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mech7220-hw3-solns

# mech7220-hw3-solns - mech7220-hw3-solns.nb 1 In[239:=...

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In[239]:= Remove @ "Global` " D In[240]:= Off @ General::"spell1", General::"spell" D sp @ x_ D : = Simplify @ PowerExpand @ x DD con @ x_ D : = x ê . Complex @ 0, n_ D → − Complex @ 0, n D fs @ x_ D : = FullSimplify @ x D fs @ x_, b_ D : = FullSimplify @ x, b D Here are the momentum and energy equations. Velocity has been made dimensionless (which accounts for the reynolds number), yet temperature is still dimensional In[245]:= mde = u @ x, y D D @ u @ x, y D , x D + v @ x, y D D @ u @ x, y D , y D 1 ê re D @ u @ x, y D , 8 y, 2 <D Out[245]= v @ x,y D u H 0,1 L @ x,y D u H 0,2 L @ x,y D cccccccccccccccc ccccccccccccc re + u @ x,y D u H 1,0 L @ x,y D In[246]:= ede = u @ x, y D D @ t @ x, y D , x D + v @ x, y D D @ t @ x, y D , y D 1 ê H pr re L D @ t @ x, y D , 8 y, 2 <D Out[246]= v @ x,y D t H 0,1 L @ x,y D t H 0,2 L @ x,y D cccccccccccccccc ccccccccccccc prre + u @ x,y D t H 1,0 L @ x,y D The streamfunction substition In[247]:= u @ x_, y_ D : = D @ psi @ x, y D , y D v @ x_, y_ D : = − D @ psi @ x, y D , x D In[249]:= sp @ mde D Out[249]= psi H 0,3 L @ x,y D cccccccccccccccc cccccccccccccccc cccc re psi H 0,2 L @ x,y D psi H 1,0 L @ x,y D + psi H 0,1 L @ x,y D psi H 1,1 L @ x,y D

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mech7220-hw3-solns - mech7220-hw3-solns.nb 1 In[239:=...

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