The optimal thickness of a wall with convection on one side

Lim, Ji Sun; Bejan, Adrian; Kim, J.H.

doi:10.1016/0017-9310(92)90138-i

Cited by 11 publications

(3 citation statements)

References 1 publication

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“…Although, uniform distribution of insulation material is easy to implement (Bejan, 1993;Bejan et al, 1996), it may be necessary to consider variable insulation thickness over the surface to be insulated when convective and radiative boundary conditions cause variations in heat transfer to or from the ambient along the surface (Lim and Bejan, 1992;Bejan, 1995).…”

Section: Introductionmentioning

confidence: 99%

Optimal insulation of ducts in extraterrestrial applications

Sahin

2004

Int. J. Energy Res.

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SUMMARYOptimum insulation thickness of a circular duct subjected to external radiative heat transfer is studied for a given amount of insulation material. A circular duct through which fluid is transported from one end to the other is considered. The thickness of the insulation is assumed to be linearly varying since this is easy to implement in practice. Thus the slope of the insulation thickness is considered as the parameter for optimum insulation. Variations of the bulk temperature of the fluid as well as the temperature of the outer surface of the insulation are evaluated. It is shown that linearly decreasing insulation thickness with minimum slope provides the best insulation under the radiation heat transfer condition.

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Section: Introductionmentioning

confidence: 99%

Optimal insulation of ducts in extraterrestrial applications

Sahin

2004

Int. J. Energy Res.

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“…On the other hand, only a few papers deal with the propagation of cylindrical thermal waves. Kim [13] and Louis [14] solved the hyperbolic conduction equation for a finite solid cylinder under a non-stationary boundary heat flux. Barletta and Pulvirenti have obtained the temperature field in a solid cylinder with constant as well as exponentially decaying boundary heat flux [15].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Thermal Response in Micromachine under the Thermal Shock

Wang

Song

2011

KEM

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The thermal response for given micromachine with the boundary surface exposed to sudden temperature change is studied by deriving an analytical solution of the hyperbolic heat conduction equation. Using the obtained analytical expression, the temperature profiles at the outer surface and interior of the micro beam are evaluated for various thermal relaxation times. The behaviors of hyperbolic heat propagation in micro beam are analyzed and possible anomalies are discussed by comparing the thermal behaviors of Fourier heat conduction.

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“…1,2 Very few studies can be found in the literature regarding the optimal distribution of insulation thickness. In an effort to minimize the total heat transfer through a wall that is subjected to convective heat loss on one side, Lim et al 3 studied the optimum wall thickness variation using variational calculus. They found that the total heat transfer rate in the case of forced convection can be minimized when the wall thickness decreases in an optimal manner in the direction of ow.…”

Section: Introductionmentioning

confidence: 99%

Optimal Insulation of Structures with Varying Thermal Conductivity

Sahin

1997

Journal of Thermophysics and Heat Transfer

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The optimal distribution of a limited amount of insulation material on a composite structure is obtained. Three cases for the variation of the composite wall thermal conductivity were considered. These are 1) power, 2) linear, and 3) exponential types of variation of wall thermal conductivity with an inplane direction along the surface of the wall. The surfaces of the wall are assumed to either have constant temperatures or be exposed to ambient at given temperatures. The variation of the optimum insulation thickness is shown to be relatively smooth and easily applicable for all three pro les of thermal conductivity. For a certain optimum length of composite structure, optimal distribution of the insulation material provides maximum percent energy savings. Optimal distribution of the insulation material may require partially covering the surface. Fig. 1 Composite wall with varying insulation thickness. Nomenclature a = k 1 L b = kt w/ k 0F = integrand of k = thermal conductivity, W/mK k i = thermal conductivity of insulation material, W/mK k 0 = thermal conductivity of composite wall at x = 0, W/mK k 1 = dimensional constant, 1/m L = length of the composite wall, m q = total heat transfer per unit width of the composite wall, W/m q = local heat ux, W/m 2 q = average heat ux, W/m 2 q min = average minimum heat ux, W/m 2 T = temperature, K T i = inner surface temperature of the composite wall, K T o = outer surface temperature of the composite wall, K t w = thickness of the composite wall, m x = spatial coordinate, m = insulation thickness, m = average insulation thickness, m opt = optimum insulation thickness, m = Lagrange multiplier = x/L = aggregate integral

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The optimal thickness of a wall with convection on one side

Cited by 11 publications

References 1 publication

Optimal insulation of ducts in extraterrestrial applications

Optimal insulation of ducts in extraterrestrial applications

Analysis of the Thermal Response in Micromachine under the Thermal Shock

Optimal Insulation of Structures with Varying Thermal Conductivity

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