# CONVECTION HEAT TRANSFER CLASS NOTES FOR MECHANICAL ENGINEERING

## convection heat transfer.

### (i) Free Convectionor natural convection heat transfer Fig. Free Convection Boundary Layer Over a Heated Vertical Plate

### (a) Forced Convection Over a Flat Plate Fig. Hydrodynamic Boundary Layer in Forced Convection Over a Flat Plate

### (b) Forced Convection Heat Transfer in flow

It is further of two types.

(i) Laminar flow in a pipe

(a) shear stress distribution

τ = -(∂p/∂x) (r/2)

τmax = -(∂p/∂x) (R/2)

Negative sign shows pressure decreases in the direction of flow

(b) Velocity distribution

u = -(1/4μ )(∂p/∂x) (R2 –r2)

(c) Temperature distribution

ts–t = (umax/α)(∂t/∂x)[3R2/16 -r2/4 + r4/16R2] Fig. Shear stress and velocity distribution during laminar flow in a pipe Fig. Velocity & Temperature distribution during laminar flow in a pipe

Turbulent Flow in a Pipe

(i) Shear stress distribution

τmax = (f/8)ρU2

u/umax = (y/R)1/7   (Power Law)

Boundary layer thickness

δ/x = 0.371/(Rex)1/5 Fig. Velocity and temperature profiles during turbulent flow in a pipe

#### Comparison of Hydrodynamic & Thermal Boundary Layers for different fluids Fig. HBL and TBL for Air & Gases  (δTBL = δHBL) Fig. HBL and TBL for Oils  (δTBL < δHBL) Fig. HBL and TBL for Liquid Metals  (δTBL > δHBL)

### METHODS  FOR THE ANALYSIS OF FORCED CONVECTION HEAT TRANSFER

#### It is an empirical equation of Nusselt number in terms of Reynolds and Prandtl numbers.

TABLE: Boundary layer parameters for different velocity profiles

### Q. Write the formula for Grashoff’s number and discuss its importance.

#### Grashoff’s number used in the analysis of free convection (laminar flow).

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