# Dissipative Nanofluid Slip-Flow and Heat Transfer in a Permeable Stretching Vertical Channel with Internal Heat Generation

### Abstract

A comparative investigation is carried out in this paper to study the inuence of Alumina

and Titanium oxide water based nanouids abound and ow in a vertical channel whose one of

its parallel walls is both permeable and extensible in the presence of thermal dissipation and

internal heat source/sink. The governing basic partial dierential equations are formulated and

reduced to ordinary dierential equations by means of existing transformation, thereafter solved

using Homotopy Perturbation Method (HPM). Excellent validation of the HPM results has

been assessed through comparison with the fourth-fth-order Runge-Kutta-Fehlberg numerical

quadrature by means of tables. For some selected values of various basic ow parameters,

tables are contextualized on the skin-friction parameters as well as the surface heat transfer

rate. The inuence of nanouid volume fraction, Echert number, viscosity based Reynolds

numbers, internal heat generation/absorption, wall mass ux and velocity slip are investigated

by means of plotted axial and transverse velocity graphs as well as temperature proles, and

they are found to be highly signicant on both velocity and temperature elds. Also, the results

indicate that relative dierences of the values due to Titanium Oxide from those of the Alumina

none-negative in almost all cases with exception of mass ux eect at the wall. In particular,

the inuence of the nanoparticle volume fraction is to intensify the wall uid characteristics in

both Alumina and Titanium Oxide nanouids.

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*International Journal of Mathematical Sciences and Optimization: Theory and Applications*,

*2020*(1), 669 - 688. Retrieved from http://ijmso.unilag.edu.ng/article/view/948