Homogeneous flow model is used to study the flow and heat transfer of carbon nanotubes (CNTs) along a flat plate subjected to Navier slip and uniform heat flux boundary conditions. This is the first paper on the flow and heat transfer of CNTs along a flat plate. Two types of CNTs, namely, single-and multi-wall CNTs are used with water, kerosene or engine oil as base fluids. The empirical correlations are used for the thermophysical properties of CNTs in terms of the solid volume fraction of CNTs. For the effective thermal conductivity of CNTs, Xue (Phys B Condens Matter 368:302-307, 2005) model has been used and the results are compared with the existing theoretical models. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically using a very efficient finite difference method with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated and presented in graphical and tabular forms. The numerical results of skin friction and Nusselt numbers are compared with the available data for special cases and are found in good agreement.

This work theoretically examines the flow and heat transfer characteristics due to an exponentially stretching sheet in a Powell-Eyring fluid. Governing partial differential equations are nondimensionalized and transformed into non-similar forms. Explicit analytic expressions of velocity and temperature functions are developed by homotopy analysis method (HAM). The Numerical solutions are obtained by using shooting method with fourth-order Runge-Kutta integration technique. The fields are influence appreciably with the variation of embedding parameters. We noticed that the velocity ratio has a dual behaviour on the momentum boundary layer. On the other hand the thermal boundary layer thins when the velocity ratio is increased. The results indicate a significant increase in the velocity and a decrease in thermal boundary layer thickness with an intensification in the viscoelastic effects.

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This framework presents heat transfer analysis for swirling flow of viscoplastic fluid bounded by a permeable rotating disk. Problem formulation is made through constitutive relations of Bingham fluid model. Viscous dissipation effects are preserved in the mathematical model. Entropy production analysis is made which is yet to be explored for the von-Kármán flow of non-Newtonian fluids. Having found the similarity equations, these have been dealt numerically for broad parameter values. The solutions are remarkably influenced by wall suction parameter and Bingham number which measures the fluid yield stress. Akin to earlier numerical results, thermal boundary layer suppresses upon increasing wall suction velocity. Thermal penetration depth is much enhanced when fluid yield stress becomes large. Higher heat transfer rate can be accomplished by employing higher suction velocity at the disk. However, deterioration in heat transfer is anticipated as fluid yield stress enlarges. Current numerical results are in perfect line with those of an existing article in limiting sense.

Locally similar solutions are developed for aiding or opposing MHD flow near stagnation-point on a vertical stretchable surface immersed in a generalized Newtonian fluid obeying Cross rheology equation. Heat transfer problem is resolved by assuming a linear surface temperature distribution. Furthermore, fluid having variable thermal conductivity is treated. By choosing the usual transformations, the governing equations of fluid motion and energy transfer are changed into similar forms. The structure of boundary layer is controlled by a parameter measuring the ratio of free stream velocity to the wall velocity. Numerical computations are performed to address the influences of Cross fluid parameters on mean physical quantities. In particular, shear thinning character of Cross fluid is visible from the obtained simulations. Computations are found in perfect line with those of the existing literature. The physical outcomes concerning the effects of embedded parameters on wall drag coefficient and heat transfer rates are also explained in detail.

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Stokes' first problem is studied to investigate the effects of nanofluid parameters on momentum, heat and mass transfers using the Buongiorno model. The experimental correlations for the properties of nanofluids are incorporated in the governing equations. A similarity analysis is performed to generate a set of ordinary differential equations describing the momentum, energy and mass transfers in the flow. These equations are solved numerically using the Runge-Kutta-Fehlberg method, which produces a fifth-order accurate solution. The numerical results are compared with the exact solutions for the regular fluids in the absence of nanofluid parameters and are found to be in good agreement. The results for the dimensionless velocity, temperature, wall shear stress, Nusselt and Sherwood numbers are presented graphically and compared for water-based nanofluids with ethylene-glycol-based nanofluids.