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The present work focuses on the convection flow of a Bingham liquid in a circular pipe with permeable wall using nonlinear density temperature variation (NDT) relationship. The novelty of this communication is to study the impression of yield stress, NDT parameter on convective flow of Bingham liquid in a circular pipe with heat source. The governing flow equations are nonlinearly coupled and therefore complex to solve. Hence, perturbation method is applied to transform into linear ordinary differential equation to obtain the velocity and temperature fields. The expressions for velocity, plug flow velocity, temperature, plug flow temperature and heat transfer rate are derived. The outcomes of heat source parameter, permeable parameter, slip parameter and yield stress parameter on the fluid momentum and dimensionless temperature are obtained. The velocity field decreases with increase in yield stressand for negative values of NDT parameter. The increase in the NDT parameterincreases the rate of heat transfer. When the yield stressand permeability parameter, our results concur with [Bhargava, R., and R. S. Agarwal. 1979. “Fully Developed Free Convection Flow in a Circular Pipe.”  Indian Journal of Pure and Applied Mathematics  10 (3): 357–365]. The results obtained for the flow characteristics reveal many interesting behaviours that warrant further investigation on the non-Newtonian fluid phenomena and NDT variation.

Fully developed free convective flow of a Bingham fluid in a circular pipe with permeable wall