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Purpose The purpose of this paper is to improve the lattice Boltzmann method’s ability to simulate a microflow under constant heat flux. Design/methodology/approach Develop the thermal lattice Boltzmann method based on double population of hydrodynamic and thermal distribution functions. Findings The buoyancy forces, caused by gravity, can change the hydrodynamic properties of the flow. As a result, the gravity term was included in the Boltzmann equation as an external force, and the equations were rewritten under new conditions. Originality/value To the best of the authors’ knowledge, the current study is the first attempt to investigate mixed-convection heat transfer in an inclined microchannel in a slip flow regime.

SUMMARYThis paper studied on magnetohydrodynamics flow and heat transfer outside a stretching cylinder. Momentum and energy equations are reduced using similarity transformation and converted into a system of ordinary differential equations which are solved analytically by the homotopy analysis method. The effects of the parameters involved, namely the magnetic parameter (M), Prandtl number (Pr) and Reynolds number (Re) on the velocity and temperature fields are investigated.The obtained results are valid for the whole solutions' domain with high accuracy. These methods can be easily extended to other linear and nonlinear equations and so can be found widely applicable in engineering and sciences.

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