Increasing Biot Number Research Articles

Mixed convective heat and mass transfer analysis for peristaltic transport in an asymmetric channel with Soret and Dufour effects

The present investigation addresses the simultaneous effects of heat and mass transfer in the mixed convection peristaltic flow of viscous fluid in an asymmetric channel. The channel walls exhibit the convective boundary conditions. In addition, the effects due to Soret and Dufour are taken into consideration. Resulting problems are solved for the series solutions. Numerical values of heat and mass transfer rates are displayed and studied. Results indicate that the concentration and temperature of the fluid increase whereas the mass transfer rate at the wall decreases with increase of the mass transfer Biot number. Furthermore, it is observed that the temperature decreases with the increase of the heat transfer Biot number.

Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects

This paper investigates combined heat and mass transfer by mixed magneto-convective flow of an electrically conducting flow along a moving radiating vertical flat plate with hydrodynamic slip and thermal convective boundary conditions. The governing transport equations are converted into a system of coupled nonlinear ordinary differential equations with prescribed boundary conditions using similarity variables developed by Lie group theory. The transformed nondimensional boundary value problem is then solved numerically with MAPLE13 quadrature. Excellent correlation with previous nonmagnetic, no-slip studies is achieved. Surface shear stress function and local Nusselt number (heat transfer gradient at the wall) are increased with Richardson number, whereas local Sherwood number is found to initially decrease then subsequently increase. The “thermally thick” scenario (Biot number > 0.1) is investigated and increasing Biot number is observed to enhance shear stress function (skin friction), local Nusselt number, and local Sherwood number. Increasing thermal radiation flux increases thermal boundary layer thickness as does increasing the magnetic field effect. Increasing hydrodynamic slip parameter reduces skin friction but enhances local Nusselt and Sherwood numbers. The study has applications in high-temperature polymeric synthesis and magnetic field flow control.

Simultaneous effects of convective conditions and nanoparticles on peristaltic motion

This article models the peristaltic transport of viscous nanofluid in an asymmetric channel. The channel walls satisfy the convective conditions. Effects of Brownian motion and thermophoresis are taken into account. The relevant flow analysis is first modeled and then computed for the series solutions of temperature and concentration fields. Closed form expression of stream function is constructed. Plots are prepared for a parametric study reflecting the effects of Brownian motion, thermophoresis, Prandtl, Eckert and Biot numbers. It is seen that temperature is an increasing function of Brownian motion, thermophoresis, Eckert and Prandtl numbers. However temperature is found to decrease when Biot number increases. It is also observed that the nanoparticle volume fraction field has opposite results for Brownian motion and thermophoresis parameters. Heat transfer coefficient increases via Biot, Brownian, thermophoresis, Prandtl and Eckert parameters. It is also worth mentioning to point out that the trapping increases for channel width and it decreases when the flow rate is increased.

Natural convection and radiation in porous fins

Purpose – The purpose of this paper is to conduct a numerical study of the convection heat transfer in porous media by the homotopy analysis method (HAM). The geometry considered is that of a rectangular profile fin. The porous fin allows the flow to infiltrate through it and solid-fluid interaction takes place. This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The theory section addresses the derived governing equation. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed. The results suggest that the radiation transfers more heat than a similar model without radiation. The auxiliary parameter in the HAM is derived by using the averaged residual error concept which significantly reduces the computational time. The use of optimal auxiliary parameter provides a superior control on the convergence and accuracy of the analytic solution. Design/methodology/approach – This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed. Findings – The HAM has been successfully applied for the thermal performance of a porous fin of rectangular profile. Solutions are derived for three cases of tip condition: an infinitely long fin with tip in thermal equilibrium with the ambient, a finite fin with an insulated tip and a finite fin with a convective tip. The performance of the fin depends on three dimensionless parameters; porosity parameter Sh, radiation-conduction parameter G and a dimensionless temperature relating the ambient and base temperatures. The results show that the base heat flow increases when the permeability of the medium is high and/or when the buoyancy effect induced in the fluid is strong. The base heat flow is enhanced as the surface radiation or the tip Biot number increases. Research limitations/implications – The analysis is made for the Darcy's model. Non-Darcy effects will be investigated in a future work. Practical implications – The approach is useful in enhancing heat transfer rates. Originality/value – The results of the study will be interested to the researchers of the field of heat exchanger designers.

Mixed convective peristaltic transport in a vertical channel with Robin’s condition

This paper describes the mechanism of the mixed convective peristaltic flow of a viscous fluid in an asymmetric vertical channel. A new type of boundary conditions is introduced in which one wall is kept at a constant temperature, while a convective heat flux is taken on the other wall. The Boussinesq’s and long wavelength approximations are employed in the process of modelling. The problems associated with the fluid motion and heat transfer are solved and exact solutions have been obtained in the wave frame of reference. Effects of Biot number, Grashof number and source/sink parameter have been analyzed through graphs. It is observed that increasing Biot number decreases the temperature, whereas temperature increases with an increase in the values of source/sink parameter. The pressure drop decreases with ascending values of Biot number and descending values of source/sink parameter and Grashof number. The pressure gradient is less in magnitude in absence of buoyancy forces, convective heat exchange at the boundary and source/sink. An increase in Biot number and a decrease in source/sink parameter and Grashof number results an increase in the size of the left part of the bolus.

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

Scaling of Thermal Positioning in Microscale and Nanoscale Bridge Structures

Heat transfer in a thermally positioned doubly clamped bridge is simulated to obtain a universal scaling for the behavior of microscale and nanoscale bridge structures over a range of dimensions, materials, ambient heat transfer conditions, and heat loads. The simulations use both free molecular and continuum models to define the heat transfer coefficient, h. Two systems are compared: one doubly clamped beam with a length of 100 μm, a width of 10 μm, and a thickness of 3 μm, and a second beam with a length of 10 μm, a width of 1 μm, and a thickness of 300 nm, in the air at a pressure from 0.01 Pa to 2 MPa. The simulations are performed for three materials: crystalline silicon, silicon carbide, and chemical vapor deposition (CVD) diamond. The numerical results show that the displacement and the response of thermally positioned nanoscale devices are strongly influenced by ambient cooling. The displacement depends on the material properties, the geometry of the beam, and the heat transfer coefficient. These results can be collapsed into a single dimensionless center displacement, δ* = δk/q″αl2, which depends on the Biot number and the system geometry. The center displacement of the system increases significantly as the bridge length increases, while these variations are negligible when the bridge width and thickness change. In the free molecular model, the center displacement varies significantly with the pressure at high Biot numbers, while it does not depend on cooling gas pressure in the continuum case. The significant variation of center displacement starts at Biot number of 0.1, which occurs at gas pressure of 27 kPa in nanoscale. As the Biot number increases, the dimensionless displacement decreases. The continuum-level effects are scaled with the statistical mechanics effects. Comparison of the dimensionless displacement with the thermal vibration in the system shows that CVD diamond systems may have displacements that are at the level of the thermal noise, while silicon carbide systems will have a higher displacement ratios.

Augmentation of heat transfer in wall‐rooted‐fins systems

PurposeThe purpose of this work is to consider heat transfer inside wall‐rooted‐fins systems.Design/methodology/approachThe coupled two‐dimensional heat diffusion equations are nondimensionlaized and solved numerically using an iterative finite volume method. Approximate fine analytical solutions for various augmentation indicators are derived. Excellent agreement is obtained between the numerical and the analytical results. A parametric study including all of the involved dimensionless parameters is conducted and presented graphically. Accurate correlations are generated.FindingsIt is found that fin‐roots with large root lengths experience bi‐directional heat transfer rates. Moreover, the wall‐rooted‐fins system is found to possess an effectiveness that can be more than 60 percent above that with rootless fins at wall Biot numbers of unity order. This value is found to increase as the Biot number increases or as the wall‐to‐fin thermal conductivities and volumes ratios decrease. In addition, heat transfer rates through wall‐rooted‐fins systems can be more than 100 percent above those having uniform thermal conductivities. Eventually, the heat transfer coefficient between the fin‐roots and wall are derived, which is found to be independent on the wall thickness.Originality/valueFinally, this work paves a way for an effective passive method for augmenting heat transfer inside wall‐fins systems.

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 Hybrid Differential Transformation and Finite Difference Method on the Laser Heating Problem

A hybrid numerical technique which combines the differential transformation and finite difference approximation is employed to predict the laser heating problem. The energy transfer induced by laser irradiation in the solid is described by Fourier's law of conduction with an energy source modeled by Beer's law. The influences of convective boundary and dimensionless energy absorption at the surface are examined. It is found that at low Biot number, the peak temperature occurs at the surface. As the biot number increases, the location of the peak temperature moves inwards. In addition, the differential transformation results in a concise procedure than other integral transform methods.

Fouling behavior of coconut milk at pasteurization temperatures

Abstract Fouling by coconut milk at different heating temperatures (50–54.5 °C, 60–64.5 °C, and 70–74.5 °C) and at three volumetric flows (2,4 and 6 LPM) in a test section equipped with four flat plates was studied. Measurement of the overall heat transfer coefficient ( U ) and the compositions of deposit mass were completed in order to obtain fouling factors ( R f ) and an empirical model for the rate of increase of Biot number (∆ Bi /∆ t ) as a function of the temperature ( T ) and the flow ( F ). The results illustrated that the fouling factor increased, when the temperature fell due to a combination of chemical reaction fouling from proteins and precipitation fouling from fat. The fouling factor also increased, when the flow was lowered due to a slow rate of deposit removal introduced by small shear force. Combination of the two effects revealed that the effect of flow was less significant at higher temperatures. All results can be confirmed by an analysis of fouling compositions. At high temperature conditions, more denaturation of proteins resulted in less ability to entrap fat globules onto heating surface. The heat resistance was found decreasing with increasing temperature.

Forced convection of gaseous slip-flow in porous micro-channels under Local Thermal Non-Equilibrium conditions

Steady laminar forced convection gaseous slip-flow through parallel-plates micro-channel filled with porous medium under Local Thermal Non-Equilibrium (LTNE) condition is studied numerically. We consider incompressible Newtonian gas flow, which is hydrodynamically fully developed while thermally is developing. The Darcy–Brinkman–Forchheimer model embedded in the Navier–Stokes equations is used to model the flow within the porous domain. The present study reports the effect of several operating parameters on velocity slip and temperature jump at the wall. Mainly, the current study demonstrates the effects of: Knudsen number (Kn), Darcy number (Da), Forchheimer number (Γ), Peclet number (Pe), Biot number (Bi), and effective thermal conductivity ratio (KR) on velocity slip and temperature jump at the wall. Results are given in terms of skin friction (CfRe*) and Nusselt number (Nu). It is found that the skin friction: (1) increases as Darcy number increases; (2) decreases as Forchheimer number or Knudsen number increases. Heat transfer is found to (1) decreases as the Knudsen number, Forchheimer number, or KR increases; (2) increases as the Peclet number, Darcy number, or Biot number increases.

Dynamics of a thin film with temperature-dependent viscosity on a rotating disk

The thermal effects on the dynamics of an axisymmetric flow of a non-volatile incompressible viscous thin liquid film on a rotating disk due to viscosity variation depending exponentially on temperature are considered. The nonlinear evolution equation is solved numerically. The numerical results reveal that heating the film from below enhances the rate of thinning. The increase in Biot number increases the film thickness, when the film is heated from below. Further, the relative amount of fluid retained on the substrate decreases as the film is heated from below. The results are reversed for the case of a film which is cooled from below. The rate of thinning of the film is more (less) for the case of temperature dependent viscosity when the film is heated (cooled) from below than for the case of constant viscosity of the fluid.

EFFECT OF HEAT TRANSFER COEFFICIENT ERROR ON FREEZING TIME ESTIMATION METHODS

The freezing of food is one of the most significant applications of refrigeration. In order for freezing operations to be cost-effective, it is necessary to optimally design the refrigeration equipment. This requires estimation of the freezing times of foods. Numerous semi-analytical/empirical methods for predicting food freezing times have been proposed, all of which require knowledge of the surface heat transfer coefficient. The empirical nature of the surface heat transfer coefficient can introduce significant error in the freezing time calculation. Therefore, a sensitivity analysis was performed on various freezing time estimation methods to determine the impact of errors in the heat transfer coefficient upon the calculated freezing times. A condition number was defined which allows for the quantification of the error in the calculated freezing time due to error in the heat transfer coefficient. Condition numbers were determined for seven common freezing time estimation methods applicable to regularly shaped food items. For these freezing time estimation methods, the sensitivity to errors in the heat transfer coefficient decreases as the Biot number increases. In addition, for Biot numbers greater than one half, these seven freezing time estimation methods were found to attenuate error in the heat transfer coefficient, thus resulting in smaller error in the calculated freezing time.

Thermocapillary Convection in Liquid Bridges with Undeformable Curved Surfaces

Thermocapillary convection in differentially heated cylindrical liquid bridges is investigated by two- and threedimensional numerical simulations. The nondeformable free surface is either e at or curved as determined by the e uid volume and the Young ‐Laplace equation. With Prandtl numbers of 1 and 4 and a e at surface, our computed results for onset of oscillations are in good agreement with linear theory. Convection is steady and axisymmetric at sufe ciently low values of Reynolds number with either e at or curved interfaces. Only steady convection is possibleat all Reynoldsnumbersconsidered in strictly axisymmetriccomputations. Transition to oscillatory threedimensional motions occurs as the Reynolds number increases beyond a critical value, dependent on the Prandtl number and liquid volume. Rotating waves with wave numbers of 1 or 2 are observed. The critical wave number depends on the Biot number. Heat loss from the free surface stabilizes the e ow, and the critical Reynolds number increases with increasing Biot number. With nonzero Biot number, two different branches can exist in the stability diagram. The numerical results are in reasonable agreement with experiments.

Thermal Stresses Owing to Convective Heating at Surface

Thermal stress wave generation and propagation inside solid substrates due to convective heating conditions at the surface find wide application in industry for the surface hardening and non-destructive testing of solid substrates. In the present study, analytical solutions for the temperature distribution and thermal stress wave generation during convective heating of a solid substrate are presented. A Laplace transformation method is used to obtain the closed form solutions. The resulting equations for temperature and thermal wave distributions are computed for a steel substrate. It is found that the thermal stress waves are compressive and the magnitude of stress increases as the Biot number increases. Moreover, the location of maximum stress moves away from the surface as the heating period progresses.

Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall

Double — diffusive natural convection in fluid saturated porous medium has been investigated using a generalised porous medium model. One of the vertical walls of the porous cavity considered is subjected to convective heat and mass transfer conditions. The results show that the flow, heat and mass transfer become sensitive to applied mass transfer coefficient in both the Darcy and non-Darcy flow regimes. It is also observed that the Sherwood number approaches a constant value as the solutal Biot number increases.

Oscillatory thermocapillary flow in a rectangular cavity

In this study, thermocapillary convection in a two-dimensional rectangular cavity with an upper, deformable free surface has been studied numerically. A wide range of values of the Marangoni number, Ma, is considered for the low Prandtl number fluid ( Pr = 0.01) with the aspect ratio ( A = height/length) fixed to be 0.5. The present computational results show that the thermocapillary flow may undergo an oscillatory motion when the Marangoni number is larger than a certain critical value, with a frequency of oscillation. If the Marangoni number is less than this critical value, the steady thermocapillary convection is obtained. The critical Marangoni number for the appearance of the oscillatory flow increases as the capillary number decreases and the Biot number increases.

A study on the behavior of a crack located at the striping zone in a thermally stratified pipe

The behavior of a small crack located at the thermal striping zone in a thermally stratified piping is numerically investigated. The effects of the parameters such as fluctuation frequency/ amplitude of the density interface, heat transfer coefficient near the thermal striping zone, and crack depth on the behavior of the crack are examined to identify the governing parameters. The effect of the contact surfaces on the stress intensity factor range is also examined for several levels of the internal fluid pressure. The stress intensity factor range, ΔK I , is used to describe the crack behavior due to the thermal striping. The findings of the numerical investigation are as follows: (1) the value of ΔK I increases up to a specific Fourier number and then decreases beyond the specific Fourier number. (2) With the increasing Biot number the value of ΔK I increases and the Fourier number(Fo) at which the ΔK I vs. Fo curve has a peak decreases. This means that the behavior of a crack located at the thermal striping zone has a large dependence on the oscillating frequency of the density interface and the heat transfer coefficients. (3) The value of ΔK I increases up to a specific crack depth and then decreases beyond the specific crack depth. (4) If the fluid pressure is lower than a specific value, the value of ΔK I decreases because of the crack surface contact.

Indicial response of the electric resistance thermometer composed of three concentric cylinders.

To account for the experimental characteristic of the Platinum electric resistance thermometer that it does not follow a first order system in usual meteorological conditions, the indicial response of a model for the electric resistance thermometer is obtained by analytically solving its thermal diffusion equation. The model is so simplified as to be composed of three infinite concentric cylinders, i.e., protector sheath, filling material and electric resistance element. The theoretical indicial response is evaluated for various model thermometers with different properties in the filling material. The major results are as follows: (1) over a certain Fourier number the indicial response can be approximated with one term of the exponential function C exp (-t/λ) including two parameters, coefficient C (>1) and exponent λ; (2) when the Biot number is small, the response speed hardly depends upon the inner structure. It becomes, however, sensitive to the thickness and thermal properties of the filling material as the Biot number increases; (3) the thermal properties of protector sheath and electric resistance element have little effect on the response speed, so long as the filling material is thermally insulating.