A study on heat transfer in a second‐grade fluid through a porous medium with the modified differential transform method

This study investigates the boundary‐layer flow and heat transfer characteristics in a second‐grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM‐Padé. The DTM‐Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary‐layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM‐Padé with numerical solution (fourth‐order Runge–Kutta with shooting method) illustrates that the DTM‐Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030     

Flow and Heat Transfer of Maxwell Fluid Over an Exponentially Stretching Sheet: A Non‐similar Solution

In this investigation, the boundary layer flow and heat transfer analysis in a Maxwell fluid over an exponentially continuous moving sheet are studied. The transformed boundary layer equations are solved numerically for a non‐similar solution using a shooting method with the Runge–Kutta algorithm. The purpose of this article is to look into the influence of the Deborah number on the velocity, temperature, and Nusselt number. The obtained results show that an increase in the Deborah number decreases the fluid velocity and boundary layer thickness. On the other hand, it increases the temperature and thermal boundary layer thickness. It is also found that the numerical results are in excellent agreement with the previous existing results for the case of a Newtonian fluid (λ = 0). © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 233–242, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21074     

MHD boundary‐layer flow over a stretching surface with internal heat generation or absorption

This article is concerned with the steady laminar magnetohydrodynamic boundary‐layer flow past a stretching surface with uniform free stream and internal heat generation or absorption in an electrically conducting fluid. A constant magnetic field is applied in the transverse direction. A uniform free stream of constant velocity and temperature is passed over the sheet. The effects of free convection and internal heat generation or absorption are also considered. The governing boundary layer and temperature equations for this problem are first transformed into a system of ordinary differential equations using similarity variables, and then solved by a new analytical method and numerical method, by using a fourth‐order Runge–Kutta and shooting method. Velocity and temperature profiles are shown graphically. It is shown that the differential transform method solutions are only valid for small values of independent variables but the results obtained by the DTM‐Padé are valid for the entire solution domain with high accuracy. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21054     

Solving of boundary‐layer equations with transpiration effects,governance on a vertical permeable cylinder using modified differential transform method

The suction and injection effects on the free convection boundary‐layer flow over a vertical cylinder are studied. The main stream velocity and wall temperature are proportional to the axial distance along the surface of the cylinder. Both analytic and numerical solutions of the arising mathematical problem are obtained. An analytic solution is derived by a new analytical method (DTM‐Padé) and numerical solutions have been performed by using a fourth‐order Runge–Kutta and shooting methods. Velocity and temperature profiles are shown graphically. It is shown that the differential transform method (DTM) solutions are only valid for small values of the independent variable but the obtained results by DTM‐Padé are valid for the whole solution domain with high accuracy. These methods can be easily extended to other linear and nonlinear equations and so can be found widely applicable in engineering and sciences. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20366     

Double diffusive convection of a micropolar fluid saturated in a sparsely packed porous medium

This study examines the double diffusive convection of a sparsely packed micropolar fluid‐saturated porous medium by using a linear stability analysis. The Darcy–Brinkman–Forchheimer model is employed for the porous fluid layer. The stability criterion is sought analytically with the simple free‐free, iso‐thermal, and iso‐solutal boundary conditions. The dependence of stationary or oscillatory convection on the porous parameter, Lewis number, solutal Rayleigh number, and parameters involved in micropolar fluids is drawn and discussed. The results show that the critical wave number is found to be insensitive to the variation of governing parameters except for the porous parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21052     

Solution of nonlinear boundary layer equation for flat plate via optimal homotopy asymptotic method

In this article, we use the optimal homotopy asymptotic method (OHAM) to compute the solution of two‐dimensional incompressible laminar boundary layer flow over a flat plate (Blasius problem). The obtained results for the stream function and velocity profile were comparable in terms of accuracy with that obtained by Esmaeilpour and Ganji (2007) who studied the same problem using the homotopy perturbation method and results obtained by using a numerical method (RK4). The good agreement obtained shows the effectiveness of OHAM. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 197–203, 2014; Published online 19 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21070     

Thermal Radiation and Heat Source Effects on a MHD Nanofluid Past a Vertical Plate in a Rotating System with Porous Medium

This article studies the effect of thermal radiation on a MHD free convection flow of a nanofluid bounded by a semi‐infinite vertical plate with a constant heat source in a rotating frame of reference. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The dimensionless governing equations for this investigation are solved analytically using the regular perturbation method. The effect of various important parameters entering into the problem on velocity and temperature fields within the boundary layer are discussed for three different water‐based nanofluids such as Cu, Al₂O₃, and TiO₂ with the help of graphs. The predicted results clearly indicate that the presence of nanoparticles in the base fluid enhances the heat transfer process significantly. The present work shows the need for immediate attention in next‐generation solar film collectors, heat‐exchanger technology, material processing exploiting vertical surface, geothermal energy storage, and all those processes which are greatly exaggerated by heat‐enhancement concepts. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21101     

Nonsimilar solutions for mixed convection of water at 4°C over a vertical surface with a convection boundary condition in a porous medium

A boundary layer analysis has been presented for the mixed convection of water at 4°C over a vertical plate embedded in a porous medium. The Robin or convective boundary condition at the surface has been considered where the heat lost from the surface is the product of a heat transfer coefficient and the temperature difference between the surface and the free stream. The governing non‐similar boundary layer equations for both the forced and free convection dominated regimes were solved numerically by means of an implicit finite difference method. The friction factor and dimensionless heat transfer rate (Nusselt number) are presented for several values of the dimensionless heat transfer coefficient and buoyancy parameter. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21022     

Heat Transfer in a Casson Rheological Fluid from a Semi‐infinite Vertical Plate with Partial Slip

The laminar boundary layer flow and heat transfer of Casson non‐Newtonian fluid from a semi‐infinite vertical plate in the presence of thermal and hydrodynamic slip conditions is analyzed. The plate surface is maintained at a constant temperature. Increasing velocity slip induces acceleration in the flow near the plate surface and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in the Casson rheological parameter acts to elevate considerably the skin friction (non‐dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures, however, are very slightly decreased with increasing values of Casson rheological parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21115     

Unsteady MHD Mixed Convective Boundary‐Layer Slip Flow and Heat Transfer with Thermal Radiation and Viscous Dissipation

A numerical analysis has been carried out to investigate the problem of MHD boundary‐layer flow and heat transfer of a viscous incompressible fluid over a moving vertical permeable stretching sheet with velocity and temperature slip boundary condition. A problem formulation is developed in the presence of radiation, viscous dissipation, and buoyancy force. A similarity transformation is used to reduce the governing boundary‐layer equations to coupled higher‐order nonlinear ordinary differential equations. These equations are solved numerically using the fourth‐order Runge–Kutta method along with shooting technique. The effects of the governing parameters such as Prandtl number, buoyancy parameter, slip parameter, magnetic parameter, Eckert Number, suction, and radiation parameter on the velocity and temperature profiles are discussed and shown by plotting graphs. It is found that the temperature is a decreasing function of the slip parameter S_T. The results also indicate that the cooling rate of the sheet can be improved by increasing the buoyancy parameter. In addition the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form. The numerical results are compared and found to be in good agreement with previously published results on special cases of the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 412–426, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21086     

Computational modeling and analysis of thermal characteristics of a rotating spacecraft subjected to solar radiation

This paper presents a computational modeling for the temperature distribution of a rotating thick‐walled cylindrical spacecraft subjected to solar radiation. The inner surface of the spacecraft is thermally insulated while the outer surface is subjected to concurrent events of solar incidence and radiative heat dissipation to space. The governing equation for the normalized temperature is discretized using a finite difference scheme and Successive Line Over‐Relaxation (SLOR) is used to solve the resulting system of algebraic equations. Numerical simulations of temperature distribution on the spacecraft for different spinning speeds, angular positions, and different radii are discussed and evaluated for both linearized and nonlinear boundary conditions. Comparative analysis between the computational modeling and the exact analytical solution for the linearized boundary condition is presented. The results indicate that the outer surface temperature distribution of the spacecraft is nearly independent of the angular position; at sub‐cylindrical surface, this independence is achieved at low angular velocity. Moreover, numerical simulations show that the use of the linearized boundary condition at the outer surface presents a good approximation for the case of high‐speed spinning spacecrafts, while it results in significant errors in the temperature field in the case of stationary and low‐speed spinning spacecrafts. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20368     

Mixed Convection Over a Vertical Plate in a Doubly Stratified Fluid‐Saturated Non‐Darcy Porous Medium with Cross‐Diffusion Effects

The present article investigates the influence of Dufour and Soret effects on mixed convection heat and mass transfer over a vertical plate in a doubly stratified fluid‐saturated porous medium. The plate is maintained at a uniform and constant wall heat and mass fluxes. The Darcy–Forchheimer model is employed to describe the flow in porous medium. The nonlinear governing equations and their associated boundary conditions are initially transformed into dimensionless forms. The resulting system of nonlinear partial differential equations is then solved numerically by the Keller‐box method. The variation of the dimensionless velocity, temperature, concentration, heat, and mass transfer rates for different values of governing parameters involved in the problem are analyzed and presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21114     

Analytical and numerical investigation of fin efficiency and temperature distribution of conductive,convective, and radiative straight fins

In this study, fin efficiency, temperature distribution, and effectiveness of conductive, convective, and radiative straight fins with temperature dependent thermal conductivity are solved using the differential transformation method (DTM).The concept of differential transformation is briefly introduced, and then it is employed to derive the solutions of nonlinear governing equations of fins with highly nonlinear terms because of existing radiation in this study. The obtained results of DTM are compared with those of the Galerkin method (GM) and numerical boundary value problem method (BVP) to verify the accuracy of the proposed method. Furthermore, the effects of some physical appropriate parameters such as thermo‐geometric fin parameters and thermal parameters are analyzed. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20341     

MHD Flow and Heat Transfer of a Dusty Fluid Over a Stretching Hollow Cylinder with a Convective Boundary Condition

In this study, we deal with the problem of a steady two‐dimensional magnetohydrodynamic (MHD) flow of a dusty fluid over a stretching hollow cylinder. Unlike the commonly employed thermal conditions of constant temperature or constant heat flux, the present study uses a convective heating boundary condition. The multi‐step differential transform method (multi‐step DTM), one of the most effective methods, is employed to find an approximate solution of the system of highly nonlinear differential equations governing the problem. Comparisons are made between the results of the proposed method and the numerical method in solving this problem and excellent agreement has been observed. The influence of important parameters on the flow field and heat transfer characteristics are presented and discussed in detail. The results show that both the thermal boundary layer thickness and the heat transfer rate at the wall increases with increasing Biot number Bi, while it has no effect on the skin friction coefficient. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 221–232, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21073     

Optimal homotopy asymptotic method for heat transfer in hollow sphere with robin boundary conditions

In this article, we have investigated heat transfer from a hollow sphere using a powerful and relatively new semi‐analytic technique known as the optimal homotopy asymptotic method (OHAM). Robin boundary conditions are applied on both the inner and outer surfaces. The effects of Biot numbers, uniform heat generation, temperature‐ dependent thermal conductivity, and temperature parameters on the dimensionless temperature and heat transfer are investigated. The results of OHAM are compared with a numerical method and are found to be in good agreement. It is shown that the dimensionless temperature increases with an increase in Biot number at the inner surface and temperature and heat generation parameters, whereas it decreases with an increase in the Biot number at the outer surface and the dimensionless thermal conductivity and radial distance parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 124‐133, 2014; Published online 20 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21067     

Theoretical Evaluation of a 10‐Watt Cooling Power Thermoacoustic Refrigerator

This article deals with the design, simulation, and analysis of a 10‐watt capacity thermoacoustic refrigerator using short‐stack boundary layer approximation assumptions and dimensional normalization technique. The variation of stack diameter with average gas pressure and cooling power is studied. The theoretical evaluation of quarter‐wavelength and one‐fifth‐wavelength resonator using helium gas is discussed for an operating frequency ranging from 300–500 Hz in the steps of 50 Hz. For the optimized stack, a 38.5% improvement in the stack performance for a 10‐watt cooling power quarter‐wavelength hemispherical‐ended resonator operating at 350 Hz frequency resulted in a 13.5% improvement in the coefficient of performance (COP) compared to published results. The resonator design is tested with DeltaEC software with 2% and 3% drive ratios using helium, hydrogen, neon, air, and carbon dioxide as working gases and the results are discussed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 577–591, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21094     

Effects of physical parameters on natural convection in a solar collector filled with nanofluid

Solar energy is one of the best sources of renewable energy with minimal environmental impact. A numerical study has been conducted to investigate the natural convection inside a solar collector having a flat‐plate cover and a sine‐wave absorber. The water‐alumina nanofluid is used as the working fluid inside the solar collector. The governing differential equations with boundary conditions are solved by the penalty finite element method using Galerkin's weighted residual scheme. The effects of physical parameters on the natural convection heat transfer are simulated. These parameters include the number of wave λ and non‐dimensional amplitude A of the sinusoidal corrugated absorber. Comprehensive average Nusselt number, average temperature, and mean velocity field for both nanofluid and base fluid within the collector are presented as functions of the parameters mentioned above. Comparison with previously published work is made and found to be in excellent agreement. The numerical results show that the highest heat transfer rate is observed for both the largest λ and A. In addition, the design for enhancing the performance of the collector is determined by examining the above‐mentioned results. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21026     

Coupled heat and mass transfer by MHD free convection flow along a vertical plate with streamwise temperature and species concentration variations

The problem of steady, laminar, coupled heat and mass transfer by MHD free convective boundary‐layer flow along a vertical flat plate with the combined effects of streamwise sinusoidal variations of both the surface temperature and the species concentration in the presence of Soret and Dufour effects is considered. A suitable set of dimensionless variables is used to transform the governing equations of the problem into a non‐similar form. The resulting non‐similar equations have the property that they reduce to various special cases previously considered in the literature. An adequate and efficient implicit, tri‐diagonal finite difference scheme is employed for the numerical solution of the obtained equations. Various comparisons with previously published work are performed and the results are found to be in excellent agreement. A representative set of numerical results for the velocity, temperature, and concentration profiles as well as the surface shear stress, rate of heat transfer, and the rate of mass transfer is presented graphically for various parametric conditions and is discussed. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21033     

Heat transfer from hollow cylinder using optimal homotopy asymptotic method

Optimal homotopy asymptotic method (OHAM) is employed to investigate steady‐state heat conduction with temperature dependent thermal conductivity and uniform heat generation in a hollow cylinder. Analytical models are developed for dimensionless temperature distribution and heat transfer for two cases using mixed boundary conditions (Dirichlet, Neumann, and Robin). The inner cylinder is assumed to be insulated in both cases. In the first case, the outer cylinder is assumed to be isothermal whereas in the second case, the outer cylinder is convectively cooled by a fluid of temperature T₂ through a uniform heat transfer coefficient h. The effects of Biot number, dimensionless heat generation, and thermal conductivity parameters on the temperature distribution and heat transfer are determined analytically and validated numerically using MAPLE 14. In both cases, the results obtained by OHAM are found to be in good agreement with the numerical results. It is found that as the Biot number increases, the results approach that of the isothermal case. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20407     

Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet

In the present article, the transient rheological boundary layer flow over a stretching sheet with heat transfer is investigated, a topic of relevance to non‐Newtonian thermal materials processing. Stokes couple stress model is deployed to simulate non‐Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The nondimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter (), unsteadiness parameter (), Prandtl number (Pr), buoyancy parameter . The semi‐analytical differential transform method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built‐in solver “bvp4c” to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter, whereas it is decreased with unsteadiness parameter. Temperature is elevated with couple stress parameter, whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid), whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness, and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach.