Consider two-dimensional steady conduction near a curved boundary. Determine the difference equation for an appropriate control volume near the node (i, j). The boundary experiences convective heat transfer through a coefficient h to ambient temperature Ta. The surface of the boundary is given by ys = f(x).
GIVEN
- Two-dimensional steady conduction near a curved surface
- Convective boundary condition
- Curved surface given by ys = f(x)
FIND
(a) Difference equation for a node i, j near the surface
SKETCH
Consider a control volume for the node i, j as shown below
Heat can flow into or out of the control volume at four surfaces. An energy balance on the control
volume is given by
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