18.13:
Conduction, Convection and Radiation: Problem Solving
A 13 cm thick wall with a 100 m2 area and 1.5 W/mK thermal conductivity separates a room from the outer atmosphere, which is at 3 degrees Celsius.
The outside surface of the wall is at 10 degrees Celsius, and its emissivity is 0.8. If the convective heat transfer coefficient is 15 W/m2K , find the total heat loss rate to the surrounding. Also, calculate the temperature of the inner surface of the wall.
Here, all three mechanisms of heat transfer are involved. Heat is transferred from the inner to the outer surface of the wall through conduction, while heat loss to the surroundings occurs due to convection and radiation.
The rate of heat loss through convection depends on the temperature gradient, surface area, and heat transfer coefficient.
So, total heat loss to the surrounding due to convection and radiation can be calculated as 13.27 x 103 W.
Employing the conservation of energy and substituting the terms in the heat equation, the temperature of the inner surface of the wall can be calculated.
18.13:
Conduction, Convection and Radiation: Problem Solving
There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting characteristics, but all three have two things in common: they transfer heat solely because of a temperature difference; and the greater the temperature difference, the faster the heat transfer.
In order to solve a problem related to heat transfer, first of all, the situation needs to be examined to determine the type of heat transfer involved. This could be conduction, convection, radiation, or all three of them. The second step is to identify and write down the unknown quantities in the problem. A list can be prepared of what is given or what can be inferred from the problem as stated, i.e., the known quantities, followed by solving the appropriate equation for the quantity to be determined.
For heat transfer through conduction, the following equation should be used.
For convection, the rate of heat loss depends on the temperature gradient, surface area, and heat transfer coefficient.
The following equation gives the net heat transfer rate for radiation.
Substituting the known quantities along with their units into the appropriate equation and solving it numerically gives the correct solution.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer