HEAT CONDUCTIONPREAPARED

BY ASHA KUMAWAT

DIFFERENTIAL EQUATION OF HEAT CONDUCTIONDifferential element of dimensions dx- dy-dz

differential element in Cartesian co-ordinate system

From Fourier law,1.Heat conducted into differential element in X-direction

2. Heat conducted out of the differential element in X-direction From the fundamental principle of differentiation, we get

Substituting the value of dqx we get

Net amount of heat conducted in X-direction= dqx- dqx+dx

Similarly for Y and Z directions, we can write

Therefore net amount of heat conducted into the differential element per unit time in all directions, is given by

q be the rate of heat of generated per unit volumeThe amount of heat generated in the differential element per unit time

Where V-volume of element =dx.dy.dz

•The energy contained by the body is termed as internal energy. •The flow of heat as well as generation of energy will result in change in internal energy•The rate of change of internal energy of the element per unit volume is given by

Now balance for the differential element as Rate of heat conduction into the element + rate of heat generation in the element=rate of change of internal energy of the elementSubstituting the corresponding values and simplifying we get

Thermal diffusivityIt indicates the case at which energy gets diffused in the volume of the substance. It is define as the ratio of thermal conductivity to the heat capacity of a substance. It is given by

By substituting above assumptions in the heat conducting equation we get

Heat conduction through a composite wall

Thermal conduction resistance (L/KA)

Thermal contact resistance

Overall heat transfer coefficient

iv

v

vi