Heat Transfer To Power-law Fluids Research Articles

Convection Heat Transfer of Power-Law Fluids Along the Inclined Nonuniformly Heated Plate With Suction or Injection

A comprehensive analysis to convection heat transfer of power-law fluids along the inclined nonuniformly heated plate with suction or injection is presented. The effects of power-law viscosity on temperature field are taken into account in highly coupled velocity and temperature fields. Analytical solutions are established by homotopy analysis method (HAM), and the effects of pertinent parameters (velocity power-law exponent, temperature power index, suction/injection parameter, and inclination angle) are analyzed. Some new interesting phenomena are found, for example, unlike classical boundary layer problem in which the skin friction monotonically increases (decreases) with suction increases (injection increases), but there exists a special region where the skin friction is not monotonic, which is strongly bound up with Prandtl number, which have never been reported before. The nonmonotony occurs in suction region for Prandtl number Npr < 1 and injection region for Npr > 1. Results also illustrate that the velocity profile decreases but the heat convection is enhanced obviously with increasing in temperature power exponent m (generalized Prandtl number Npr has similar effects), the decreases in inclination angle lead to the reduction in convection and heat transfer efficiency.

Marangoni abnormal convection heat transfer of power-law fluid driven by temperature gradient in porous medium with heat generation

In this paper we investigate Marangoni convection heat transfer of power-law fluids in porous medium with heat generation. The convection is driven by a temperature gradient that the surface tension is a quadratic function of the temperature. A new heat transfer constitutive equation is proposed based on N-diffusion proposed by Philip and the abnormal convection–diffusion model proposed by Pascal in which we assume that the heat diffusion depends non-linearly on both the temperature and the temperature gradient with modified Fourier heat conduction for power-law fluid. The governing partial differential equations are reduced to ordinary differential equations by suitable similarity transformations. Approximate analytical solution is obtained using homotopy analytical method (HAM) which is compared with numerical ones for particular cases in good agreement. The transport characteristics of velocity and temperature fields are analyzed in detail.

Laminar MHD flow and heat transfer of power-law fluids in square microchannels

The steady fully developed laminar flow and heat transfer of electrically conducting non-Newtonian fluids through square microchannels at the presence of transverse magnetic field are investigated with emphasis on viscous dissipation and joule heating effects. The governing continuity, momentum and energy equations are being discretized using a finite difference approach using Modified Power-Law (MPL) model and have been solved iteratively, through Alternating Direction Implicit (ADI) scheme with successive over-relaxation under the classical boundary conditions of no-slip velocity and uniform constant heat flux for flow and thermal fields.The velocity, temperature profiles, product of friction factor–Reynolds number and Nusselt number are computed for various values of flow index and dimensionless shear rate parameter of modified power-law fluids. Also, the effect of Hartmann number and Brinkman number on velocity, temperature distributions and Nusselt number are discussed. It is shown that the results are in good agreement with the previous studies.

Unsteady Convective Heat Transfer of Power-Law Fluid with Variable Fluid Properties in a Concentric Annulus Originating from a Polymer Flooding Process

We study the unsteady convective heat transfer of power-law fluid with variable fluid properties in a concentric annulus with isothermal surface. The problem is originated from the polymer flooding process between a sucker rod and oil well. A new power-law rheological model is proposed, which takes the effects of temperature on fluid viscosity and thermal conductivity into account. Numerical solutions are presented for velocity and temperature fields using the Chebyshev spectral method coupled with the strong stability-preserving Runge–Kutta time discretization. The exponential convergence is verified by accuracy testing between a smooth exact solution of the Partial Differential Equations (PDEs) with source terms and the numerical approximation of manufactured solutions. It is found that heat transfer is enhanced in the variable power-law index model, and a decrease in power-law index of pseudoplastic fluids promotes heat transfer due to the increased Nusselt number. Moreover, the influences of other parameters on convective heat transfer behaviors are discussed in detail.

Forced Convection Heat Transfer in Power-Law Fluids Around a Semicircular Cylinder at Incidence

Two-dimensional steady flow and convective heat transfer of power-law fluids past a semicircular cylinder are investigated in the reported work. The heated semicircular cylinder is placed in an unconfined domain at different angles facing the incoming free-stream flow of power-law fluids having a generalized Prandtl number (Pr) = 100. Particular emphasis is given to studying the effect of angle of incidence (0 ≤ α ≤ 180°) on fluid dynamics and thermal transport around the semicircular object for varying Reynolds number (10 ≤ Re ≤ 40) and power-law index (0.4 ≤ n ≤ 1.8). A finite volume-based method is adopted for the numerical computation. The flow and heat transfer phenomena are visualized through the streamline and isotherm profiles at various operating conditions. Also, the pressure coefficient, drag coefficient, and Nusselt number on the surface of the object are presented and discussed.

Mixed Convection in Power-Law Fluids from a Heated Semicircular Cylinder: Effect of Aiding Buoyancy

Laminar aiding-buoyancy mixed-convection heat transfer in power-law fluids from a heated semicircular cylinder with its flat base facing the oncoming flow was studied in this work. The coupled momentum and energy equations were solved numerically over the following ranges of conditions: Richardson number (0 ≤ Ri ≤ 2), Reynolds number (0.1 ≤ Re ≤ 25), Prandtl number (1 ≤ Pr ≤ 100), and power-law index (0.3 ≤ n ≤ 1.8). Extensive results on the velocity and temperature fields are presented and discussed in terms of the streamline and isotherm contours adjacent to the heated object. Similarly, the distribution of the pressure coefficient and the local Nusselt number along the surface of the semicircular cylinder are analyzed to delineate the influence of the relevant dimensionless parameters listed above. Next, the pressure and total drag coefficient and surface average values of the Nusselt number describe the momentum and heat transfer aspects at the gross macroscopic level. Both the pressure and total drag coefficient exhibit the expected dependence on Richardson number, Prandtl number, and Reynolds number. Similarly, the average Nusselt number bears a positive dependence on each Richardson number, Prandtl number, and Reynolds number. Broadly, under otherwise identical conditions, heat transfer is augmented in shear-thinning fluids (n < 1) whereas it is somewhat impeded in shear-thickening fluids (n > 1) with reference to that in Newtonian fluids. Finally, the present numerical results of the average Nusselt number (recast in terms of the Colburn j H factor) were correlated as functions of the modified Reynolds number, Prandtl number, and power-law index thereby enabling its prediction in a new application.

Laminar Free Convection in Power-Law Fluids from a Heated Hemisphere

Extensive results are presented on the laminar free convection heat transfer in power-law fluids from a heated hemisphere in two orientations, namely, its flat base oriented upward (inverted) or downward (upright). The coupled field equations have been numerically solved over wide ranges of conditions as follows: Grashof number (), Prandtl number () and power-law index (). Detailed flow and temperature fields are visualized in terms of the streamline and isotherm contours, respectively. At the next level, the results are analyzed in terms of the total drag coefficient and local Nusselt number variation along the surface of the hemisphere, together with its surface averaged value. The average Nusselt number increases with both the Grashof and Prandtl numbers. Furthermore, for fixed values of the Grashof and Prandtl numbers, and for a given orientation, shear-thinning behavior () enhances the rate of heat transfer whereas shear-thickening () impedes it with reference to that in Newtonian fluids, especially when there is a reasonable degree of advection. Finally, the present numerical results of drag coefficient and Nusselt number have been correlated using a general composite parameter, which is essentially a modified Rayleigh number. The use of such a Rayleigh number also emphasizes the varying nature of dependence of the average Nusselt number on the Grashof and Prandtl numbers governed by the type of fluid behavior, i.e., shear-thinning () or shear-thickening ().

Effect of Orientation on the Steady Laminar Free Convection Heat Transfer in Power-Law Fluids from a Heated Triangular Cylinder

In this work, the influence of orientation on the steady laminar free convection heat transfer from a heated triangular cylinder (flat side facing downward and upward) in quiescent power-law fluids has been investigated. In particular, the coupled momentum and energy equations have been solved numerically over wide ranges of the relevant dimensionless parameters as: Grashof number (10 ≤ Gr ≤ 105), Prandtl number (0.72 ≤ Pr ≤ 100), and power-law index (0.3 ≤ n ≤ 1.8). The detailed flow and temperature fields in the vicinity of the heated cylinder are visualized in terms of the streamline and isotherm contours, respectively. At the next level, the influence of each of the governing parameters, namely, Grashof number (Gr), Prandtl number (Pr), and power-law index (n) on the local and average Nusselt number and drag coefficient, is examined. The flow separation was found to occur at high Grashof numbers and low Prandtl numbers, but only in shear-thickening and Newtonian fluids (n ≥ 1) for the cylinder orientated with its flat side facing upward. Over the range of conditions spanned here, for equal surface area, the rate of heat transfer and drag coefficient are always higher for the cylinder oriented with its flat side facing upward. Broadly speaking, over the range of conditions embraced here, shear-thinning fluid behaviour enhances heat transfer and shear-thickening impedes it. Finally, the present numerical values of the Nusselt number and drag coefficient have been correlated via a simple expression using a composite parameter consistent with the boundary layer analysis. Naturally, this parameter is more effective only at large values of the Grashof and Prandtl numbers, an assumption inherent in the boundary layer approximation.

Magnetohydrodynamics Thermocapillary Marangoni Convection Heat Transfer of Power-Law Fluids Driven by Temperature Gradient

This paper presents an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient. The surface tension is assumed to vary linearly with temperature and the effects of power-law viscosity on temperature fields are taken into account by modified Fourier law for power-law fluids (proposed by Pop). The governing partial differential equations are converted into ordinary differential equations and numerical solutions are presented. The effects of the Hartmann number, the power-law index and the Marangoni number on the velocity and temperature fields are discussed and analyzed in detail.

Natural convection in power-law fluids from two square cylinders in tandem arrangement at moderate Grashof numbers

In this work, free convective flow and heat transfer in power-law fluids from two heated square cylinders in tandem arrangement is studied. The governing differential equations have been solved numerically over wide ranges of Grashof number, 10 ≤ Gr ≤ 1,000, Prandtl number, 0.71 ≤ Pr ≤ 50 and power-law index, 0.4 ≤ n ≤ 1.8. In order to elucidate the extent of inter-cylinder interaction, the non-dimensional inter-cylinder spacing, L/d is varied in the range, 2 ≤ L/d ≤ 6. The results are interpreted in terms of streamline and isotherm contours in the proximity of two cylinders to gain physical insights into the nature of flow. At the next level, the distribution of the local Nusselt number along the surface of the cylinders is presented. At the minimum inter-cylinder spacing due to the intense interference, the downstream cylinder contributes much less to the overall heat transfer whereas it experiences much higher hydrodynamic drag than the upstream cylinder. Broadly, the local and average Nusselt number for both cylinders show a positive dependence on both Grashof and Prandtl numbers. Also, all else being equal, shear-thinning fluid behaviour promotes the rate of heat transfer and shear-thickening fluid behaviour impedes it. Finally, the present numerical results have been correlated by using simple forms of equations thereby enabling the estimation of Nusselt number in a new application.

Variable viscosity and slip velocity effects on the flow and heat transfer of a power-law fluid over a non-linearly stretching surface with heat flux and thermal radiation

The flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching surface has been studied numerically under conditions of constant heat flux and thermal radiation and evaluated for the effect of wall slip. The governing partial differential equations are transformed into a set of coupled non-linear ordinary differential equations which are using appropriate boundary conditions for various physical parameters. The remaining set of ordinary differential equations is solved numerically by fourth-order Runge–Kutta method using the shooting technique. The effects of the viscosity, the slip velocity, the radiation parameter, power-law index, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.

Effects of inclination angle on the steady flow and heat transfer of power-law fluids around a heated inclined square cylinder in a plane channel

The incompressible Poiseuille flow and heat transfer of a power-law fluid across an inclined long square cylinder confined in a two-dimensional channel is investigated numerically in the steady laminar flow regime. The effects of inclination angle, α, and power-law index, n, on the non-dimensional pumping power and the Nusselt number are studied for the conditions: 1 ⩽ Re ⩽ 40, 0 ⩽ α ⩽ 45, 0.4 ⩽ n ⩽ 1.8, Pr = 50 and blockage ratio β = 1/4. It is verified that the flow is steady in these ranges of conditions and the vortex shedding occurs only for n = 0.4 and α = 45 at Re ⩾ 33. In the steady flow regime the results show that the total drag coefficient on the cylinder increases with an increase in the power-law index and the maximum total lift coefficient occurs at α = 15. Moreover, a decrease in the power-law index and/or an increase in the inclination angle increase the Nusselt number and decrease the non-dimensional local pumping power. Simple correlations are also introduced for drag coefficient, local pressure drop and Nusselt number as functions of n, α and Re.

Simultaneous Effects of MHD and Thermal Radiation on the Mixed Convection Stagnation-Point Flow of a Power-Law Fluid

Magnetohydrodynamic (MHD) mixed convection stagnation-point flow and heat transfer of power-law fluids towards a stretching surface is investigated. The homotopy analysis method (HAM) is used in finding the series solution for a nonlinear problem. Closed form solutions for velocity and temperature fields are presented in the limiting cases. Graphical results are shown. It is found that velocity and temperature are decreasing functions of power law index. Numerical computations for shear stress coefficient and local Nusselt number are reported. The present results are also compared with the existing numerical solution in a limiting sense.

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in power-law fluids in the steady flow regime

The continuity, momentum and energy equations describing the flow and heat transfer of power-law fluids over a semi-circular cylinder have been solved numerically in the two-dimensional steady flow regime. The influence of the Reynolds number ( Re), Prandtl number ( Pr) and power-law index ( n) on the local and global flow and heat characteristics have been studied over wide ranges of conditions as follows: 0.01 ⩽ Re ⩽ 30, 1 ⩽ Pr ⩽ 100 and 0.2 ⩽ n ⩽ 1.8. The variation of drag coefficient and Nusselt number with the Reynolds number, Prandtl number and power-law index is shown over the aforementioned ranges of conditions. In addition, streamline and isotherm profiles along with the recirculation length and distribution of pressure coefficient and Nusselt number over the surface of the semi-circular cylinder are also presented to gain further insights into the nature of the underlying kinematics. The wake size (recirculation length) shows almost linear dependence on the Reynolds number ( Re ⩾ 1) for all values of power-law index studied herein. The drag values show the classical inverse variation with the Reynolds number, especially for shear-thinning fluids at low Reynolds numbers. The point of maximum pressure coefficient is found slightly displaced from the front stagnation point for highly shear-thinning fluids, whereas for shear-thickening and Newtonian fluids, it coincides with the front stagnation point. For fixed values of the Prandtl number and Reynolds number, the rate of heat transfer decreases with the gradual increase in power-law index; this effect is particularly striking at high Prandtl numbers due to the thinning of the thermal boundary layer. Conversely, as expected, shear-thinning behavior facilitates heat transfer and shear-thickening impedes it. The effect of power-law index on both momentum and heat-transfer characteristics is seen to be appreciable at low Reynolds numbers and it gradually diminishes with the increasing Reynolds number.

Laminar Forced Convection Heat Transfer from a Rotating Cylinder to Power-Law Fluids

Forced convection heat transfer from a heated cylinder rotating in streaming power-law fluids has been investigated in this work. The governing differential equations have been solved numerically to elucidate the influence of power law index (n = 0.2, 0.6, and 1), Prandtl number (1 ≤ Pr ≤ 100), Reynolds number (1 ≤ Re ≤ 40), and nondimensional rotational velocity (0 ≤ α ≤ 6) on the detailed temperature field, distribution of Nusselt number on the surface of the cylinder and on the mean Nusselt number. As expected, the mean Nusselt number shows positive dependence on both Reynolds and Prandtl numbers, which is obviously due to the gradual thinning of the boundary layer. Furthermore, the mean Nusselt number also conforms to the conventional scaling of Pr1/3 . For a non-rotating cylinder, all else being equal, shear-thinning facilitates heat transfer. This is also true for a rotating cylinder up to Re ∼ 1 and rotational velocity α ≤ 4 for all values of Prandtl number used in this work. As the Reynolds number is increased, though the main flow strengthens but anticlockwise rotation of the cylinder somewhat counters it. Thus, depending upon the values of the Re, α, and n, there is an envelope of conditions in which the rotation has a negative influence on heat transfer. Indeed, depending upon the values of the power-law index, α, Re, and Pr the rate of heat transfer from a rotating cylinder can reduce by up to 60–70% below the corresponding value for a non-rotating cylinder. Therefore, a judicious choice of parameters may be useful to regulate the rate of heat transfer in power-law fluids.

Steady flow and heat transfer of the power-law fluid over a rotating disk

This paper deals with the steady flow and heat transfer of a viscous incompressible power-law fluid over a rotating infinite disk. Assumed the thermal conductivity follows the same function as the viscosity, the governing equations in the boundary layer are transformed into a set of ordinary differential equations by generalized Karman similarity transformation. The corresponding nonlinear two-point boundary value problem was solved by multi-shooting method. Numerical results indicated that the parameters of power-law index and Prandtl number have significant effects on velocity and temperature fields. The thickness of the boundary layer decays with power-law index. The peak of the radial velocity changes slightly with power- law index. The values near the boundary are affected dramatically by the thickness of the boundary layer. With the increasing of the Prandtl number the heat conducts more strongly.

Numerical prediction of flow and heat transfer of power-law fluids in a plane channel with a built-in heated square cylinder

Structure of unsteady laminar flow and heat transfer of power-law fluids in two-dimensional horizontal plane channel with a built-in heated square cylinder is studied numerically. The governing equations are solved using a control volume finite element method (CVFEM) adapted to the staggered grid. Computations are performed over a range of Reynolds and Richardson numbers from Re = 20 to 200 and from Ri = 0 to 8, respectively at fixed Prandtl number Pr = 50 and blockage ratio value β′ = 1/8. Three different values of the power-law index ( n = 0.5, 1 and 1.4) are considered in this study to show its effect on the value of the critical Reynolds number defining the transition between two different flow regimes (symmetrical and periodic flows), the variations of Strouhal number, drag and lift coefficients and the heat transfer from the square cylinder as function of Reynolds number. Heat transfer correlations are obtained through forced convection. A discussion about the buoyancy effect on the flow pattern and the heat transfer for different power-law index is also presented.

Two-dimensional unsteady forced convection heat transfer in power-law fluids from a cylinder

Forced convection heat transfer characteristics of a cylinder (maintained at a constant temperature) immersed in a streaming power-law fluids have been studied numerically in the two-dimensional (2-D), unsteady flow regime. The governing equations, namely, continuity, momentum and thermal energy, have been solved using a finite volume method based solver (FLUENT 6.3) over wide ranges of conditions (power law index, 0.4 ⩽ n ⩽ 1.8; Reynolds number, 40 ⩽ Re ⩽ 140; Prandtl number, 1 ⩽ Pr ⩽ 100). In particular, extensive numerical results elucidating the influence of Reynolds number, Prandtl number and power-law index on the isotherm patterns, local and average Nusselt numbers and their evolution with time are discussed in detail. Over the ranges of conditions considered herein, the nature of flow is fully periodic in time. The heat transfer characteristics are seen to be influenced in an intricate manner by the value of the Reynolds number ( Re), Prandtl number ( Pr) and the power-law index ( n). Depending upon the value of the power-law index ( n), though the flow transits from being steady to unsteady somewhere in the range ∼33 < Re < 50, the fully periodic behavior is seen only beyond the critical value of the Reynolds number ( Re). As expected, the average Nusselt number increases with an increase in the values of Reynolds and/or Prandtl numbers, irrespective of the value of the flow behavior index. A strong influence of the power-law index on both local and time-averaged Nusselt numbers was observed. Broadly, all else being equal, shear-thinning behavior ( n < 1) promotes heat transfer whereas shear-thickening behavior ( n > 1) impedes it. Furthermore, this effect is much more pronounced in shear-thinning fluids than that in shear-thickening fluids.

Suction, viscous dissipation and thermal radiation effects on the flow and heat transfer of a power-law fluid past an infinite porous plate

This paper presents a study of the flow and heat transfer of an incompressible Ostwald de-Waele power-law fluid past an infinite porous plate, subject to suction at the plate. The power-law index n satisfies 0 < n < 1 (shear-thinning fluid only) provided that there is suction at the plate. Three cases are studied, namely, (i) the plate with constant surface temperature (CST case), (ii) the plate with prescribed surface temperature (PST case), and (iii) the plate with prescribed heat flux (PHF case). The effects of viscous dissipation and thermal radiation are also considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with various parameters are graphed and tabulated.

Fluid Flow and Heat Transfer in Power-Law Fluids Across Circular Cylinders: Analytical Study

An integral approach of the boundary layer analysis is employed for the modeling of fluid flow around and heat transfer from infinite circular cylinders in power-law fluids. The Von Karman-Pohlhausen method is used to solve the momentum integral equation whereas the energy integral equation is solved for both isothermal and isoflux boundary conditions. A fourth-order velocity profile in the hydrodynamic boundary layer and a third-order temperature profile in the thermal boundary layer are used to solve both integral equations. Closed form expressions are obtained for the drag and heat transfer coefficients that can be used for a wide range of the power-law index, and generalized Reynolds and Prandtl numbers. It is found that pseudoplastic fluids offer less skin friction and higher heat transfer coefficients than dilatant fluids. As a result, the drag coefficients decrease and the heat transfer increases with the decrease in power-law index. Comparison of the analytical models with available experimental/numerical data proves the applicability of the integral approach for power-law fluids.