A Similarity Solution for Natural Convection Flow near a Vertical Plate with Thermal Radiation
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ORIGINAL ARTICLE
A Similarity Solution for Natural Convection Flow near a Vertical Plate with Thermal Radiation Basant K. Jha 1 & Gabriel Samaila 2 Received: 16 May 2020 / Accepted: 2 September 2020 # Springer Nature B.V. 2020
Abstract This paper examined the fluid transport on boundary layer near a vertical wall with thermal radiation effect. The coupled nonlinear partial differential equations are reduced to a system of ordinary differential equations through similarity transformation. The resultant system of ordinary differential equations is integrated with maple software using RKF45 method. The effect of the active parameters such as Grashof number, thermal radiation parameter, temperature difference, Prandtl number, and local convective heat transfer parameter on the velocity profile, skin friction, temperature profile and Nusselt number are presented using graphs and tables. The outcome of the study revealed that the Prandtl number has a decreasing effect on thermal boundary layer thickness. It also revealed that the thermal radiation has an increasing effect on the Nusselt number, temperature distribution, temperature gradient and skin friction. The temperature distribution increases with increasing values of the temperature difference and local convective heat transfer parameter whereas decreases with Grashof number. Keywords Similarity solution . Thermal radiation . Convective boundary condition . Vertical plate
Nomenclature CT temperature difference parameter Bix local convective heat transfer parameter R thermal radiation parameter Pr Prandtl number Grx local Grashof number Re Reynold number θ (temperature) T temperature (K) U velocity (ms−1) k thermal conductivity (W/mK) qr radiative heat flux (W/m2K) β thermal expansion coefficient (K−1)
* Gabriel Samaila [email protected] Basant K. Jha [email protected] 1
Department of Mathematics, Ahmadu Bello University Zaria, Kaduna, Nigeria
2
Department of Mathematics, Air Force Institute of Technology Kaduna, Kaduna, Nigeria
Introduction Boundary layer continues to be an interesting subject of investigation due to its practical and scientific applications in the areas such as species transport, mixing enhancement, golf ball aerodynamics, heat transfer enhancement, aerodynamics in reattachment and separation etc. Taghite et al. (1999) earlier evaluated thermal boundary layer in the plate using a heat exchanger. Further investigation on the boundary layer can be found in some recent publications include (Oh et al. 2019; Klamka et al. 2019; Zhang et al. 2019; Egorov et al. 2020). The concept of similarity transformation has been explored by several workers. Similarity transformation is used to transform the set of partial differential equations to a system of ordinary differential equations and the solution of the resulting ordinary differential equation is known as the similarity solution. Over the years, it has been an important tool in solving boundary layer related problems. Voller (2006) presented a comprehensive report on onedimensional solidif
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