Received: 31 March 2019 Revised: 16 February 2020 Accepted: 23 April 2020 DOI: 10.1002/zamm.201900095 ORIGINAL PAPER Steady natural convection Couette flow with wall conduction and thermal boundary condition of third kind Abiodun O. Ajibade Ayuba M. Umar Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria Correspondence Ayuba M. Umar, Division of Agricultural Colleges, Ahmadu Bello University, Zaria, Nigeria. Email: amumar@abu.edu.ng This study theoretically investigates the effects of viscous dissipation and bound- ary plate thickness on an incompressible heat generating/absorbing fluid with non- uniform internal temperature unlike lumped heat capacitance assumption. The flow, which is laminar is induced by free convection caused by asymmetric heating of the channel boundaries and internally generated energy caused by viscous dissipation. In addition, convection through the boundary plates is also considered in the flow formation. One of the plates channel moves along the flow direction while the other is stationary. Due to the non-linear and coupling nature of the governing flow equa- tions, homotopy perturbation method (HPM) has been adopted to analytically find the approximate solution to the problem. The effects of thermodynamic and hydrody- namic parameters are depicted in graphs and tables. It is discovered from the investiga- tion that, both the velocity and temperature profiles increase with increase in viscous dissipation. Velocity distribution decreases with increase in Biot number while the temperature distribution near the heated plate increases with increase in Biot number. The increase in boundary plate thickness  causes a boost in the fluid flow across the medium and reduces the temperature of the fluid near the heated plate. It is fur- ther discovered that the rate of heat transfer on both plates increase with increase in Biot number while they drastically dropped when the boundary plate thickness  is increased. The shear stresses on the surface of both plates increase with increase in heat generation < 0 while reverse cases were observed with increase in heat absorption > 0. It is further observed that the volume flow rate within the channel increases with increase in viscous dissipation . KEYWORDS approximate solution, Biot number, boundary wall thickness, Couette flow, free convection, homotopy perturbation method, viscous dissipation, volume flow rate 1 INTRODUCTION Fluid flow and heat transfer in channels have received great attentions for many decades due to their applications in science and engineering. Researches have been carried out to investigate the effects of thermodynamics and hydrodynamics quantities in fluid flow. Internal heat generation as a result of viscous forces of molecular fluid particles’ interactions is referred to as viscous dissipation. The mechanical energy dissipated in this form significantly affects the thermal buoyancy and thermal behaviour of a fluid in motion. In most of the lubrication industries, viscous dissipation is a very vital factor since the fluid flow and the temperature are affected by the fluid particles’ interaction. The study of viscous dissipation has received consideration due to Z Angew Math Mech. 2020;e201900095. © 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 of 18 www.zamm-journal.org https://doi.org/10.1002/zamm.201900095