Calculate the rate of heat transfer from bottom to top of the slice in W/m2

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A 5-cm thick slice of bread (k = 0.23 W/m°C) is placed on top of a hot plate at a temperature of 85oC. The top surface of the bread slice is maintained at 25°C.a.Calculate the rate of heat transfer from bottom to top of the slice in W/m2

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Step 1

Thermal Conductivity

The thermal conductivity of a substance is the measure of the ability of the substance to conduct heat. It can be defined as the rate at which heat is transferred through a unit cross-section of a material when a temperature gradient exists perpendicular to the heat flow. It is denoted by K and its SI unit is Wm-1K-1.

The amount of heat Q flowing through a slab of the cross-sectional area A and of thickness x in time t from the side at a higher temperature θ1 to the side of lower temperature θ2 is given by

             Q=KAθ1-θ2tx

Therefore the amount of heat supplied per unit area per unit time is given by

    QAt=Kθ1-θ2x

Step 2

In the question given is the thickness of the slice of bread x=5 cm=5100m=0.05 m

 the temperature of the bottom surface of the slice θ1=85°C

the temperature of the top surface of the slice θ2=25°C

Thermal conductivity of the slice K=0.23 W/m°C

Therefore the rate of heat transfer from the bottom to the top of the slice per unit area is

QAt=Kθ1-θ2x=0.23×85-250.05=276 W/m2

 

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