# Effects of thermal stratification on flow and heat transfer past a porous vertical stretching surface

## Abstract

The aim of this paper is to present the boundary layer flow of viscous incompressible fluid due to a porous vertical stretching surface with a power-law stretching velocity in a thermally stratified medium. Using a special form of Lie group transformations viz. scaling group of transformations, similarity solutions for this problem are obtained. The equations are then solved numerically. With increasing values of the stratification parameter, the velocity as well as temperature decreases. At a particular point of the porous stretching sheet, the velocity decreases with the increasing suction parameter. The dimensionless temperature at a point of the sheet decreases due to suction but increases due to injection. The findings of this study reveal that stratification and suction can be used as means of cooling the boundary layer flow region.

## Keywords

Boundary Layer Wall Shear Stress Prandtl Number Boundary Layer Flow Thermal Boundary Layer## List of symbols

*F*Non-dimensional stream function

- \( F^{*} \)
Variable

- \( F^{\prime } \)
Streamwise velocity

- Pr
Prandtl number

- St
Stratification parameter

*T*Temperature of the fluid

*T*_{w}Temperature of the wall of the surface

*T*_{∞}Free-stream temperature

*u*,*v*Components of velocity in

*x*and*y*directions*z*Variable

## Greek symbols

- \( \alpha_{1} ,\alpha_{2} ,\alpha_{3} ,\alpha_{4} ,\alpha_{5} ,\alpha_{6} \)
Transformation parameters

*β*_{1}Volumetric coefficient of thermal expansion

*η*Similarity variable

*Γ*Lie-group transformations

*κ*The coefficient of thermal diffusivity

*μ*Dynamic viscosity

*ν*Kinematic viscosity

*ψ*Stream function

- \( \psi^{*} \)
Variable

*ρ*Density of the fluid

*θ*Non-dimensional temperature

- \( \theta^{*} ,\bar{\theta } \)
Variables

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