An analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two paral... more An analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM) and compared with the direct numerical solution (NS). Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its si...
This chapter contains sections titled: Introduction Fins with Tip Heat Loss Nonuniform Heat Trans... more This chapter contains sections titled: Introduction Fins with Tip Heat Loss Nonuniform Heat Transfer Coefficients Fins with Internal Heat Generation Polygonal Fins Closure Nomenclature IntroductionFins with Tip Heat LossNonuniform Heat Transfer CoefficientsFins with Internal Heat GenerationPolygonal FinsClosureNomenclature
This chapter contains sections titled: Introduction Evaporation Boiling Performance of a Single C... more This chapter contains sections titled: Introduction Evaporation Boiling Performance of a Single Cylindrical Spine Optimum Dimensions for the Cylindrical Spine Minimum Mass Spine Extended Surfaces in Moist Air Nomenclature IntroductionEvaporationBoilingPerformance of a Single Cylindrical SpineOptimum Dimensions for the Cylindrical SpineMinimum Mass SpineExtended Surfaces in Moist AirNomenclature
This chapter contains sections titled: Introduction Bond or Contact Resistance of High-Fin Tubes ... more This chapter contains sections titled: Introduction Bond or Contact Resistance of High-Fin Tubes Fin Efficiency Approximation Air-Fin Coolers Nomenclature IntroductionBond or Contact Resistance of High-Fin TubesFin Efficiency ApproximationAir-Fin CoolersNomenclature
This chapter contains sections titled: Introduction Plain Double-Pipe Exchanger Longitudinal Fin ... more This chapter contains sections titled: Introduction Plain Double-Pipe Exchanger Longitudinal Fin Double-Pipe Exchanger Heat Transfer Coefficients in Pipes and Annuli Pressure Loss in Pipes and Annuli Complete Design Series–Parallel Arrangements Multiple-Finned Double-Pipe Exchangers Closure Nomenclature IntroductionPlain Double-Pipe ExchangerLongitudinal Fin Double-Pipe ExchangerHeat Transfer Coefficients in Pipes and AnnuliPressure Loss in Pipes and AnnuliComplete DesignSeries–Parallel ArrangementsMultiple-Finned Double-Pipe ExchangersClosureNomenclature
This chapter contains sections titled: Introduction Condensation on Single Fins Dehumidification ... more This chapter contains sections titled: Introduction Condensation on Single Fins Dehumidification of Air on Fins Horizontal Integral-Fin Tubes Internally Finned Tubes Microfin Tubes Nomenclature IntroductionCondensation on Single FinsDehumidification of Air on FinsHorizontal Integral-Fin TubesInternally Finned TubesMicrofin TubesNomenclature
This chapter contains sections titled: Introduction Longitudinal Radiating Fin of Rectangular Pro... more This chapter contains sections titled: Introduction Longitudinal Radiating Fin of Rectangular Profile Longitudinal Radiating Fins of Trapezoidal and Triangular Profile Use of the Cascade Algorithm Longitudinal Radiating Fin with Constant-Temperature Gradient Parabolic Radiating Profiles Radial Radiating Fins Closure Nomenclature IntroductionLongitudinal Radiating Fin of Rectangular ProfileLongitudinal Radiating Fins of Trapezoidal and Triangular ProfileUse of the Cascade AlgorithmLongitudinal Radiating Fin with Constant-Temperature GradientParabolic Radiating ProfilesRadial Radiating FinsClosureNomenclature
This chapter contains sections titled: Introduction Heat Transfer and Flow Friction Data ε–Ntu Me... more This chapter contains sections titled: Introduction Heat Transfer and Flow Friction Data ε–Ntu Method Design of a Compact Heat Exchanger Nomenclature IntroductionHeat Transfer and Flow Friction Dataε–Ntu MethodDesign of a Compact Heat ExchangerNomenclature
This chapter contains sections titled: Introduction Extended Surface Heat Transfer Longitudinal F... more This chapter contains sections titled: Introduction Extended Surface Heat Transfer Longitudinal Fins Radial Fins Spines Nomenclature IntroductionExtended Surface Heat TransferLongitudinal FinsRadial FinsSpinesNomenclature
This chapter contains sections titled: Introduction Regular Fins and Spines Singular Fins and Spi... more This chapter contains sections titled: Introduction Regular Fins and Spines Singular Fins and Spines The Single Series Resistance The Single Shunt Conductance Closure Nomenclature IntroductionRegular Fins and SpinesSingular Fins and SpinesThe Single Series ResistanceThe Single Shunt ConductanceClosureNomenclature
A model based on the works of Buongiorno, which includes the effects of Brownian motion and therm... more A model based on the works of Buongiorno, which includes the effects of Brownian motion and thermophoresis, is used to develop the governing equations for convection in nanofluids. The analysis includes examples with water and ethylene glycol as the base fluids and nanoparticles of Cu and Al2O3. An assumption of zero nanoparticle flux is used at the surface of the plate to make the model more physically realistic. The model accounts for the effects of both Brownian motion and thermophoresis in the mass boundary condition. Using suitable transformations, the governing partial differential equations are converted into ordinary differential equations which are solved numerically. The dimensionless velocity, temperature, and concentration gradients are used in the second law analysis to determine heat and mass transfer rates. It is shown that the dimensionless entropy generation rate strongly depends upon the solid volume fraction of the nanoparticles, local Reynolds number, and group p...
ABSTRACT In the present article, an exercise has been devoted to establish an analytical model fo... more ABSTRACT In the present article, an exercise has been devoted to establish an analytical model for the determination of temperature distribution, fin efficiency and optimum design parameters of a porous moving fin which is losing heat by simultaneous convection and radiation to its surroundings. For the adaptation of this consideration, the governing equation becomes highly nonlinear. An analytical technique called Adomian decomposition method (ADM) is proposed for the solution methodology. The accuracy of the analytic solution is validated by using a numeric scheme called finite difference method. The results indicate that the numerical data and analytical approach are in agreement with each other. As the present study is an analytic, it is extended to the analysis for determination of optimum dimensions of said fin by satisfying either the maximization of rate of heat transfer for a given fin volume or by the minimization of fin volume for a desired heat transfer rate. The study is further extended to the porous fin in stationary condition and it is found that porous fin in moving condition transfers more heat than stationary condition. Investigation has also been made on solid moving fin to compare the outcomes of these parameters.
In this paper, viscous flow with a second-order slip condition over a permeable stretching surfac... more In this paper, viscous flow with a second-order slip condition over a permeable stretching surface is solved analytically. The current work differs from the previous studies in the application of a new second-order slip velocity model. The closed form solution reported is an exact solution of the full governing Navier-Stokes equations. The effects of slip and mass transfer parameters are discussed.
Some new exact analytical solutions are reported for heat transfer in an annular fin of rectangul... more Some new exact analytical solutions are reported for heat transfer in an annular fin of rectangular profile with coordinate dependent thermal conductivity. A power law type of dependence on radial coordinate is assumed. The analysis assumes a constant base temperature and an insulated tip. Solutions are developed for the temperature distribution, the heat transfer rate, the fin efficiency, and the fin effectiveness. These solutions appear in terms of Airy wave functions or modified Bessel functions or hyperbolic functions or power functions depending on the exponent of the power law variation. Numerical results are presented to illustrate the effect of coordinate dependent thermal conductivity on the thermal performance of the fin. Comparison of exact and results based on the average thermal conductivity model reveals that the latter is in error by as much as 56 percent in a specific situation. The fin model used here is applicable to some contemporary engineering applications where...
An analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two paral... more An analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM) and compared with the direct numerical solution (NS). Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its si...
This chapter contains sections titled: Introduction Fins with Tip Heat Loss Nonuniform Heat Trans... more This chapter contains sections titled: Introduction Fins with Tip Heat Loss Nonuniform Heat Transfer Coefficients Fins with Internal Heat Generation Polygonal Fins Closure Nomenclature IntroductionFins with Tip Heat LossNonuniform Heat Transfer CoefficientsFins with Internal Heat GenerationPolygonal FinsClosureNomenclature
This chapter contains sections titled: Introduction Evaporation Boiling Performance of a Single C... more This chapter contains sections titled: Introduction Evaporation Boiling Performance of a Single Cylindrical Spine Optimum Dimensions for the Cylindrical Spine Minimum Mass Spine Extended Surfaces in Moist Air Nomenclature IntroductionEvaporationBoilingPerformance of a Single Cylindrical SpineOptimum Dimensions for the Cylindrical SpineMinimum Mass SpineExtended Surfaces in Moist AirNomenclature
This chapter contains sections titled: Introduction Bond or Contact Resistance of High-Fin Tubes ... more This chapter contains sections titled: Introduction Bond or Contact Resistance of High-Fin Tubes Fin Efficiency Approximation Air-Fin Coolers Nomenclature IntroductionBond or Contact Resistance of High-Fin TubesFin Efficiency ApproximationAir-Fin CoolersNomenclature
This chapter contains sections titled: Introduction Plain Double-Pipe Exchanger Longitudinal Fin ... more This chapter contains sections titled: Introduction Plain Double-Pipe Exchanger Longitudinal Fin Double-Pipe Exchanger Heat Transfer Coefficients in Pipes and Annuli Pressure Loss in Pipes and Annuli Complete Design Series–Parallel Arrangements Multiple-Finned Double-Pipe Exchangers Closure Nomenclature IntroductionPlain Double-Pipe ExchangerLongitudinal Fin Double-Pipe ExchangerHeat Transfer Coefficients in Pipes and AnnuliPressure Loss in Pipes and AnnuliComplete DesignSeries–Parallel ArrangementsMultiple-Finned Double-Pipe ExchangersClosureNomenclature
This chapter contains sections titled: Introduction Condensation on Single Fins Dehumidification ... more This chapter contains sections titled: Introduction Condensation on Single Fins Dehumidification of Air on Fins Horizontal Integral-Fin Tubes Internally Finned Tubes Microfin Tubes Nomenclature IntroductionCondensation on Single FinsDehumidification of Air on FinsHorizontal Integral-Fin TubesInternally Finned TubesMicrofin TubesNomenclature
This chapter contains sections titled: Introduction Longitudinal Radiating Fin of Rectangular Pro... more This chapter contains sections titled: Introduction Longitudinal Radiating Fin of Rectangular Profile Longitudinal Radiating Fins of Trapezoidal and Triangular Profile Use of the Cascade Algorithm Longitudinal Radiating Fin with Constant-Temperature Gradient Parabolic Radiating Profiles Radial Radiating Fins Closure Nomenclature IntroductionLongitudinal Radiating Fin of Rectangular ProfileLongitudinal Radiating Fins of Trapezoidal and Triangular ProfileUse of the Cascade AlgorithmLongitudinal Radiating Fin with Constant-Temperature GradientParabolic Radiating ProfilesRadial Radiating FinsClosureNomenclature
This chapter contains sections titled: Introduction Heat Transfer and Flow Friction Data ε–Ntu Me... more This chapter contains sections titled: Introduction Heat Transfer and Flow Friction Data ε–Ntu Method Design of a Compact Heat Exchanger Nomenclature IntroductionHeat Transfer and Flow Friction Dataε–Ntu MethodDesign of a Compact Heat ExchangerNomenclature
This chapter contains sections titled: Introduction Extended Surface Heat Transfer Longitudinal F... more This chapter contains sections titled: Introduction Extended Surface Heat Transfer Longitudinal Fins Radial Fins Spines Nomenclature IntroductionExtended Surface Heat TransferLongitudinal FinsRadial FinsSpinesNomenclature
This chapter contains sections titled: Introduction Regular Fins and Spines Singular Fins and Spi... more This chapter contains sections titled: Introduction Regular Fins and Spines Singular Fins and Spines The Single Series Resistance The Single Shunt Conductance Closure Nomenclature IntroductionRegular Fins and SpinesSingular Fins and SpinesThe Single Series ResistanceThe Single Shunt ConductanceClosureNomenclature
A model based on the works of Buongiorno, which includes the effects of Brownian motion and therm... more A model based on the works of Buongiorno, which includes the effects of Brownian motion and thermophoresis, is used to develop the governing equations for convection in nanofluids. The analysis includes examples with water and ethylene glycol as the base fluids and nanoparticles of Cu and Al2O3. An assumption of zero nanoparticle flux is used at the surface of the plate to make the model more physically realistic. The model accounts for the effects of both Brownian motion and thermophoresis in the mass boundary condition. Using suitable transformations, the governing partial differential equations are converted into ordinary differential equations which are solved numerically. The dimensionless velocity, temperature, and concentration gradients are used in the second law analysis to determine heat and mass transfer rates. It is shown that the dimensionless entropy generation rate strongly depends upon the solid volume fraction of the nanoparticles, local Reynolds number, and group p...
ABSTRACT In the present article, an exercise has been devoted to establish an analytical model fo... more ABSTRACT In the present article, an exercise has been devoted to establish an analytical model for the determination of temperature distribution, fin efficiency and optimum design parameters of a porous moving fin which is losing heat by simultaneous convection and radiation to its surroundings. For the adaptation of this consideration, the governing equation becomes highly nonlinear. An analytical technique called Adomian decomposition method (ADM) is proposed for the solution methodology. The accuracy of the analytic solution is validated by using a numeric scheme called finite difference method. The results indicate that the numerical data and analytical approach are in agreement with each other. As the present study is an analytic, it is extended to the analysis for determination of optimum dimensions of said fin by satisfying either the maximization of rate of heat transfer for a given fin volume or by the minimization of fin volume for a desired heat transfer rate. The study is further extended to the porous fin in stationary condition and it is found that porous fin in moving condition transfers more heat than stationary condition. Investigation has also been made on solid moving fin to compare the outcomes of these parameters.
In this paper, viscous flow with a second-order slip condition over a permeable stretching surfac... more In this paper, viscous flow with a second-order slip condition over a permeable stretching surface is solved analytically. The current work differs from the previous studies in the application of a new second-order slip velocity model. The closed form solution reported is an exact solution of the full governing Navier-Stokes equations. The effects of slip and mass transfer parameters are discussed.
Some new exact analytical solutions are reported for heat transfer in an annular fin of rectangul... more Some new exact analytical solutions are reported for heat transfer in an annular fin of rectangular profile with coordinate dependent thermal conductivity. A power law type of dependence on radial coordinate is assumed. The analysis assumes a constant base temperature and an insulated tip. Solutions are developed for the temperature distribution, the heat transfer rate, the fin efficiency, and the fin effectiveness. These solutions appear in terms of Airy wave functions or modified Bessel functions or hyperbolic functions or power functions depending on the exponent of the power law variation. Numerical results are presented to illustrate the effect of coordinate dependent thermal conductivity on the thermal performance of the fin. Comparison of exact and results based on the average thermal conductivity model reveals that the latter is in error by as much as 56 percent in a specific situation. The fin model used here is applicable to some contemporary engineering applications where...
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