When analyzing mixed convection, a parameter called the Archimedes number (Ar) parameterizes relative strength of free and forced convection. Archimedes number is defined as a ratio of Grasshoff number to a 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 is defined as a ratio of Schmidt number to Prandtl number.
Schmidt number is used mainly for diffusion in convective mass transfer calculations.
Nusselt number for heat transfer by natural convection
In natural convection heat transfer coefficient is directly proportional to volumetric expansion coefficient
14.Heat transfer balance
Heat balance during heat transfer
Reynolds analogy is best applicator gases and turbulent transport, i.e., at Pr =1.
Chilton – Colburn analogy used for flow of air over a flat plate.
17.The double pipe heat exchanger
Heat Transfer equation for double pipe heat exchanger
18.Heat Transfer by Radiation
1. Radiation heat transfer
An equation for heat transfer by radiation
Heat transfer due to radiation, i.e., a difference between a rate of heat radiated and absorbed by the surface of an insulation
2.Radiation View Factor(F)
Equations used to calculate view factor for objects exchanging heat via radiation
View factor matrix is defined as
Emissivity is defined as a ratio of heat emitted by a body to heat emitted by a black body
Sum of emissivity, transmissivity and reflectivity is equal to one
19.Heat Conduction through a hollow cylinder
Fourier second law for transient heat conduction
Prandtl number is defined as
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 A ratio of hydrodynamic boundary layer thickness to the thermal boundary layer thickness is equal to Prandtl number raised to power one-third Prandtl number
22.Evaporator economy and capacity
Evaporator capacity = amount of water evaporated
23.Energy conversion factors
BTU per pound to Joule per kilogram to kCal per kilogram
Thermal conductivity is directly proportional to square root of absolute temperature
K α √T
Final radius of bimetallic strip when exposed to final temperature T1 for time t
Peclet number in case of heat transfer is defined as a ratio of advective transport rate to diffusive transport rate
Grasshoff number is defined in case of heat transfer via natural
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
28. 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 called relaxation time.
defined as product of grasshoff number and prandtl number. It is used in case of heat transfer in creeping flow ( slow flow)
30. 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
31.Wave equation and Heat equation
32. Equivalent diameter for heat transfer
- 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
- 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 one-fourth 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 one-fifth of shell diameter.
2.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^-1m²K.
- 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.
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
4.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.
5.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.