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An analysis has been carried out to determine the momentum and heat transfer occurring in the laminar boundary layer on a continuous moving surface which has an arbitrary surface velocity and nonuniform surface temperature. Merk series types of solutions are obtained for the momentum and heat transfer for an isothermal surface. The results are expressed in terms of universal functions. For a nonisothermal surface, the procedure begins with a consideration of the solution of the energy equation for a step discontinuity in the surface temperature by the introduction of appropriate transformation variables. Equations for the temperature profile and for the local heat flux are expressed explicitly in terms of the Prandtl number and the surface velocity parameter. Numerical examples for a power law surface velocity and a linearly stretching surface velocity with nonzero slot velocity are given for the isothermal surface. The accuracy of the present solutions is also discussed.

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A procedure is described for the calculation of momentum and heat transfer rates through laminar boundary layers over rotating axisymmetric bodies in forced flow. By applying appropriate coordinate transformations and Merk’s type of series, the governing momentum equations can be expressed as a set of coupled ordinary differential equations that depend on a wedge parameter and on a rotation parameter. For the energy equation, a set of ordinary differential equations is obtained which depend explicitly on the Prandtl number and implicitly on the aforementioned parameters. These equations are numerically integrated for a range of parameter values for the special case of a rotating sphere, and the local friction coefficient and the local Nusselt number are presented for values of the rotation parameter B = 1, 4, and 10 with Prandtl numbers of 1, 10, and 100. These results are then compared with previous theoretical results. It is also shown how the flow and heat transfer characteristics for a rotating disk can be readily obtained as a special case from the formulation for the rotating sphere. The disk results are also compared with previous theoretical and experimental studies.