Heat Transfer in Fluids

OBJECTIVES:

1.To study mechanisms of heat transfer in fluids.

2.To determine procedures for calculating heat transfer coefficients in forced and free convection.

q = h A (T_W - T_a)

Fluid flow on a solid surface can occur as

-- laminar flow

-- turbulent flow

-- transition between laminar and turbulent flow

--direction of flow may be parallel or perpendicular to the solid object.

--there may be influence of the entrance region on the flow.

--properties of the fluid -- viscosity, thermal conductivity, specific heat and density-- influence the rate of heat transfer.

RATE OF HEAT TRANSFER IN FLUIDS:

q=hA(T_W-T_a)

where h = convective heat transfer coefficient, W/m² C

h = f ( density, velocity, diameter, viscosity, specific heat, thermal conductivity, viscosity of fluid at wall temperature )

The convective heat transfer coefficient is determined by dimensional analysis.

A series of experiments are conducted to determine relationships between following dimensionless numbers.

Nusselt Number = N_Nu = hD/k

Prandtl Number = N_Pr = mc_p/k

Reynolds Number = N_{Re =} rvD/m

where

D = characteristic dimension

k = thermal conductivity of fluid

v = velocity of fluid

c_p = specific heat of fluid

r = density of fluid

m = viscosity of fluid

FORCED CONVECTION:

N_Nu = f(N_Re, N_Pr)

Laminar Flow in Pipes: If N_Re < 2100:

For (N_Re x N_Pr x D/L ) < 100

For (N_Re x N_Pr x D/L) >100

All physical properties are evaluated at bulk fluid temperature, except m_w.

Transition Flow in Pipes: N_Re between 2100 and 10,000: use figure 4.26 to determine h.

Turbulent Flow in Pipes:N_Re > 10000:

FREE CONVECTION

Free convection involves the dimensionless number called Grashof Number, N_Gr

where a and m are obtained from Table 4.4 (p 167)

All physical properties are evaluated at the film

temperature T_f = (T_w + T_b)/2