Numerical analysis of heat transfer and magnetohydrodynamic flow of viscoelastic Jeffery fluid during forward roll coating process

The steady-state laminar nonisothermal, incompressible viscoelastic fluid flows with the Jeffrey model between two counterrotating (same direction) rolls are studied analytically. The Jeffrey model is reduced to the Newtonian model after some appropriate modifications. The new dimensionless governing equations are acquired through suitable nondimensional values. The lubrication approximation theory is employed for the simplification of emerging equations. The exact expressions for pressure gradient, velocity, temperature, and flow rate are accomplished whereas some quantities of interest such as pressure, coating thickness, power transmitted by rolls to the fluid, and roll separation force are computed numerically by using a numerical method. The influence of emerging parameters such as the ratio of relaxation time to the retardation time lambda(1), magnetohydrodynamic (MHD) parameter M and Brinkman number Br on velocity profile, temperature profile, pressure gradient, pressure distribution, coating thickness, power input, and force of roll separation are presented numerically in a tabular way and specific outcomes are demonstrated graphically. The MHD acts as a regulatory parameter for various quantities of important interest, such as velocity, coating thickness, and temperature. It is worth noting that the coating thickness decreases as modified capillaries number is increased.