How is heat transfer affected by velocity in convection?

Question

I would like to see an equation for heat transfer in terms of velocity. If the velocity of the air flow doubles and everything else stays the same does the heat transfer double?

Answer 1

It depends on the amount of turbulence, which Feynman called "the most important unsolved problem of classical physics". In purely laminar flow there is no mixing between the layers so heat transfer is essentially conductive (see ref.). However, a velocity increase tends to drive the average temperature of the fluid adjacent to the exchanger closer to the inlet temperature and transfer rate increases as sqrt(v). You can verify this with the calculator on the ref. page.
The bottom line seems to be that, although there is an increase of heat flow with increased velocity, the velocity exponent is only defined for laminar flow.

Answer 2

specific heat capacity of air is 1000 J kg–1 K–1
find out k.e by the formula kinetic energy=1/2 mv*v;
then you probably know that all forms of energies are same so
1/2 mv*v= m*c*rise in temperature ;[ c is the s.h.c of air i.e 1000 Jkg-1K-1)
m and m get cancelled;
so you get 1/2v2=c*rise in temperature