Short notes on Convection

While the heat flow mechanism in solids is by conduction, the mechanism of transfer within the fluid is by convection. Here the transfer occurs through the movement of the macroparticle of the fluid along the temperature gradient. Thus the concept of convection is linked to the movement of the medium itself. The fluid motion may be due to –

  • The density difference as produced by temperature gradient. This type of heat transfer is called ‘Natural convection’.
  • An external agency such as a fluid motive force for the generation of circulating currents. This type of heat transfer is called ‘Forced convection’. Transfer of heat by convection is invariably accompanied by conduction. This is due to the fact in case of a liquid or a gas in motion, individual particles which are at different temperatures, come in contact with each other resulting in conductive heat transfer between them. In engineering practice, the transfer of heat by convection between a stream of liquid or gas and a solid surface is encountered. The transfer of heat between a solid surface and a fluid in contact is importance for industrial heat exchangers. It is a case of simultaneous transfer of heat by conduction and convection. While the mode transfer from solid surface to a static fluid will be essentially by conduction, the transfer to a fluid in motion will be by convection.

Film Coefficient

Whenever a fluid flows past a solid surface, a thin film tends to adhere to the surface. In case of exchange of heat across tubes in industrial exchangers, two such films one on each side of the surface of the tube will be formed. For transfer of heat, these two films will offer resistance to convective transfer while the tube wall will offer resistance to conductive transfer. The reciprocal of convective heat transfer resistance is called the film coefficient. The film offering higher resistance to convective transfer is called the ‘controlling film’. The value of the overall heat transfer coefficient has a value nearer to the heat transfer coefficient of the controlling film.

Calculation of film coefficient in natural (free) convection

In terms of dimensionless groups, the film coefficient can be expressed as 

Where Gr = Grashof number = 

          Pr = Prandtl number = 

Here, L = characteristic length of the heat transfer surface (Length for flat surface and diameter for tubular surface), m

         β = Coefficient of volume expansion

         ν = Kinematic viscosity of fluid 

         μ = Viscosity of fluid

The film coefficient for a few cases can be calculated with the help of the following empirical equations.

  • Free convection from horizontal cylinders:

Churchill and Chu equation used for the present case over a wide range of Rayleigh number (Ra) is –

This is used for the range 

where, Ra = Gr.Pr

  • Free convection from spheres:

Yuge’s equation is used for calculating heat transfer coefficient in terms of Nusselt number, which is given as –

The above equation is applicable over the range 

Calculating of film coefficient in forced convection (without pahse change):

In terms of dimensionless groups, the film coefficient can be expressed as – 

The film coefficients for specific cases can be calculated with the help of empirical relations. A few specific cases are given below.

  • Flow inside tubes:

Laminar flow:

Sieder – Tate equation given as under is used – 

Where, Re = Reynold's number = 

           D = inside diameter of tube

           L = length of tube

           μ = fluid viscosity at bulk temperature

           μw = fluid viscosity at wall temperature

Turbulent Flow:

1. Dittus – Boeltier equation is used, which is given as –  or 

The value of 0.4 is used in case of heating and 0.3 for cooling. A more generalized form of the above equation used for both cooling and heating is –

 

2. Colburn’s equation is also used for the calculation of heat transfer coefficient expressed in terms of dimensionless group as under –

Where St = Stanton number =  = 

G = mass velocity of fluid in 

3. Flow in the annulus of a double pipe of a pipe heat exchanger. The above equations used for flow inside tubes can be used with the following modifications.

Re in the equations will be replaced by Rea, where  where  being the equivalent diameter for the annulus.

 

4. Flow in the shell side of a shell – and – tube exchanger: the equation for shell side film coefficient is given by Colburn’s equation, where shell side Reynolds number is to be used in the equation.

Where, De is the shell side equivalent diameter and Gs is the shell side fluid mass velocity to be calculated from the cross flow area.

5. Cross flow across a tube bank:

 for in-line arrangement

 for staggered arrangement

The above two equtaions are applicable over the range .

For liquids, a factor  is to be multiplied to the left hand side of the equations, where Pr and Prware evaluated from properties corresponding to free stream and wall temperature respectively. Also in all the above cases, the fluid flows at right angle to the tube bank.