Similarity Requirements for Mixed Convective Boundary Layer Flow over Vertical Curvilinear Porous Surfaces with Heat Generation/Absorption

Kh Abdul Maleque

doi:10.1155/2020/7486971

Abstract

Similarity requirements for three dimensional combined forced and free convective laminar boundary layer flows over the porous inclined vertical curvilinear surfaces with buoyancy effects and heat absorption/generation effects are investigated theoretically. The potential flow in the mainstream and Gabriel lame coefficients outside of the boundary layer are the function of ξ,η. Hence, the external velocity components (Ue, Ve) and Gabriel lame coefficients h1,h2,h3 are independent of ζ. Here, h3ξ,η=1 has been set such that ζ represents actual distance measured normal to the surface. Similarity requirements for an incompressible fluid are sought on the basis of detailed analyses in order to reduce the governing partial differential equations into a set of ordinary differential equations. Finally, different possible cases are exhibited in a tabular form with the inclusion of ΔT variations for onward flow study that are helpful to the future researchers for the flow over the orthogonal curvilinear surfaces.

Highlights

When a viscous fluid flows over a heated vertical orthogonal curved surface in inclined position, velocity and thermal boundary layers are formed over the surface
He showed that the equations were reducible to a pair of simultaneous ordinary differential equations
Hansen [3, 4] presented a table showing the nature of the variations in the mainstream components for which the governing equations were reducible to a set of ordinary differential equations

Summary

Introduction

When a viscous fluid flows over a heated (or cooled) vertical orthogonal curved surface in inclined position, velocity and thermal boundary layers are formed over the surface. The effects of temperature difference in order to predict the frictional resistance and heat transfer rate by introducing the components of the fluid velocity generated by buoyancy effects in the direction parallel to the edges of the surface were discussed by Zakerullah and Maleque [12]. In their another paper [13], they investigated the nature of free stream velocities and temperature difference variations between the ambient fluid and the threedimensional rectangular surfaces theoretically and numerically. 2 e are introduced to show the dominancy of buoyancy effect over the forced flow effect, where ðU Fðξ, ηÞ, V Fðξ, ηÞ, 0Þ are the local fluid velocity components generated by buoyancy effect only and ðUeðξ, ηÞ, Veðξ, ηÞ, 0Þ are the components of the main stream velocity

Geometry of the Problem and the Governing Equations

Similarity Transformations

MÞY SSφφ ðV MÞY S2φ γ2 U L h1

Conclusions