The Energy Equation for Steady Flow

The present book is concerned with methods of predicting heat transfer rates. These methods basically utilize the continuity and momentum equations to obtain the velocity field which is then used with the energy equation to obtain the temperature field from which the heat transfer rate can then be deduced. If the variation of fluid properties with temperature is significant, the continuity and momentum equations 

The prediction of convective heat transfer rates will, however, always involve the solution of the energy equation. Therefore, because of its fundamental importance in the present work, a discussion of the way in which the energy equation is derived will be given here [2],[3],[5],[7]. For this purpose, attention will be restricted to two-dimensional, incompressible flow. 

For this control volume, the steady flow energy equation requires that  

Rate at which Rate at which Rate at which 

Net rate at which Net rate at which = heat is transferred + work is done into control volume on control volume 

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