Question

State your opinion on the related law and expressions for the following scenario.

i)Heat transfer from a hot burner on the stove to a pot or pan

ii)Heat transfer from a hot surface of rooftop to a windy air.

ii)Heat transfer of a greenhouse effects towards global warming.

Answer 1

I) Heat transfer from a hot burner on the stove to a pot or pan

Burner uses Natural gas or any other high calorific value materials as a fuel. The temperature produced by burner is > 200⁰C. At this high temperature ranges Radiation becomes the most dominant one. So, Radiation heat transfer is importatnt in this situation. Although it have both convection and conduction here, but radiation is dominant one.

The rate of heat transfer by emitted radiation is determined by the Stefan-Boltzmann law of radiation:

Qt=σeAT4

where σ = 5.67 × 10⁻⁸ J/s · m² · K⁴ is the Stefan-Boltzmann constant,

A is the surface area of the object,

  T is its absolute temperature in kelvin,

  e - emissivity of the object,

ii) Heat transfer from a hot surface of a rooftop to windy air:

Heat transfer from hot surface to moving medicum results in convective heat transfer. Here at the interface between hot surface and Air conduction becomes dominant one, away from the hot surface convection becomes dominant one. The rate of heat transfer due to convection is given by

dT/dt = k(T_t – T_s)

Where, T_t = temperature at time t and

T_s = temperature of the surrounding,

k = Positive constant that depends on the area and nature of the surface of the body under consideration.

The above formula can also be represened by Q = h * A* T

Where h - Heat transfer coefficient

A - Area of heat transfer

T - Temperature difference between two phases

iii) Heat transfer from a green house effects towards global warming:

In this process earth is surrounded by static layer of atmosphere. Even though lower layer layers of atmosphere(Atmosphere nearer to earth) is moving it is static in top layers(away from earth). So, in this type of situations conduction heat transfer becomes important. Sometimes convection is also plays important role, but conduction is the dominant one.

Fourier's law is used in its one-dimensional form. In the x-direction,

Where

q - heat flux density, W·m⁻²

k- material's conductivity, W·m⁻¹·K⁻¹,

dT - is the temperature gradient, K·m⁻¹.

Feel free to ask if you have any question on this...