A new approach to the solution of the conjugate (coupled) heat transfer problem at the interface between nonuniform wall and gas/fluid boundary layer is presented. The present approach is based on the solution of the common energy conservation equation, valid in the flow as well as in the thickness of the nonuniform wall. This equation differs from the conventional form of the boundary-layer energy equation by the second-order derivative term describing the streamwise conductive heat transfer. Comparison of the present approach with conventional boundary-layer approximation is carried out for two cases: nonuniform wall temperature and nonuniform wall thermal resistance. The two-dimensional strongly nonlinear coupled heat transfer and the electrodynamic problem related to magnetohydrodynamic generator conditions is also considered.
Nomenclature
MI = coefficients defined by Eq. (12) .c 2 -exponents defined in Eq. (10)= effective specific heat, h/T = wall thickness = electric field vector = reference electric field = general solution of partial differential equations = influence function = static enthalpy = current density vector -Prandtl number = IP i-->Pr] = partial solution = total energy flux defined by Eq.(2) = Reynolds number = Stanton number = temperature = reference temperature = total temperature, T + u 2 /2C* -(u,v) = velocity vector = longitudinal distance along the wall = location of temperature step = normal distance from the wall = heat transfer coefficient = boundary-layer thickness = difference = total temperature profile = material thermal conductivity, \ m + \ t = molecular and turbulent thermal conductivity = nondimensional axial distance = density = electric potential = u/u , velocity profile
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