Moving Sheet With Variable Thermal Conductivity Emerging From a Slot

2007 ◽  
Author(s):  
O. Bautista ◽  
E. Bautista ◽  
F. Me´ndez
Keyword(s):  
Thermal Conductivity ◽  
Thermal Conductance ◽  
Variable Thermal Conductivity ◽  
Heat Transfer Process ◽  
Point Of View ◽  
Dimensional Parameter ◽  
Parameter Identifying ◽  
Longitudinal Coordinate ◽  
Transverse Temperature ◽  
Non Linear System

In this work, we treat the heat transfer process of a continuously moving flat sheet with variable thermal conductiviy, emerging from a slot in contact with a quiescent fluid. Due to the thermal conductivity of the sheet, strong longitudinal and transverse temperature gradients arise within it, requiring to solve simultaneously the energy equation of the sheet and fluid equations. The momentum and energy balance equations are reduced to a non-linear system of partial differential equations with four parameters: the Prandtl number, Pr, a non-dimensional sheet thermal conductance β, a non-dimensional parameter identifying the effect of the variable thermal conductivity γ and a suitable Peclet number, Pe. For finite values of the parameter γ we recognize the limits β≪1 and βPe2≪1 as the most relevant from a practical point of view. In this case, the problem is governed by an universal integro-differential equation in order to obtain the spatial evolution of the sheet temperature as a function of the nondimensional longitudinal coordinate.

Darcy-Forchheimer flow with variable thermal conductivity and Cattaneo-Christov heat flux

2016 ◽  
Vol 26 (8) ◽  
pp. 2355-2369 ◽  
Author(s):  
T. Hayat ◽  
Taseer Muhammad ◽  
Saleh Al-Mezal ◽  
S.J. Liao
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Velocity Field ◽  
Thermal Relaxation ◽  
Heat Transfer Process ◽  
Relaxation Parameter ◽  
Content Type ◽  
Opposite Behavior ◽  
Non Linear System ◽  
Forchheimer Flow

Purpose The objectives of present communication are threefolds. First is to model and analyze the two-dimensional Darcy-Forchheimer flow of Maxwell fluid induced by a stretching surface. Temperature-dependent thermal conductivity is taken into account. Second is to examine the heat transfer process through non-classical flux by Cattaneo-Christov theory. Third is to derive convergent homotopic solutions for velocity and temperature distributions. The paper aims to discuss these issues. Design/methodology/approach The resulting non-linear system is solved through the homotopy analysis method. Findings An increment in Deborah number β causes a reduction in velocity field f′(η) while opposite behavior is observed for temperature field θ(η). Velocity field f′(η) and thickness of momentum boundary layer are decreased when the authors enhance the values of porosity parameter λ while opposite behavior is noticed for temperature profile θ(η). Temperature field θ(η) is inversely proportional to the thermal relaxation parameter γ. The numerical values of temperature gradient at the sheet − θ′(0) are higher for larger values of thermal relaxation parameter γ. Originality/value To the best of author’s knowledge, no such consideration has been given in the literature yet.

Experimental and numerical study on the solar gain and heat loss of typical existing and refurbished German buildings

2020 ◽  
pp. 75-93
Author(s):  
Peter Steininger ◽  
Matthias Gaderer ◽  
Belal Dawoud
Keyword(s):  
Thermal Conductivity ◽  
Numerical Study ◽  
Thermal Conductance ◽  
Estimation Procedure ◽  
Heat Transfer Process ◽  
Simulation Software ◽  
Heat Losses ◽  
Solar Simulator ◽  
Typical Structure ◽  
Existing Building

This communication introduces an experimental setup for investigating the effect of solar radiation on the reduction of transmission heat losses and the steady state thermal conductance of uninsulated and insulated multi-layer wall samples. The setup consists of two adjacent climatic chambers, which share a common wall, in which the multi-layer wall samples are mounted. A solar simulator is applied within the outdoor air climatic chamber, whose radiation spectrum and radiation intensity are approximately equivalent to those of the sun. The first tests have been carried out on a wall sample with a typical structure of existing buildings from the year 1930 in Germany. In addition, a high-performance insulating plaster layer has been applied on a basic test sample (with existing building structure) to replicate and assess the refurbished scenario. Furthermore, a numerical investigation on the transient heat transfer process is carried out by using the simulation software COMSOL Multiphysics®. The experimental results of both uninsulated and insulated wall samples are validated against 1D and 3D models. As seen, the uninsulated wall, whose thermal conductance was experimentally determined to be equal to 1.79 W/(m²K), absorbs a heat flux of 208 W/m² through its external wall surface over a period of 8 hours. A fraction of 9.8 % of the absorbed heat arrives as a gain on the internal wall and reduces the transmission heat losses by 11.7 % over a period of 55 hours. On the other hand, the thermal conductivity of the insulation layer of the refurbished wall sample with micro hollow glass spheres was estimated by a parameter estimation procedure using the 3D model and the obtained experimental data. Using the estimated thermal conductivity, a thermal conductance of 0.42 W/(m²K) has been obtained for the refurbished wall sample.

scholarly journals Numerical simulation of variable thermal conductivity on 3D flow of nanofluid over a stretching sheet

2020 ◽  
Vol 9 (1) ◽  
pp. 233-243 ◽  
Author(s):  
Nainaru Tarakaramu ◽  
P.V. Satya Narayana ◽  
Bhumarapu Venkateswarlu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Variable Thermal Conductivity ◽  
Normal Velocity ◽  
Transfer Coefficients ◽  
Similarity Transformations ◽  
Frictional Coefficients ◽  
The Impact

AbstractThe present investigation deals with the steady three-dimensional flow and heat transfer of nanofluids due to stretching sheet in the presence of magnetic field and heat source. Three types of water based nanoparticles namely, copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are considered in this study. The temperature dependent variable thermal conductivity and thermal radiation has been introduced in the energy equation. Using suitable similarity transformations the dimensional non-linear expressions are converted into dimensionless system and are then solved numerically by Runge-Kutta-Fehlberg scheme along with well-known shooting technique. The impact of various flow parameters on axial and transverse velocities, temperature, surface frictional coefficients and rate of heat transfer coefficients are visualized both in qualitative and quantitative manners in the vicinity of stretching sheet. The results reviled that the temperature and velocity of the fluid rise with increasing values of variable thermal conductivity parameter. Also, the temperature and normal velocity of the fluid in case of Cu-water nanoparticles is more than that of Al2O3- water nanofluid. On the other hand, the axial velocity of the fluid in case of Al2O3- water nanofluid is more than that of TiO2nanoparticles. In addition, the current outcomes are matched with the previously published consequences and initiate to be a good contract as a limiting sense.

scholarly journals Effect of magnetized variable thermal conductivity on flow and heat transfer characteristics of unsteady Williamson fluid

2020 ◽  
Vol 9 (1) ◽  
pp. 338-351
Author(s):  
Usha Shankar ◽  
N. B. Naduvinamani ◽  
Hussain Basha
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Fluid Flow ◽  
Velocity Profile ◽  
Variable Thermal Conductivity ◽  
Flow Index ◽  
Williamson Fluid ◽  
Flow Equations ◽  
Velocity Parameter ◽  
Squeezed Flow

AbstractA two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with variable thermal conductivity and exterior squeezing with viscous dissipation effect is investigated, numerically. Present flow model is developed based on the considered flow geometry. Effect of Lorentz forces on flow behaviour is described in terms of magnetic field and which is accounted in momentum equation. Influence of variable thermal conductivity on heat transfer is considered in the energy equation. Present investigated problem gives the highly complicated nonlinear, unsteady governing flow equations and which are coupled in nature. Owing to the failure of analytical/direct techniques, the considered physical problem is solved by using Runge-Kutta scheme (RK-4) via similarity transformations approach. Graphs and tables are presented to describe the physical behaviour of various control parameters on flow phenomenon. Temperature boundary layer thickens for the amplifying value of Weissenberg parameter and permeable velocity parameter. Velocity profile decreased for the increasing squeezed flow index and permeable velocity parameter. Increasing magnetic number increases the velocity profile. Magnifying squeezed flow index magnifies the magnitude of Nusselt number. Also, RK-4 efficiently solves the highly complicated nonlinear complex equations that are arising in the fluid flow problems. The present results in this article are significantly matching with the published results in the literature.

Effects of variable thermal conductivity and electrical conductivity on flow of williamson nanofluid between two parallel disks

2021 ◽  
Author(s):  
Mazmul Hussain ◽  
Nargis Khan
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Electric Conductivity ◽  
Variable Temperature ◽  
Lewis Number ◽  
Variable Thermal Conductivity ◽  
Industrial Applications ◽  
Weissenberg Number ◽  
Modeling And Analysis ◽  
Variable Nature

The variable nature of the thermal conductivity of nanofluid with respect to temperature plays an important role in many engineering and industrial applications including solar collectors and thermoelectricity. Thus, the foremost motivation of this article is to investigate the effects of thermal conductivity and electric conductivity due to variable temperature on the flow of Williamson nanofluid. The flow is considered between two stretchable rotating disks. The mathematical modeling and analysis have been made in the presence of magnetohydrodynamic and thermal radiation. The governing differential equations of the problem are transformed into non-dimensional differential equations by using similarity transformations. The transformed differential equations are thus solved by a finite difference method. The behaviors of velocity, temperature and concentration profiles due to various parameters are discussed. For magnetic parameter, the radial and tangential velocities have showed decreasing behavior, while converse behavior is observed for axial velocity. The temperature profile shows increasing behavior due to an increase in the Weissenberg number, heat generation parameter and Eckert number, while it declines by increasing electric conductivity parameter. The nanoparticle concentration profile declines due to an increase in the Lewis number and Reynolds number.

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