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Effect of temperature-dependent viscosity on slip flow in the momentum and thermal boundary layers

Marcel M. Louis1,*, Lekwetje Maureen Ramaube2,†, Sonya T. Smith2,‡, and Howard A. Stone1,§

  • 1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
  • 2Department of Mechanical Engineering, Howard University, Washington DC 20059, USA

  • *Contact author: mmlouis@princeton.edu
  • †Contact author: lekwetje.ramaube@bison.howard.edu
  • ‡Contact author: ssmith@howard.edu
  • §Contact author: hastone@princeton.edu
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Phys. Rev. Fluids 11, 064105 – Published 29 June, 2026

DOI: https://doi.org/10.1103/kj66-8y66

Abstract

We investigate the influence of a temperature-dependent viscosity on the flow over a heated flat plate, with a slip velocity condition at the wall as can occur with flow past solvophobic surfaces. This slip velocity can reduce the local shear stress on the wall compared to a no-slip boundary condition. An applied heating at the wall decreases viscosity in this region, which can further decrease wall stress. The extent of the contribution to this reduction in stress by the applied heating will depend on the temperature-dependent viscosity and the Prandtl number. We explore the link between the slip parameter, temperature-dependent viscosity, and the Prandtl number to investigate the drag reduction and heat transfer. We expand the momentum and energy boundary-layer equations assuming the slip parameter is small and use similarity solutions to solve for the first- and second-order corrections to the velocity and temperature fields. The asymptotic solutions show that the slip contributions to the flow are enhanced by temperature-dependent viscosity and the Prandtl number and we show their combined effect on the coefficients of friction and the Nusselt number. Our results indicate that increasing the coefficient of the temperature-dependent viscosity and the slip parameter complimentarily reduces friction and heat transfer effectiveness in the small slip parameter limit.

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Outline

Information

Phys. Rev. Fluids 11, 064105– Published 29 June, 2026
  • Received 3 February 2026
  • Accepted 1 June 2026
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