Temperature-dependent Heat Source Research Articles

MHD free and forced convection flow past an infinite vertical plate with heat source

An analytical study is performed to examine the effects of magnetic field and temperature-dependent heat source on the free and forced convection flow past an infinite vertical plate. The expressions for the velocity field, penetration distance and skin-friction have been obtained by Laplace transform technique. The influence of the various parameters entering into the problem is extensively discussed.

Free-convective flow of non-Newtonian fluid with heat sources

An analytical study is performed to examine the effects of temperature-dependent heat source on free-convective flow of non-Newtonian fluid (Walters's liquidB′). The expression for the velocity field has been obtained by the Laplace transform technique. The influence of the various parameter entering into the problem is extensively discussed.

MHD oscillatory flow through porous medium

In this work we present the effects of temperature-dependent heat source on hydromagnetic free-convection flow (set up due to temperature as well as species concentration) of an electrically-conducting incompressible viscous fluid past a steady moving vertical porous plate through high porous medium when the free stream oscillates in magnitude. The flow is subjected to a constant suction through the porous plate. As the mean steady flow has been presented gy Gholizadeh (1990), only the solution for the transient velocity profiles, transient temperature profiles, the skin-friction (steady+unsteady), and rate of heat transfer are presented in this work.

Role of magnetic field on transient forced and free-convection flow past an infinite vertical porous plate through porous medium with heat source

Effects of magnetic field and permeability of the porous medium on unsteady forced and free-convection flow past an infinite vertical porous plate in presence of temperature-dependent heat source have been analysed. The Laplace transform method is used to obtain the expression for velocity field, skin friction, and leading edge effects. During the course of discussion, the effects ofM (magnetic parameter),S (heat source parameter), λ (suction parameter), andK (permeability of porous medium) on velocity field, skin friction, and leading edge effect have been extensively discussed.

A two-dimensional nonlinear response matrix method with scattering and absorption-emission

Abstract A response matrix method is formulated for time-independent multi-dimensional, grey radiative transfer problems in which both scattering and absorption-emission are present and which are nonlinear as a result of temperature-dependent heat sources. The method is in sharp contrast to iterative techniques in which each iteration consists of a computation of the radiation intensity over the entire space-angle domain before the temperature field is updated. The nonlinear response matrix approach is unique in that within each spatial cell the temperature and outgoing radiation intensity are calculated in response only to the incoming radiation intensity. The updating of the temperature distribution therefore is placed within the iterative solution for the radiation intensity, rather than being placed outside of it. The method is implemented using the diamond-differenced discrete ordinate approximation and incorporated into one and two-dimensional computer codes utilizing standard red-black solution algorithms. Results are obtained for a number of problems both with fixed sources and with highly temperature-dependent combustion sources, the latter being characteristic of coal suspensions. Unaccelerated comparisons with standard discrete ordinate solution algorithms indicate improved efficiency to result from the response matrix method provided the spatial mesh is sufficiently coarse.

MHD oscillatory flow past a vertical porous plate through porous medium in the presence of thermal and mass diffusion with constant heat source

Effects of temperature-dependent heat source on hydromagnetic free-convection flow (set up due to temperature as well as species concentration) of an electrically-conducting incompressible viscous fluid past a steadily moving vertical porous plate through high porous medium has been analysed when the free stream oscillates in magnitude. The flow is subjected to a constant suction, through the porous plate. The mathematical analysis is presented for the hydromagnetic flow without taking into account the induced magnetic field. This is a valid assumption for small magnemtic Reynold number. Approximate analysis for the velocity and temperature field and their related quantities are obtained. The influence of various parameters entering into the problem is extensively discussed with the help of graphs and tables.

Modelling transient heat transfer through the skin and a contact material

Two thermal models of the skin and superficial tissues are described, both of which incorporate the thermal effects of subcutaneous and dermal blood flow through temperature-dependent heat sources. The model which represents the dermal blood flow as the perfusion of a region of finite thickness gives rise to purely numerical solutions for the transient temperatures. Representing the dermal blood flow by a heat generating surface gives rise to a model which yields explicitly analytical expressions. Although these analytical expressions require numerical integration techniques to finally evaluate them, they are of a form which allows temperature values to be derived more efficiently than by the purely numerical method. Both models are used to predict the time-dependent temperature profiles resulting with the skin surface. The predictions of the two models are compared and the limitations of the analytical model highlighted.

Treating exceptionally non‐linear temperature fields

AbstractBy some examples it is shown how to treat non‐everyday heat transfer problems which are characterized by temperature dependent heat sources and heat radiation.

Flow and heat transfer in a micropolar fluid past a flat plate with suction and heat sources

The laminar boundary layer flow of a micropolar fluid past a flat plate subject to uniform suction has been examined. The heat transfer study has been made in the presence of both constant as well as temperature dependent heat sources. The governing equations of momentum, first stress momentum and energy have been solved using numerical integration and Gauss-Seidel iterative procedure. For a particular value of suction parameter λ, as compared to the Newtonian fluid, the velocity decreases on increasing the value of micropolar parameter R. The skin friction and the Nusselt number have been calculated and presented in tables.

Numerical solution of free convection micropolar fluid flow between two parallel porous vertical plates

The fully developed free convection micropolar fluid flow between two vertical porous parallel plates is studied in the presence of temperature dependent heat sources including the effect of frictional heating. The basic equations are solved using quasi-linearization finite difference technique with an error of order 0.5 × 10 −6. The velocity, microrotation and temperature are displayed in graphs whereas the skin friction, couple stress and Nusselt numbers at the plates are shown in tables. It is noted that the couple stress on either plates increases numerically with increase in micropolar parameter. Also the Nusselt number follows the same pattern for a negative suction velocity.

Experiences in non‐linear analysis of temperature fields with finite elements

AbstractThis paper describes practical experiences in dealing with non‐linearities in temperature field calculations. First the use of the load vector for representing the heat radiation on the outer surfaces is reported. However, if there are also additional non‐linearities in the conductance matrix, then it may happen that because of possible counteractions of the non‐linearities no convergence is achieved, at least with the direct iteration. Therefore it is more appropriate to put the radiation terms into the conductance matrix where the other non‐linearities, such as temperature dependent thermal conductivity and natural convection also appear. It is shown how the Newton–Raphson iteration can be applied in an easy way. In the case of temperature dependent heat sources the load vector also needs to be considered. The appropriate special measures are described.

Effects of the external temperature-dependent heat sources on the unsteady free convective and mass-transfer hydromagnetic flow in the stokes problem

There have been considered the effects of external temperature-dependent heat sources and mass transfer on free convection flow of an electrically conducting viscous fluid past an impulsively starting infinite vertical limited surface in presence of a transverse magnetic field as considered. Solutions for the velocity and skin-friction, in closed form are obtained by using the Laplace transform technique and the results obtained for various values of the parametersSc (Schmidt number),M (Hartmann number), andS (Strength a Source or Sink) are given in graphical form. The paper is concluded with a discussion on the obtained results.

Temperature field of a plate with internal temperature-dependent heat source

The problem of asymmetric heating of a plate is considered in a medium with variable temperature in the presence of an internal heat source, the power of which is dependent on temperature and time.

Natural convection at a heated semiinfinite vertical plate with temperature dependent heat sources or sinks

Numerical results are presented for the transient and steady-state velocity field and the temperature field. These results were obtained by solving the partial differential equations describing the conservation of mass, momentum and energy by an explicit finite-difference method in time dependent form. It has been observed that the velocity componentsu, v (absolute) and the temperature0 have larger values in the presence of heat sources than in their absence. Opposite is the phenomenon in the presence of heat sinks. A worthwhile result obtained from the detailed examination of the problem is that the presence of heat sources delays the attainment of steady-state condition.

Laminar free convection heat transfer of a viscous incompressible heat generating fluid-flow past a vertical porous plate in the presence of free-stream oscillations. I

The problem noted in the title has been analysed to assess qualitatively the effect of temperature-dependent heat sources (sinks) on the flow and heat transfer. The flow and heat transfer characteristics have been found to depend on the heat source parameter α besides the other parametersG, E, P, m and ω. In Part I the mean parts of the fluid velocity and temperature have been presented and their behaviours discussed in depth. Here in Part II the fluctuating parts of the velocity and temperature and the transient velocity and temperature profiles have been derived and their behaviours discussed in detail along with the amplitudes and the phases of the skin friction and the rate of heat transfer at the wall. In general heat source parameter α has been found to delay the fluid flow reversal present in the case of air and to act as a catalyst (retarding) to the frequency parameter ω in augmenting (diminishing) the amplitude (phase) of the rate of heat transfer at the wall.

On the Feasibility of Obtaining Three-Dimensional Information From Thermographic Measurements

Despite its many advantages, thermography as a medical diagnostic tool has two basic limitations: 1 its images are indirect manifestations of interior thermal structure and hence do not yield explicit spatial information; 2 it is fundamentally two-dimensional. It is shown in the present paper that the three-dimensional variations of the temperature-dependent volume heat source, often called the blood perfusion term in the bio-heat equation, can be extracted from time dependent thermographic observations. On the other hand, spatial variations of the metabolic healing term cannot be determined from a similar procedure. Numerical experiments are performed to explore the sensitivity of the technique in determining the magnitude and location of a hypothetical lesion. Limitations of the technique in terms of the thermal penetration depth and signal-to-noise ratio are also examined.

On laminar free convection stagnation heat transfer from an isothermal cylinder with internal sources-sinks

An analysis of the laminar free convection stagnation heat transfer from an isothermal horizontal cylinder with internal sources and/or sinks within the fluid is presented. Solutions are given for two cases: one in which only the x-direction momentum equation is used and the other in which the two dimensional Navier-Stokes equations are combined into one momentum equation which makes the heat transfer variable θ′(0) and the velocity and temperature profiles to be determined as explicit functions of the Grashof number. Heat transfer results are obtained for Prandtl number of 0.72. Two temperature dependent heat source functions are investigated. It is found that the consideration of the second momentum equation has a moderate but significant effect on the heat transfer results.

Combined Natural and Forced Convection Hydromagnetic Flow in Vertical Channels

AbstractThe combined natural and forced convection fully developed flow and heat transfer of an electrically conducting fluid with and without temperature dependent heat sources in a vertical channel has been studied under the influence of transverse applied magnetic field and external circuit. The two plane walls of the channel are having the same temperature gradient along their lengths but both are art different temperatures. The system of non‐linear integro‐differential equations have been solved by an iteration method and the shearing stress and Nusselt number at the walls have been calculated. It has been found that the temperature dependent heat sources impose oscillatory behaviour on the temperature profiles and the heat transfer between the wall and the adjacent fluid changes its direction for different ranges of values of the heat source per unit volume. The magnetic field reduces the velocity but increases the temperature and the presence of linear variation of the wall temperature helps in cooling the walls.

Heat transfer in multi-layered media with temperature dependent sources

The paper describes a theoretical investigation of heat transfer in stratified horizontal slab and spherical shell containing temperature dependent heat sources. The desired expressions of temperatures contain only ordinary functions suitable for high speed computation. The results can find applications in defining the local and global temperature distributions in the earth's crust.

Heat Transfer in the Presence of Temperature Dependent Heat Sources in the Flow over a Flat Plate with Suction

Heat Transfer in the Presence of Temperature Dependent Heat Sources in the Flow over a Flat Plate with Suction