Simple D Derivation

66 If we consider a unit thickness, 2D differential body of dimensions dx by dy, Fig. 6.4 then

1. Rate of heat generation/sink is

2. Heat flux across the boundary of the element is shown in Fig. ?? (note similarity with equilibrium equation)

Figure 6.4: Flux Through Sides of Differential Element Figure 6.5: *Flow through a surface r

3. Change in stored energy is

where we define the specific heat c as the amount of heat required to raise a unit mass by one degree.

67 From the first law of thermodaynamics, energy produced I2 plus the net energy across the boundary 11 must be equal to the energy absorbed I3, thus

dā€” dxdy + dq^ dydx + Qdxdy ā€” cpd^dxdy = 0 (6.73-b)

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