Thermal management through entire new development of slip condition in Oldroyd-B nanomaterial

• Magnetohydrodynamic flow of an Oldroyd-B nanomaterial over stretching boundary is addressed. • Correct velocity slip condition for an Oldroyd-B fluid is first time developed. • Innovative characteristics regarding Brownian diffusion, heat source and thermophoresis are discussed. Thermal management through rheological nanomaterial is influential in the heat exchangers, chemical reactions, automation and energy and cooling systems. Heat transfer investigation in flow by stretching boundary with slip condition has key role for material processing and thermal management situations. To our knowledge the correct velocity slip condition for an Oldroyd-B fluid is first time developed. Such consideration is vital for microfluidics. Specifically, the slip condition at boundary is useful for polymer process and development of microscale heat exchangers. Significance of thermal transport through Buongiorno's model is described. Energy equation with heat generation is discussed. Concentration expression is with chemical reaction of first order. Fluid is considered magnetohydrodynamic (MHD). Dimensionless ordinary differential systems are obtained. Numerical solutions by employing Newton built in-shooting scheme are arranged. Physical quantities for fluid flow, concentration and temperature are graphically examined. Physical interpretation of thermal and mass transport rates is organized. Higher magnetic field and retardation time Deborah number have reverse response for velocity. However, velocity field for slip variable and Deborah number for relaxation time has similar response. Thermal distribution for Prandtl number is different when compared with random motion variable. Thermal distribution augmentation is witnessed for thermophoresis and heat generation variables. Larger Schmidt number lead to decrease in concentration. Concentration has reverse impact for reaction and thermophoresis variables. Thermal and mass transport rates for Deborah number through relaxation and retardation times have opposite response.