The dual-phase-lag ( DPL ) heat conduction model was used to study transient free convection flow in vertical plates with isoflux and adiabatic thermal boundary conditions at one insulated wall. The DPL model expression was used to formulate the energy equation. The time-dependent governing equations are solved via the Laplace transform technique. Semi-analytical solutions for temperature, velocity, and skin friction are obtained through the inversion of solutions in the Laplace domain to the time domain by a numerical procedure called Riemann sum approximation. The effects of significant parameters on temperature and velocity are graphically and in tabular form. Also, the skin friction is presented in tabular form with the aid of the MATLAB program. It is imperative to give remark that, temperature decreases and increases before and after a critical ( C r ) point as thermal retardation time and Prandtl number increase with time. However, the converse was the case when τ q and Pr number increased at a fixed time. Also, velocity increases at a low Prandtl number and increases at a high Prandtl number as thermal retardation time increases. Conversely, the reverse was the case on velocity due to increased thermal relaxation time.

This work investigates the effect of Joule heating and viscous dissipation due to electric double layer (EDL) and electroosmotic effect on steady fully developed electromagnetohydrodynamic flow in a porous microchannel. Dimensionless formulations of the Poisson-Boltzmann, momentum, and energy equations are derived for the electric potential, velocity profile and temperature distribution in the microchannel. Exact solutions for the temperature distributions and velocity profile were obtained using the method of undeterminate coefficients. The Debye-Hückel linearization is used to get exact solution for the electric potential. The results showed that Brinkmann number ( Br ) , Joule heating parameter ( J ) , Debye-Hückel parameter ( Κ ) , Hartmann number ( M ) , electric field ( E z ) and suction/injection parameter ( S ) have a substantial impact on flow formation and heat transfer. Using MATLAB software, graphical simulations are provided in order to deliver a greater understanding of the influence of relevant parameters on the results achieved.