Variable heat flux effect on magnetohydrodynamic flow and heat transfer over an unsteady stretching sheet in the presence of thermal radiation

The unsteady laminar magnetohydrodynamic flow over an unsteady stretching sheet in the presence of thermal radiation and variable heat flux is investigated. The governing time-dependent boundary layer equations are transformed into ordinary differential equations containing a radiation parameter, space index parameter, time index parameter, Prandtl number, magnetic parameter, and unsteadiness parameter. These equations are solved numerically by applying the Chebyshev spectral method. The velocity profiles, temperature profiles, the skin friction coefficient, and the dimensionless surface temperature are computed and discussed in detail for various values of the different parameters. It is found that increasing the unsteadiness parameter leads to a fall for both the velocity and temperature distribution. Moreover, the temperature increases with the magnetic parameter, but the reverse is true for the velocity distribution. Likewise, the temperature decreases for increasing both values of space index parameter and time index parameter.