PROBLEM 4.35 KNOWN:Boundary conditions that change from specified heat flux to convection. FIND:The finite difference equation for the node at the point where the boundary condition changes. SCHEMATIC:m,nm +1,nm -1,n∆yq1q2q4q5q3h, T∞∆x∆y/2∆xm, n-1sq′′ASSUMPTIONS:(1) Two dimensional, steady-state conduction with no generation, (2) Constant properties. ANALYSIS:Performing an energy balance on the control volume ∆x • ∆y/2, inoutE-E =0±±q1 + q2 + q3 + q4 + q5= 0 Expressing q1in terms of the specified heat flux, q2in terms of the known heat transfer coefficient and environment temperature, and the remaining heat rates using the conduction rate equation,
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