Exact Analysis of Second Grade Fluid with Generalized Boundary Conditions Syed Tauseef Saeed 1 , Muhammad Bilal Riaz 2,3 , Dumitru Baleanu 4,5,7,* , Ali Akgül 6 and Syed Muhammad Husnine 1 1 Department of Science & Humanities, National University of Computer and Emerging Sciences, Lahore Campus, 54000, Pakistan 2 Department of Mathematics, University of Management and Technology, Lahore, 54000, Pakistan 3 Institute for Groundwater Studies (IGS), University of the Free State, Bloemfontein, 9301, South Africa 4 Department of Mathematics, Cankaya University, Ankara, 06790, Turkey 5 Institutes of Space Sciences, Magurele, Bucharest, 077125, Romania 6 Institutes of Sciences, Siirt University, Siirt, 56100, Turkey 7 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan  Corresponding Author: Dumitru Baleanu. Email: dumitru@cankaya.edu.tr Received: 17 December 2020; Accepted: 28 January 2021 Abstract: Convective flow is a self-sustained flow with the effect of the tempera- ture gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by mass transfer process; for instance condensation, evaporation and chemical process. Due to the applications of the heat and mass transfer combined effects in different field, the main aim of this paper is to do comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of time dependent generalized boundary conditions. The non-dimensional forms of the governing equations of the model are developed. These are solved by the classical integral (Laplace) transform technique/method with the convolution theorem and closed form solutions are developed for tem- perature, concentration and velocity. Obtained generalized results are very impor- tant due to their vast applications in the field of engineering and applied sciences. The attained results are in good agreement with the published results. Addition- ally, the impact of thermal radiation with the magnetic field is also analyzed. The influence of physical parameters and flow is analyzed graphically via compu- tational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect. Keywords: MHD second grade fluid; dynamical analysis; time dependent velocity; porous medium; Laplace transformation; radiation effect 1 Introduction Numerous engineering practices such as drag reduction, transpiration cooling, thermal retrieval of oil, and thermite welding demand a radical knowledge of heat transfer during viscous and non-Newtonian fluids’ flow in diverse geometries. Therefore, various attempts are used to analyze and update the existing This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Intelligent Automation & Soft Computing DOI:10.32604/iasc.2021.015982 Article ech T Press Science