Heat Generation/Absorption Effect on Natural Convection Flow in a Vertical Annulus with Time-Periodic Boundary Conditions

Michael O Oni,Basant K Jha

doi:10.3844/jastsp.2019.183.196

Michael O Oni, Basant K Jha

Open Access

https://doi.org/10.3844/jastsp.2019.183.196

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Abstract

The role of heat generation/absorption on natural convection flow formation in a vertical annulus with prescribed time-periodic heating is investigated in this article. The governing continuity, momentum and energy equations are converted into ordinary differential equation using suitable transformations and closed form expressions are obtained for temperature distribution, velocity profile, Nusselt number, skin friction and mass flow rate in terms of Bessel’s function and modified Bessel’s function of first and second kinds. Based on depicted line and contour graphs, results show that the inclusion of heat generation/absorption parameter removes the singularity point in periodic velocity and skin friction for unity Prandtl number. In addition, heat generation/absorption parameter respectively increase/decrease periodic temperature distribution, velocity profile, Nusselt number and skin-friction at the surfaces of the cylinders.

Highlights

Thermal response in transient heating/cooling problems, such as engine cooling, or how fast a car heats up in the sun and how is it affected by the shape of the windshield has been widely studied
The Nusselt number which measures the rate of heat transfer between the surfaces of the cylinders and the fluid is obtained by taking the first derivative of the periodic temperature distribution as follows: ( ) dG
The solutions obtained are physical presented in terms of line and contour graphs in order to show the effects of governing parameters (Strouhal number (St), Prandtl number (Pr), heat generation/absorption parameter (H) and ratio of radiuses (λ)

Summary

Introduction

Thermal response in transient heating/cooling problems, such as engine cooling, or how fast a car heats up in the sun and how is it affected by the shape of the windshield has been widely studied. The Nusselt number which measures the rate of heat transfer between the surfaces of the cylinders and the fluid is obtained by taking the first derivative of the periodic temperature distribution as follows: ( ) dG

Results

Conclusion