The Equations for Turbulent Convective Heat Transfer

In all of the above discussion it was assumed that the flow was laminar. The majority of flows encountered in practice are, however, turbulent. Consideration must, therefore, be given to the question of how these equations must be modified in order to apply them to turbulent flow. 

In turbulent flows, even when the mean flow is steady (see below), the flow variables, i.e-., velocity, pressure, and temperature, all fluctuate randomly with time due to the superposition of the turbulent eddies on the mean flow. For example, if the temperature at some point in the flow is measured by means of some device which has very good time response characteristics and the output of this device is displayed on a suitable instrument then a signal resembling that shown in Fig. 2.10 will be obtained in turbulent flow. 

7 = Instantaneous Value T = Fluctuating Component 7 - Mean Value 

Temperature variation with time in turbulent flow. 

Because the flow variables are fluctuating with time in this way it is necessary to clearly define what is meant by steady turbulent flow. To do this, mean values of the variables are defined in the following way [3],[7],[10],[11],[12]  

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