Asolid plate, with a thickness of 15 cm and a thermal conductivity of 80 w/m·k, is being cooled at the upper surface by air. the air temperature is 10°c, while the temperatures at the upper and lower surfaces of the plate are 650 50 and 60°c, respectively. determine the convection heat transfer coefficient of air at the upper surface and discuss whether the value is reasonable or not for force convection of air.

To solve this problem we will use the two principles that are visible according to the phenomena described in the problem: Heat transfer by conductivity and Heat transfer by convection.

This thermal transfer will be equivalent and with it we can find the value asked.

Note: We will assume that the temperature value at the plate surface is: 60 ° C (For the given value of 650 50)

For Thermal Transfer by Conduction

Where,

k = Thermal conductivity

A = Cross-sectional Area

= Temperature of the bottom surface

= Temperature of the top surface

L = Length

Replacing we have that

For Thermal Transfer by Convection

Where,

h = Convection heat transfer coefficient

= Surrounding temperature

A = Surface Area

Replacing we have that

Since the rate of heat transfer by convection is equal to that given by conduction we have to:

It is stated that the typical values of forced convection of gases lies in the range of . The obtained value is reasonable for forced convection of air.