Abdul Hafeez1, Masood Khan2, Jawad Ahmed3. 1. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan. Electronic address: ahafeez@math.qau.edu.pk. 2. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan. 3. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan; Department of Basic Sciences, University of Engineering and Technology, Taxila 47050, Pakistan.
Abstract
BACKGROUND: In general, heat transfer describes the flow of heat (thermal energy) due to temperature differences. The phenomenon of transfer of heat from one body to another body or in same type bodies occurs because of the temperature difference. As heat transfer is a natural phenomenon, therefore much attentions have developed among the researchers to observe the heat transfer mechanism in the systems. To examine the heat and mass transport mechanism in the fluid, the Cattaneo-Christov theory is adopted instead of classical Fourier's and Fick's laws in the current study. Further, the stagnation point flow of Oldroyd-B fluid is explored. Here the flow is generated by a rotation of the disk. Additionally, the porous disk is considered here. The von Karman similarity variables are used to transform the partial differential equations (PDEs) into ordinary differential equations (ODEs). METHOD: To handle the system of non-linear equations, we use a built-in technique (BVP Midrich) in Maple software to acquire numerical solution. RESULTS: The solution of the governing system of equations are presented graphically in the form of velocity fields, temperature and concentration distributions. It is noted that the higher values of thermal and solutal relaxation time parameters reduce the thermal and concentration distributions, respectively. Moreover, the comparison tables are presented to assure the validity of our numerical results with the past outcomes.
BACKGROUND: In general, heat transfer describes the flow of heat (thermal energy) due to temperature differences. The phenomenon of transfer of heat from one body to another body or in same type bodies occurs because of the temperature difference. As heat transfer is a natural phenomenon, therefore much attentions have developed among the researchers to observe the heat transfer mechanism in the systems. To examine the heat and mass transport mechanism in the fluid, the Cattaneo-Christov theory is adopted instead of classical Fourier's and Fick's laws in the current study. Further, the stagnation point flow of Oldroyd-B fluid is explored. Here the flow is generated by a rotation of the disk. Additionally, the porous disk is considered here. The von Karman similarity variables are used to transform the partial differential equations (PDEs) into ordinary differential equations (ODEs). METHOD: To handle the system of non-linear equations, we use a built-in technique (BVP Midrich) in Maple software to acquire numerical solution. RESULTS: The solution of the governing system of equations are presented graphically in the form of velocity fields, temperature and concentration distributions. It is noted that the higher values of thermal and solutal relaxation time parameters reduce the thermal and concentration distributions, respectively. Moreover, the comparison tables are presented to assure the validity of our numerical results with the past outcomes.
Authors: Muhammad Sohail Khan; Sun Mei; Nehad Ali Shah; Jae Dong Chung; Aamir Khan; Said Anwar Shah Journal: Nanomaterials (Basel) Date: 2022-02-16 Impact factor: 5.076