Modeling Transient Heat Transfer Through the Skin and Superficial Tissues—1: Surface Insulation

1986 ◽  
Vol 108 (2) ◽  
pp. 183-188 ◽  
Author(s):  
D. A. Hodson ◽  
G. Eason ◽  
J. C. Barbenel
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Transient Heat Transfer ◽  
Transient Problem ◽  
Finite Slab ◽  
Infinite Slab ◽  
Flow Through ◽  
Superficial Tissues

Two models of transient heat transfer through the skin and superficial tissues are presented. One model comprises a finite slab and semi-infinite slab, representing the epidermis and subdermal tissues, respectively, and a heat-generating interface representing the thermal effect of blood flow through the dermis. A model is also considered where the three tissue regions are represented more conventionally by three finite slabs. A transient problem arising from surface insulation is examined and analytical solutions derived from the first model are compared with numerical solutions derived from the second.

Analytical Solutions to the Problem of Transient Heat Transfer in Living Tissue

1978 ◽  
Vol 100 (4) ◽  
pp. 202-210 ◽  
Author(s):  
A. Shitzer ◽  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Temperature Profile ◽  
Analytical Solutions ◽  
Biological Tissue ◽  
Geometrical Parameter ◽  
Convective Transport ◽  
Transient Heat Transfer ◽  
Living Tissue ◽  
Cylindrical Coordinates

An analytical model of transient heat transfer in living biological tissue is considered. The model includes storage, generation, conduction, and convective transport of heat in the tissue. Solutions for rectangular and cylindrical coordinates are presented and discussed. Transient times for reaching the “locally fully developed” temperature profile were found to be of the order of 5–25 min. These transients are dominated by a geometrical parameter and, to a lesser extent, by a parameter representing the ratio of heat supplied by blood flow to heat conducted in the tissue.

Analytical Prediction of the Heat Transfer From a Blood Vessel Near the Skin Surface Cooled by a Symmetrical Strip

1975 ◽  
Vol 97 (1) ◽  
pp. 61-65 ◽  
Author(s):  
J. C. Chato ◽  
A. Shitzer
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Steady State ◽  
Carotid Artery ◽  
Blood Vessel ◽  
Analytical Method ◽  
Skin Surface ◽  
Analytical Prediction ◽  
Flow Through ◽  
Optimum Width

A steady-state analytical method has been developed to estimate the amount of heat extracted from a blood vessel running close to the skin surface which is cooled in a symmetrical fashion by a cooling strip. The results indicate that the optimum width of a cooling strip is approximately three times the depth to the centerline of the blood vessel. The heat extracted from a blood vessel similar to the carotid artery by such a strip is about 0.9 w/m-deg C, which is too small to affect significantly the temperature of the blood flow through a main blood vessel, such as the carotid artery.

scholarly journals Thermal Step Response of N-Layer Composite Walls—Accurate Approximative Formulas

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Carl-Eric Hagentoft ◽  
Simon Pallin
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Flow ◽  
Numerical Solutions ◽  
Step Change ◽  
Step Response ◽  
Surface Boundary ◽  
Multilayer Composites ◽  
Flow Through ◽  
Multiple Variables

Abstract For many industrial applications, heat flow through composites relates directly to energy usage and thus is of highest interest. For multilayer composites, the heat flow is a result of multiple variables, such as the temperature gradient over the surface boundaries and each material's thermal conductivity, specific heat, and thickness. In addition, the transient heat flux also depends on how the materials are aligned together. The heat flow through composites can be estimated using advanced computer simulations for applied heat transfer. Although these tools are powerful, they are also time consuming. Therefore, approximations that allow the estimation of heat flow through composites can be very useful. This paper presents approximations to solve transient heat transfer in multilayer composites, with and without an interior surface resistance. Since the energy use for various applications relates to the heat transferred at the surface boundary, the main focus of this paper is to define approximate solutions for interior heat flow. In other words, these approximations are found by applying a unit step change in temperature on one side of a composite and then in real-time emulating the surface heat flux on the opposite side from which the step change occurs. The approximations are presented based on lumped analyses and Laplace network solutions and are validated against analytical and numerical solutions.

scholarly journals ANALYTICAL STUDY FOR THE BOUNDARY LAYER FLOW IN THE PRESENCE OF HEAT TRANSFER THROUGH A POROUS MEDIUM

2021 ◽  
Vol 8 (65) ◽  
pp. 15142-15146
Author(s):  
Ram Naresh Singh
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Finite Difference Schemes ◽  
Local Similarity ◽  
High Porosity ◽  
Flow Through ◽  
Layer Flow

In this paper we study a problem of the boundary layer flow through a porous media in the presence of heat transfer. Here we consider high porosity bounded by a semi-infinite horizontal plate. The main aim of this study is to point out local similarity transformations for the boundary layer flow, through a homogeneous porous medium. Here we applying finite difference schemes to find out the numerical solutions of the problem. The free stream velocity and the temperature far away from the plate are exponential function of variables.

scholarly journals Groundwater flow equation, overview, derivation, and solution

2021 ◽  
Vol 314 ◽  
pp. 04007
Author(s):  
Lhoussaine El Mezouary ◽  
Bouabid El Mansouri
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Groundwater Flow ◽  
Numerical Solutions ◽  
Flow Equation ◽  
Heat Transfer Equation ◽  
Flow Equations ◽  
Basic Law ◽  
Flow Through ◽  
Groundwater Flow Equation

Darcy’s law is the basic law of flow, and it produces a partial differential equation is similar to the heat transfer equation when coupled with an equation of continuity that explains the conservation of fluid mass during flow through a porous media. This article, titled the groundwater flow equation, covers the derivation of the groundwater flow equations in both the steady and transient states. We look at some of the most common approaches and methods for developing analytical or numerical solutions. The flaws and limits of these solutions in reproducing the behavior of water flow on the aquifer are also discussed in the article.

Analytical Solutions for Heat Transfer During Cyclic Melting and Freezing of a Phase Change Material Used in Electronic or Electrical Packaging

2003 ◽  
Vol 125 (1) ◽  
pp. 126-133 ◽  
Author(s):  
Suman Chakraborty ◽  
Pradip Dutta
Keyword(s):  
Heat Transfer ◽  
Phase Change ◽  
Phase Change Material ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Electronics Cooling ◽  
Form Solution ◽  
Transfer Model ◽  
Change Material

In this paper, we develop an analytical heat transfer model, which is capable of analyzing cyclic melting and solidification processes of a phase change material used in the context of electronics cooling systems. The model is essentially based on conduction heat transfer, with treatments for convection and radiation embedded inside. The whole solution domain is first divided into two main sub-domains, namely, the melting sub-domain and the solidification sub-domain. Each sub-domain is then analyzed for a number of temporal regimes. Accordingly, analytical solutions for temperature distribution within each sub-domain are formulated either using a semi-infinity consideration, or employing a method of quasi-steady state, depending on the applicability. The solution modules are subsequently united, leading to a closed-form solution for the entire problem. The analytical solutions are then compared with experimental and numerical solutions for a benchmark problem quoted in the literature, and excellent agreements can be observed.

scholarly journals UNSTEADY TWO-LAYERED BLOOD FLOW THROUGH A -SHAPED STENOSED ARTERY USING THE GENERALIZED OLDROYD-B FLUID MODEL

2016 ◽  
Vol 58 (1) ◽  
pp. 96-118 ◽  
Author(s):  
AKBAR ZAMAN ◽  
NASIR ALI ◽  
O. ANWAR BEG ◽  
M. SAJID
Keyword(s):  
Blood Flow ◽  
Differential Equations ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Initial Boundary ◽  
Momentum Conservation ◽  
Rheological Parameters ◽  
Stenosed Artery ◽  
Flow Through

A theoretical study of an unsteady two-layered blood flow through a stenosed artery is presented in this article. The geometry of a rigid stenosed artery is assumed to be$w$-shaped. The flow regime is assumed to be laminar, unsteady and uni-directional. The characteristics of blood are modelled by the generalized Oldroyd-B non-Newtonian fluid model in the core region and a Newtonian fluid model in the periphery region. The governing partial differential equations are derived for each region by using mass and momentum conservation equations. In order to facilitate numerical solutions, the derived differential equations are nondimensionalized. A well-tested explicit finite-difference method (FDM) which is forward in time and central in space is employed for the solution of a nonlinear initial boundary value problem corresponding to each region. Validation of the FDM computations is achieved with a variational finite element method algorithm. The influences of the emerging geometric and rheological parameters on axial velocity, resistance impedance and wall shear stress are displayed graphically. The instantaneous patterns of streamlines are also presented to illustrate the global behaviour of the blood flow. The simulations are relevant to haemodynamics of small blood vessels and capillary transport, wherein rheological effects are dominant.

scholarly journals CONVECTIVE HEAT TRANSFER ON STENOSED BLOOD FLOW THROUGH PERMEABLE MICROCIRCULATION IN THE PRESENCE OF A MAGNETIC FIELD

2020 ◽  
Author(s):  
Alana Sankar ◽  
Sreedhara Rao Gunakala ◽  
Donna Comissiong
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Reynolds Number ◽  
Blood Flow ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Hartmann Number ◽  
Darcy Number ◽  
Flow Through

Blood flow through permeable microcirculation in the presence of a composite stenosis, an external magnetic field and convective heat transfer was examined. A two-layered model for the blood consisting of a fluid-particle suspension in the core region with a peripheral cell-free plasma layer was used. The proposed system of equations was solved and plots were generated. In the presence of permeable walls, an external magnetic field and convective heat transfer, the temperature of the blood, friction-factor Reynolds number and Nusselt number were investigated. The temperature of the blood increased when the Hartmann number increased, Darcy number increased, haematocrit level increased or the peripheral layer thinned. The friction-factor Reynolds number product increased as the haematocrit, Hartmann number, stenosis height or Darcy number increased. The Nusselt number decreased as the Hartmann number, haematocrit, stenosis height or Darcy number increased. These results were interpreted in terms of the physical situation. This study aids in understanding the effects of wall permeability, a magnetic field and the presence of heat transfer on different diseased arterial systems in the future.

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