.
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.
Schmidt number is used mainly for diffusion in convective mass transfer calculations.
 Natural Convection
Nusselt number for heat transfer by natural convection
In natural convection heat transfer coefficient is directly proportional to volumetric expansion coefficient
 Heat transfer balance
Heat balance during heat transfer
 Reynolds Analogy
Reynolds analogy is best applicable for gases and turbulent transport, i.e., at Pr =1.
 ChiltonColburn Analogy
Chilton – colburn analogy used for flow of air over flat plate.
 Double pipe heat exchanger
Heat Transfer equation for double pipe heat exchanger
 Heat Transfer by Radiation
 Radiation heat transfer
Equation for heat transfer by radiation
Heat transfer due to radiation , i.e., difference between rate of heat radiated and absorbed by the surface of insulation
 Radiation View Factor(F)
Equations used to calculate view factor for objects exchanging heat via radiation
View factor matrix is defined as
 Emissivity
Emissivity is defined as ratio of heat emitted by a body to heat emitted by a black body
Sum of emissivity, transmissivity and reflectivity is equal to one
 Heat Conduction through hollow cylinder
 Fourier law
Fourier second law for transient heat conduction
 Prandtl number
Prandtl number is defined as
It used in forced and free convective heat transfer calculations.
Prandtl number for liquids ~ 2 * 10^{4}Prandtl 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 onethird
 Evaporator economy and capacity
Evaporator capacity = amount of water evaporated
 Energy conversion factors
BTU per cubic feet to kCal per cubic meter to Joule per cubic meter
BTU per pound to Joule per kilogram to kCal per kilogram
 Thermal Conductivity
Thermal conductivity is directly proportional to square root of absolute temperature
 Bimetallic Strip
Final radius of bimetallic strip when exposed to final temperature T_{1} for time t
 Peclet number
Peclet number in case of heat transfer is defined as ratio of advective transport rate to diffusive transport rate
 Grasshoff number
Grasshoff number is defined in case of heat transfer via natural convection
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
In case of ideal gas, coefficient of thermal expansion β is inversely proportional to its absolute temperature
 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)
 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
 Wave equation and Heat equation
 Equivalent diameter for heat transfer
 Heat Transfer
 Heat exchangers


 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.
 If baffle spacing in a shell and tube heat exchanger increases, then shell side Reynolds number decreases.
 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.
 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.
 Air is to be heated by condensing steam. The best arrangement is finned tube heat exchanger with air outside and steam inside.
 Baffles are used in exchangers to promote cross flow and turbulence in the shell side fluid.
 Triangular pitch permits using more number of tubes for a given shell diameter.
 Tube side clearance should not be less than onefourth of tube diameter. The pressure drop on tube side is less than 10 psi.
 Baffle spacing should not be greater than diameter of shell or less than onefifth of shell diameter.

 Heat transfer coefficient


 Heating oils have lower heat transfer coefficient than boiling water.
 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.
 Object having highest surface area per unit volume undergoes fastest transient heat change. t ∝ 1/(A/V).
 Unit of resistance to heat transfer W^{1}m^{2}K.
 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


 The advantage of backward feed multi effect evaporator over forward feed units is that “most concentrated liquor is at highest temperature”.
 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


 Amount of heat generated due to reaction is equal to product of moles reacted per unit time and heat of reaction.

 Boiling and condensation

 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.