This paper deals with entropy generation of two immiscible fluids inside an inclined channel under the influence of a uniform magnetic field. The channel consists of two regions such that a viscous fluid occupies the region I and an electrically conducting fluid occupies the region II. The governing equations of momentum and energy for two regions are solved by Mathematica package BVPh 2.0 which is based on homotopy analysis method. The analytical results are validated against other numerical simulations and experimental data and excellent agreements are achieved. The entropy generation components due to heat transfer and fluid friction for two immiscible fluids are formulated and then the total entropy generation is computed. The influence of various parameters including Grashof number, Hartmann number and inclination angle on the total entropy generation and its components is examined and discussed. Results show that total entropy generation has a direct relationship with Grashof number and inclination angle, while it has a reverse relationship with Hartmann number. It can also be found that although the enlargement of Hartmann number increases the contribution of entropy generation due to Ohmic dissipation, it still reduces the total entropy generation inside the channel.

A theoretical study is presented for the problem of orthogonal axisymmetric stagnation flow towards an infinite horizontal plate with a constant velocity in the presence of viscous dissipation and heat generation. The governing equations are reduced to a system of nonlinear ordinary differential equations by means of appropriate transformations for the velocity components and temperature. The similarity equations are solved numerically using the Matlab routine bvp4c. The results are compared with those known from the literature and an excellent agreement is found. The effects of involved parameters on the x-wise velocity component, temperature, skin friction, heat transfer and entropy generation rate are presented in graphical and tabular forms. It was found that the Eckert number Ec, the Prandtl number Pr and the heat generation parameter α play a significant role on the temperature, heat transfer and entropy generation rate.

An analytical study on entropy generation considering viscous dissipation effect in the circular microchannel is reported. The fluid flow is steady, laminar, hydrodynamically fully developed and thermally developing. In the first law analysis, appropriate dimensionless variables are applied to solve the energy equation in the thermal entrance region of microchannel. Subsequently the obtained temperature field is used to derive an expression for entropy generation rate. The effect of Knudsen number and Brinkman number on the entropy generation rate and Bejan number in different axial location is presented.