Cylindrical Heat Transfer & Exchanger Principles

Heat Conduction Through a Single-Layer Cylinder

From this equation, the following is derived:

Boundary Conditions

• t(r = r1) = t1
• t(r = r2) = t2

We are looking for a function t = f(r). The resulting equation is t = B * ln(r) + C.

t1 = B * ln(r1) + C

t2 = B * ln(r2) + C

Where A_r represents the average area.

The values for t, where t = B * ln(r) + C, are shown below:

To refer to the inner area, the expression is divided and multiplied by r1:

To refer to the outer area, the expression is divided and multiplied by r2:

Cylinder Heat Transfer Coefficient: Fouling & Clean

The standard heat transfer rate varies during operation due to fouling of the exchanger walls.

The coefficient is at its minimum when fully fouled and at its maximum (clean) at the beginning of operation.

For the calculation of the overall heat transfer coefficient (U), a fouling coefficient is determined for both the annulus and the interior or exterior of the tube.

For a Cylinder:

When considering fouling, the fouling coefficients are added:

Where represents the fouling coefficient inside the inner tube.

represents the fouling coefficient of the annulus.

Key Terms in Heat Exchangers

Pitch

The pitch is the center-to-center distance between two consecutive tubes in a shell-and-tube heat exchanger.

BMG (Birmingham Wire Gauge)

BMG (Birmingham Wire Gauge) refers to units used to measure the size or thickness of tube walls in shell-and-tube heat exchangers.

Number of Passes

The number of passes refers to the number of times fluids flow through the tubes and the shell. For example, a 2-4 exchanger has two shell passes and four tube passes.

Triangular Tube Pitch

Triangular distribution is one of the possible tube arrangements in a shell-and-tube heat exchanger. This arrangement typically yields the best heat transfer coefficient by maximizing the tube surface area. However, a significant disadvantage is that the tube surface is difficult to clean by mechanical means.

Further Definitions

Transverse Surface Area Flux

Transverse surface area flux refers to the heat transfer rate per unit of surface area.

Shell-Side Equivalent Diameter

The shell-side equivalent diameter is calculated as shown:

Heat Flow in a Double-Layer Cylinder

Determine the heat flow for a double-layer cylinder when both its inner and outer surfaces are bathed in liquid.

Convection (1-2)

Conduction (2-4)

Convection (4-5)

Overall Heat Transfer (1-5)