This article emphases on the study of the flow, heat and mass transfer from an exponentially stretching surface in a viscous fluid with heat source. The viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The equations of the flow are converted into ordinary differential equations by utilizing the similarity transformations. The resulting non-linear system is solved applying the Successive linearization method along with the Chebyshev collocation method. The physical quantitites of the flow problem are computationally analyzed and exhibited via graphs. It is noticed that the rate of heat transfer increased with raise in Biot and decreased with increase in the value of thermal conductivity and heat source parameters. While, the rate of mass transfer increased with increase in the values of Biot, thermal conductivity and heat source parameters and skin-friction is increasing with viscosity parameter and decreasing with thermal conductivity and heat source parameters.
convective thermal conditions, variable thermal conductivity, variable viscosity, stretching sheet
 Sakiadas BC. (1961). Boundary-layer equations for two-dimensional and axisymmetric flow. A. I. Ch. E. Journal 7(1): 26-28.
 Sakiadas BC. (1961). The boundary layer on a continuous flat surface. A. I. Ch. E. Journal 7(2): 221-225.
 Crane LJ. (1970). Flow past a stretching plate. Journal of Applied Mathematics and Physics 21(4): 645-647.
 Kumaran V, Ramanaiah G. (1996). A note on the flow over a stretching sheet. Acta Mechanica 116: 229-233.
 Magyari E, Keller B. (1999). Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. Journal of Physics D: Applied Physics 32(5): 577-585.
 Sajid M, Hayat T. (2008). Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. International Communications in Heat and Mass Transfer 35: 347-356.
 Malvandi A, Hedayati F, Domairry G. (2013). Stagnation point flow of a nanofluid toward an exponentially stretching sheet with non-uniform heat generation/absorption. Journal of Thermodynamics 2013.
 Rohni M, Ahmad S, Pop I. (2014). Flow and heat transfer at a stagnation-point over an exponentially shrinking vertical sheet with suction. International Journal of Thermal Sciences 75: 164-170.
 Hussain S, Ahmad F., (2015). On the study of viscous fluid due to exponentially shrinking sheet in the presence of thermal radiation. Thermal Science 19(Suppl.1): 191-196.
 Ur-Rehman S, Nadeem S, Lee C. (2016). Series solution of magneto-hydrodynamic boundary layer flow over bi-directional exponentially stretching surfaces. Journal of the Brazilian Society of Mechanical Sciences and Engineering 38(2): 443-453.
 Emama TG, Elmaboud TA. (2017). Three-dimensional magneto-hydrodynamic flow over an exponentially stretching surface. Int. J. of Heat and Technology 35(4): 987-996.
 Kumar PBS, Gireesha BJ, Gorla RSR, Mahanthesh B. (2017). Magnetohydrodynamic flow of Williamson nanofluid due to an exponentially stretching surface in the presence of thermal radiation and chemical reaction. J. of Nanofluids 6(2): 264-272.
 Aleng NL, Bachok N, Arifin NM. (2018). Dual solutions of exponentially stretched/shrinked flows of nanofluids. Journal of Nanofluids 7(1): 195-202.
 Srinivasacharya D, Jagadeeshwar P. (2018). Flow over an exponentially stretching porous sheet with cross-diffusion effects and convective thermal conditions. Int. J. of Engineering Transactions A: Basics 31(1): 120-127.
 Hayat T, Nadeem S. (2018). Flow of 3D Eyring-Powell fluid by utilizing Cattaneo-Christov heat flux model and chemical process over an exponentially stretching surface. Results in Physics 8: 397-403.
 Lai FC, Kulacki FA. (1991). The effect of variable viscosity on convective heat and mass transfer along a vertical surface in saturated porous media. Int. J. of Heat and Mass Transfer 33: 1028-1031.
 Chaim TC. (1996). Heat transfer with variable thermal conductivity in a stagnation-point flow towards a stretching sheet. Int. Commun. Heat Mass Transfer 23(2): 239-248.
 Chiam TC. (1998). Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet. Acta Mechanica 129: 63-72.
 Khan Y, Wua Q, Faraz N, Yildirim A. (2011). The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet. Computers and Mathematics with Applications 61: 3391-3399.
 Rahman GMA. (2013). Effects of variable viscosity and thermal conductivity on unsteady MHD flow of non-Newtonian fluid over a stretching porous sheet. Thermal Science 17(4): 1035-1047.
 Siddheshwar PG, Sekhar GN, Chethan AS. (2014). Flow and heat transfer in a Newtonian liquid with temperature dependent properties over an exponential stretching sheet. Journal of Applied Fluid Mechanics 7(2): 367-374.
 Hayat T, Muhammad T, Shehzad SA, Alsaedi A. (2015). Soret and Dufour effects in three-dimensional flow over an exponentially stretching surface with porous medium, chemical reaction and heat source/sink. International Journal of Numerical Methods for Heat \& Fluid Flow 25(4): 762-781.
 Megahed AM. (2015). Flow and heat transfer of Powell-Eyring fluid due to an exponential stretching sheet with heat flux and variable thermal conductivity. Zeitschrift für Naturforschung A 70(3): 163-169.
 Hazarika GC, Phukan B. (2017). Effects of variable viscosity and thermal conductivity on steady magnetohydrodynamic flow of a micropolar fluid through a specially characterized horizontal channel. Modelling Measurement and Control B 86(1): 1-13.
 Srinivasacharya D, Jagadeeshwar P. (2018). Effect of variable viscosity, thermal conductivity and Hall currents on the flow over an exponentially stretching sheet with heat generation/absorption. International Journal of Energy for a Clean Environment 19(1): 1-17. 10.1615/InterJEnerCleanEnv.2018021746
 Motsa SS, Shateyi S. (2011). Successive Linearisation solution of free convection non-Darcy flow with heat and mass transfer. Advanced Topics in Mass Transfer 19: 425-438.
 Awad FG, Sibanda P, Motsa SS, Makinde OD. (2011). Convection from an inverted cone in a porous medium with cross-diffusion effects. Computers and Mathematics with Applications 619(5): 1431-1441.
 Canuto, Hussaini MY, Quarteroni A, Zang TA. (2006). Spectral Methods: Fundamentals in Single Domains. Springer-Verlag Berlin Heidelberg.