Application of integral transform technique to the transient laminar flow heat transfer in the ducts

Hadiouche, Ahmed; Mansouri, Kacem

doi:10.1016/j.ijthermalsci.2009.05.012

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…An alternative to traditional numerical methods, is the hybrid analytical-numerical method known as the Generalized Integral Transform Technique (GITT) [14], which is based on seeking solutions in terms of orthogonal eigenfunction expansions. Among the recent advancements of GITT solution in internal forced convection problems, one should mention [15], which investigates the effect of periodically varying inlet temperature, [16], which deals with non-Newtonian flows in circular shaped ducts, [17], which presents a solution for non-Newtonian flows in elliptical cross-section ducts, and [18], which investigates the MHD flow and heat transfer within parallel-plates channels. Other recent applications of the GITT include a variety of problems, such as the intensification of thermophysical properties [19] and conjugated convection-conduction problems [20].…”

Section: Introductionmentioning

confidence: 99%

Integral transform solution for heat transfer in parallel-plates micro-channels: Combined electroosmotic and pressure driven flows with isothermal walls

Sphaier

2012

International Communications in Heat and Mass Transfer

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Section: Introductionmentioning

confidence: 99%

Integral transform solution for heat transfer in parallel-plates micro-channels: Combined electroosmotic and pressure driven flows with isothermal walls

Sphaier

2012

International Communications in Heat and Mass Transfer

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“…Moreover, the tube wall temperature of channel flows for particular types of position/time-dependent heat fluxes was studied in the literature [23][24][25][26][27]. A number of studies were conducted on effects of periodic inlet temperature on the heat transfer characteristics of a convective tube flow under step wall temperature [28][29][30][31][32][33]. Most studies on unsteady internal forced convection are limited to homogeneous/ constant boundary conditions at the tube wall, i.e., isothermal or isoflux; a summary of the available studies is presented in Table 1.…”

mentioning

confidence: 99%

Unsteady Internal Forced-Convective Flow Under Dynamic Time-Dependent Boundary Temperature

Fakoor-Pakdaman

Ahmadi

Bahrami

2014

Journal of Thermophysics and Heat Transfer

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A new all-time analytical model is developed to predict transient internal forced-convection heat transfer under arbitrary time-dependent wall temperature. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step wall temperature is generalized for arbitrary time variations in surface temperature using Duhamel's theorem. A harmonic boundary temperature is considered, and new compact closed-form relationships are proposed to predic: 1) fluid temperature distribution; 2) fluid bulk temperature; 3) wall heat flux; and 4) the Nusselt number. An optimum value is found for the dimensionless angular frequency of the wall temperature to maximize the heat transfer rate of the studied unsteady forced-convective process. Such dimensionless parameter depends upon the imposed-temperature angular frequency, fluid thermophysical properties, and tube geometrical parameters. A general surface temperature is considered, and the temperature field inside the medium is obtained using a superposition technique. An independent numerical simulation is performed using ANSYS® Fluent. The comparison between the obtained numerical data and the present analytical model shows good agreement: a maximum relative difference less than 4.9%. NomenclatureA = cross-sectional area, Eq. (13), m 2 a = half-width of spacing between parallel plates, or circular tube radius, m c p = heat capacity, J∕kg · K Fo = Fourier number; αt∕a 2 J = Bessel function, Eq. (6a) k = thermal conductivity, W∕m · K Nu = Nusselt number, ha∕K n = positive integer, Eq. (6b) p = 0 for parallel plate and 1 for circular tube, Eqs. (3) and (14) Pr = Prandtl number (ν∕α) q w = dimensionless wall heat flux Re = Reynolds number, 2Ua∕ν r = radial coordinate measured from circular tube centerline, m T = temperature, K U = velocity magnitude, m∕s u = velocity vector, Eq. (2) x = axial distance from the entrance of the heated section, m y = normal coordinate measured from centerline of parallel plate channel, m α = thermal diffusivity, m 2 ∕s γ = function for circular tube [Eq. (6a)] or for parallel plate [Eq. (6b)] Δφ = thermal lag (phase shift) ζ = dummy X variable η = dimensionless radial/normal coordinate for circular tube equal to r∕a or for parallel plate equal to y∕a θ = dimensionless temperature; T − T 0 ∕ΔT R λ n = eigenvalues, Eq. (6) ν = kinematic viscosity, m 2 ∕s ξ = dummy Fo variable ρ = fluid density, kg∕m 3 ψ = arbitrary function of Fo Ω = imposed-temperature angular frequency, rad∕s ω = dimensionless temperature angular frequency, Subscripts m = mean or bulk value R = reference value s = step wall (surface) temperature w = wall 0 = inlet

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An analytical study of the periodic laminar forced convection of non-Newtonian nanofluid flow inside an elliptical duct

Ragueb

Mansouri

2018

International Journal of Heat and Mass Transfer

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Application of integral transform technique to the transient laminar flow heat transfer in the ducts

Cited by 5 publications

References 23 publications

Integral transform solution for heat transfer in parallel-plates micro-channels: Combined electroosmotic and pressure driven flows with isothermal walls

Integral transform solution for heat transfer in parallel-plates micro-channels: Combined electroosmotic and pressure driven flows with isothermal walls

Unsteady Internal Forced-Convective Flow Under Dynamic Time-Dependent Boundary Temperature

An analytical study of the periodic laminar forced convection of non-Newtonian nanofluid flow inside an elliptical duct

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