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The heat transfer characteristics of a viscous liquid film flow over an unsteady stretching sheet subject to variable heat flux are investigated numerically. The effect of thermal radiation applying to an optically thick medium is also considered. The governing boundary layer equations are transformed into a set of nonlinear ordinaiy differential equations using an efficient fifth-order step-adapted Runge-Kutta integration scheme together with Newton-Raphson method. The dimensionless temperature is plotted for various governing parameters; say, unsteadiness parameter, effective Prandtl number, distance index, as well as time index. It is found that the heat transfer aspects are strongly influenced by the relevant parameters.

In this study, the effect of magnetic field, viscous dissipation, nonuniform heat source, and/ or sink and thermal radiation onflow and heat transfer in a hydromagnetic liquid film over an unsteady stretching sheet with prescribed heat flux condition is investigated. The governing equations are transformed into a set of ordinary differential equations with six free parameters by using a similarity transformation before being solved numerically. The temperature profiles depending on the governing parameters are displayed in graphical form and the relevant thermal characteristics are depicted in tabular representation. It is found that the dimensionless temperature profile, sheet temperature, and free surface temperature, with a specific unsteadiness parameter, are enhanced as the increase in magnetic parameter, Eckert number, space-and temperature-dependent parameters, and they are reduced for increasing effective Prandtl number.

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Convective flow and heat transfer in an inclined channel bounded by two rigid plates is studied, where the lower plate is fixed and upper plate is moving with a constant velocity. One of the regions filled with clear viscous fluid and the other region filled with the porous matrix saturated with a viscous fluid different from the fluid in the first region are considered. The coupled nonlinear equations are mainly solved numerically using finite difference method. It is found that the presence of porous matrix in one of the region reduces the velocity and temperature. Both the velocity and temperature profiles enhance as the values of buoyancy parameter GP, height ratio h, Brinkman number Br, density ratio n and thermal expansion ratio b increase but reduce as the values of porous parameter , viscosity ratio  and thermal conductivity ratio  T increase. The Nusselt numbers at upper plate diminish as GP, h and Br increase, whereas they increase as ,  and  T increase. The lower plate Nusselt numbers are reversely affected by the relevant parameters. The effect of  and GP on shear stress profiles are drawn and discussed.