HEAT TRANSFER COEFFICIENTS FOR FORCED CONVECTION IN TUBES

HEAT TRANSFER COEFFICIENTS FOR FORCED CONVECTION IN TUBES

For a tube of radius R and length L , the total heat flow into the fluid at the pipe wall is :-

                           ………..Eq 1

This statement is being valid for laminar or turbulent flow. The +ve sign appears here because the heat is added to the system in the-r direction.

Solving equation 1  for h1 ,we get

              ……Eq 2

Next we introduce the dimensionless quantities as, 

We know,

Multiplying Equation 2 by D/K ,we get,

……Eq 3

Boundary Conditions :

 

The dimensionless time-smoothened temperature will have the following dependence:-

                                                  ……Eq 9

Substitution of this relation in to equation 3 gives :-

In most practical situations, the viscous dissipation effects are small so that the Brinkman group can be neglected. 

Hence Dimensional analysis has told us that for forced convection in tubes with constant wall temperature,The Heat Trasfer Coefficient  h1  may be correlated in terms of dimensionless group Nu1 .