Mathematical Solution for Free Convection Flow of Brinkman Type Fluid in the Channel with the Effect of Accelerated Plate

Mohamad Riduan Hashim; Zulkhibri Ismail; Ahmad Qushairi Mohamad; Muhammad Atif Akashah; Wan Nura'in Nabilah Noranuar; Lim Yeou Jiann; Sharidan Shafie

doi:10.37934/arnht.15.1.5368

Authors

Mohamad Riduan Hashim Centre for Mathematical Sciences, College of Computing and Applied Sciences, Universiti Malaysia Pahang Al-Sultan Abdullah, Lebuhraya Tun Razak, 26300 Gambang, Pahang, Malaysia
Zulkhibri Ismail
Ahmad Qushairi Mohamad Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia
Muhammad Atif Akashah Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia
Wan Nura'in Nabilah Noranuar Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia
Lim Yeou Jiann Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia
Sharidan Shafie Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia

DOI:

https://doi.org/10.37934/arnht.15.1.5368

Keywords:

Analytical Solution, Brinkman Type Fluid, Free Convection Flow, Channel, Accelerated Plate, Laplace Transform

Abstract

The main purpose of this research is to formulate the mathematical models and solution for the effect of accelerated plate on free convection flow in Brinkman type fluid through two vertical channels. Using the appropriate dimensionless variables, the dimensional governing energy and momentum equations are reduced to dimensionless equations subjected to the associated initial boundary conditions. The analytical solutions are obtained by using Laplace transform method. Dimensionless parameters are obtained through dimensionless processes such as Grashof number Gr, Acceleration plate parameter, R, Prandtl number Pr, Brinkman type fluid parameter and time, t. The mathematical findings for velocity and temperature are graphically plotted to investigate the influence of dimensionless variables on profiles. It is observed that fluid velocity increases with increasing of Gr and t whereas it decreases with increasing of , R and Pr. Besides that, it is found that temperature profiles decrease with a high value of Prandtl number, Pr while increase with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and also with numerical Gaver-Stehfest algorithm. Both comparisons show that the solution is to be in a mutual agreement.

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