Question

In heat transfer for a heating radiator

When width is given

Height is given

Surface temp is given

Maintained Room temperature is given

Radiator surface emissivity is given

And radiator back is insulated

How would one

1. Calculate rate at which energy is lost from radiation ?

2. Calculate rate at which energy is lost from surface by convection

3. Calculate proportion of total energy lost by radiation heat transfer from the radiator

Answer 1

width = W

Height = H

Surface temp = T1

Maintained Room temperature = T2

Radiator surface emissivity = e

Part 1

energy is lost from radiation

Qrad = Ae (T1⁴ - T2⁴ )

Qrad = e x H x W x (T1⁴ - T2⁴ )

Part 2

Calculate the Reynolds number

Re = Length x velocity x density / viscosity

Fluid properties are constant at particular temperature

Prandtl number

Pr = specific heat capacity x viscosity / thermal conductivity

If Re < 2100

Flow is laminar

Heat transfer coefficient is calculated from seder tate equation

h = 0.027 (Re^0.8) (Pr^0.33) (/_s)^(0.14)

If Re > 4000

Flow is turbulent

Heat transfer coefficient is calculated from dittus boelter equation

h = 0.023 (Re^0.8) (Pr^n)

For heating n = 0.4

For cooling n = 0.3

energy is lost from surface by convection

Qconv = hA (T1 - T2)

Part 3

proportion of total energy lost by radiation

= Qrad x 100 / (Qrad + Q conv)