Page 102 - Introduction to Computational Fluid Dynamics
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                        4.6 BOUNDARY CONDITIONS
                        4.6.2 Wall      0 521 85326 5                              May 25, 2005  11:7  81
                        The term wall signifies a solid boundary. However, it must be remembered that
                        when a gas flows over a liquid surface, the gas–liquid interface too will act like a
                        wall. For different  s, the wall boundary conditions are also different. We consider
                        them in turn.


                        Velocity Variables   = u or w
                        For these variables,
                                                u b = u wall ,  w b = w wall .             (4.53)

                        Thus, if the surface is rotating about the axis of symmetry (see Figure 4.1) with
                        angular velocity  , then the surface fluid velocity will be w wall = r I  . Similarly,
                        the streamwise velocity will always be zero unless the surface itself is moving with
                        velocity u wall . Equation 4.53, therefore, signifies the no-slip condition.
                           In some circumstances, a fluid may be injected (by blowing) into the boundary
                        layer or the boundary layer fluid may be withdrawn (by suction) through the wall.
                        Alternatively,incaseofevaporation orsurfaceburning,masswill betransferredinto
                        theboundarylayer.Inallsuchcases ˙ m b isknownorknowableandtheconsequenceis

                                             ψ b (x) = ψ b (x −  x) − r b ˙ m b  x.        (4.54)


                        Thermal Variables   = T or h
                        For these variables, typically two types of conditions are specified. In the first, the
                        value of the variable itself is specified. Thus,

                                              T b = T wall (x),  h b = h wall (x).         (4.55)
                        In the second, the heat flux q b is specified. Then, at the I boundary, for example,


                                              ∂T           k ∂h             ∂h
                                      q b =−k         =−             =−
           .       (4.56)
                                              ∂y          C p ∂y            ∂y
                                                  y=0             y=0          y=0
                           The flux boundary condition is effected by adding q b  x to the source term of
                        Equation 4.43 for j = 2 and, further, by setting AS 2 = 0, the values of T b or h b can
                        be extracted in the usual manner. A similar procedure is adopted if q b is specified
                        at the E boundary.
                           In a chemically reacting boundary layer, the mass transfer flux at the wall ˙ m is

                                                                                             b
                        given by
                                                                            ∂T


                                     ˙ m = (h b − h T ) −1      ∂ω k               ,       (4.57)
                                      b                   ρ m D k  ∂y  h k + k m  ∂y
                                                      k                         y=0
                        where h T is the enthalpy of the mixture deep inside the I boundary. If the Lewis
                        number is taken to be unity (i.e., Pr = Sc) or a simple chemical reaction (SCR)
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