Temperature-dependent viscosity effects on heat transfer characteristics of grade three fluid in electromagnetohydrodynamic flow between large parallel plates maintained at uniform temperatures

Heat transfer characteristics in the electromagnetohydrodynamic flow of a third-grade fluid between parallel plates have already been examined by researchers, but studies on the effect of temperature-dependent viscosity on velocity, temperature, and heat transfer coefficients are very few. The present study investigates the heat transfer behavior of a third-grade fluid flow between large parallel plates, taking temperature-dependent viscosity when magnetic and electric fields are imposed externally. The plate walls are subjected to uniform temperatures. Consideration of temperature-dependent viscosity results in the formulation of the phenomenon by nonlinear, coupled differential equations, which are solved by applying the least-square method (LSM). Solving coupled, nonlinear equations by the LSM requires a great deal of modification in the implementation process. The obtained results in terms of dimensionless velocity are validated with the results of earlier studies and are also in a close match with the results of the Adomian decomposition method of the current study. Results indicate that for a higher value of the viscosity parameter, at first, velocity increases with an increase in the non-Newtonian parameter. Beyond a certain value of the non-Newtonian parameter, velocity starts reducing. Temperature, at all points of any cross-section, increases up to a certain non-Newtonian parameter and then reduces with the rise in the same parameter. For higher values of the viscosity parameter and low non-Newtonian parameters, the upper plate requires an enhanced rate of cooling. Whereas, for higher values of the non-Newtonian parameter at higher viscosity parameters, a lower heating rate is required. The results of the mathematical model can serve to be useful in the field of liquid metal flows in metallurgical industry, micropumps, medical and biological sectors, and microelectromechanical applications.