Prescribed Wall Heat Flux Research Articles

Heat transfer in the thermal entrance region for flow through rectangular porous passages

The study of heat transfer in rectangular passages with prescribed wall heat flux is of practical interest. These passages could be open or filled with saturated porous materials. A solution that uses the Green’s function can accommodate the inclusion of heat flux over the entire surface area or over isolated sections of the boundary. Also, this solution permits the inclusion of frictional heating. Two different boundary conditions are considered: constant wall temperature and constant wall heat flux. The computed heat transfer coefficients show that the thermally fully developed condition may not be attainable in practical applications for very narrow passages with prescribed wall heat flux.

Heat transfer in a visco-elastic fluid past a stretching sheet with viscous dissipation and internal heat generation

This paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of a visco-elastic fluid over a linearly stretching continuous surface with variable wall temperature subjected to suction or blowing. The study considers the effects of frictional heating (viscous dissipation) and internal heat generation or absorption. An analysis has been carried out for two different cases of heating processes namely: (i) Prescribed surface temperature (PST) and (ii) Prescribed wall heat flux (PHF) to get the effect of visco-elastic parameter for various situations. Further increase of visco-elastic parameter is to decrease the skin friction on the sheet. The solutions for the temperature and the heat transfer characteristics are obtained in terms of Kummers function.

Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet

We study the MHD flow and also heat transfer in a viscoelastic liquid over a stretching sheet in the presence of radiation. The stretching of the sheet is assumed to be proportional to the distance from the slit. Two different temperature conditions are studied, namely (i) the sheet with prescribed surface temperature (PST) and (ii) the sheet with prescribed wall heat flux (PHF). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The resulting non-linear momentum differential equation is solved exactly. The energy equation in the presence of viscous dissipation (or frictional heating), internal heat generation or absorption, and radiation is a differential equation with variable coefficients, which is transformed to a confluent hypergeometric differential equation using a new variable and using the Rosseland approximation for the radiation. The governing differential equations are solved analytically and the effects of various parameters on velocity profiles, skin friction coefficient, temperature profile and wall heat transfer are presented graphically. The results have possible technological applications in liquid-based systems involving stretchable materials.

Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective flow and mass transfer over an accelerating surface with a heat source in the presence of suction and blowing in the case of variable viscosity

An analysis has been carried out to obtain the thermal-diffusion and the diffusion-thermo effects on the mixed free-forced convective and mass transfer steady laminar boundary-layer flow over an accelerating surface with a heat source in the presence of suction and blowing. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equations which is solved numerically by applying the shooting method. The results for an impermeable accelerating surface are discussed. The effects of the variable viscosity parameter θr, the thermal diffusion parameter Sr, the diffusion-thermo parameter Df, suction or blowing parameter m, heat flux parameter s and Schmidt number Sc have been examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair. The effects of varying these parameters are studied in the case of a surface with prescribed wall temperature and a surface with prescribed wall heat flux.

The Graetz problem with viscous dissipation for FENE-P fluids

The solution of thermal entry problem for pipe and channel flow of highly viscous liquids having viscoelastic properties, here modeled by the FENE-P constitutive equation, is obtained semi-analytically. Two types of boundary condition are considered, either an imposed wall temperature or a prescribed wall heat flux, and the effects of viscous dissipation are also taken into account. The analysis leads to a Sturm-Liouville problem similar to that found for the simplified Phan-Thien–Tanner fluid with linear stress coefficient, provided an adequate transformation of constitutive variables is performed first. The way to do this is explained and representative results for thermal entry flow of the FENE-P fluid are given.

Combined forced and free flow in a vertical rectangular duct with prescribed wall heat flux

In this paper, combined forced and free convection is studied in a vertical rectangular duct with a prescribed uniform wall heat flux (H2 boundary condition). A different heat flux value for each plane wall is considered; the condition of a uniform wall heat flux throughout the duct results as a special case. The local momentum and energy balance equations are written in a dimensionless form and solved numerically, by means of a Galerkin finite element method. The numerical solution gives the dimensionless velocity and temperature distributions, together with the values of the Fanning friction factor, of the Nusselt number, of the momentum flux correction factor and of the kinetic energy correction factor. These dimensionless parameters are reported as functions of the aspect ratio and of the ratio between the Grashof number, Gr, and the Reynolds number, Re. The threshold values of Gr/ Re for the onset of flow reversal are evaluated.

Non-Newtonian magnetohydrodynamic flow over a stretching surface with heat and mass transfer

An analysis is carried out to study the momentum, mass and heat transfer characteristics on the flow of visco-elastic fluid (Walter's liquid-B model) past a stretching sheet in the presence of a transverse magnetic field. In heat transfer, two cases are considered: 1. The sheet with prescribed surface temperature (PST case); and 2. The sheet with prescribed wall heat flux (PHF case). The solution of equations of momentum, mass and heat transfer are obtained analytically. Emphasis has been laid to study the effects of various parameters like magnetic parameter Mn, visco-elastic parameter k 1, Schmidt number Sc, and Prandtl number Pr on flow, heat and mass transfer characteristics.

Friction dominated, subsonic compressible flow in channels of slowly varying cross section

Abstract Friction dominated, subsonic compressible flow in micro-channels of slowly varying cross-section is treated by developing a perturbation scheme which yields equations of “lubrication” approximation as the first order one. In this context several characteristic problems are encountered, such as isothermal flow, non-isothermal flow with prescribed wall temperature, and non-isothermal flow with prescribed wall heat flux, which includes the adiabatic wall problem as a special case. In all these problems pressure drops to zero while velocity components increase indefinitely at a finite distance along the channel – the phenomenon called “mathematical” choking observed for the first time in isothermal flow between parallel side walls, Schwartz, L.W., 1987. A perturbation solution for compressible viscous channel flows. J. Engrg. Math. 21, 69–86. The problem with prescribed wall heat flux is characterised, as by Shajii, A., Freidberg, J.P., 1996. Theory of law Mach number compressible flow in a channel. J. Fluid. Mech. 313, 131–145, by the existence of a critical heat flux above which the steady flow cannot be maintained. For the same mass flow rate this flux is considerably greater in divergent channels, than in convergent ones. These and other results obtained show how the prevailing viscosity may dramatically alter the flow characteristics in the problem considered, in comparison with more conventional high Reynolds number flows.

Heat and mass transfer over an accelerating surface with heat source in presence of suction and blowing

An analysis is made to determine the heat and mass transfer occurring in the laminar boundary layer on a linearly accelerating surface with temperature dependent heat source subject to suction or blowing. The following cases of surface conditions are studied namely: (1) a surface with prescribed wall temperature and (2) a surface with prescribed wall heat flux. The results are expressed in terms of Kummer’s function. Several closed form analytical solutions are also presented for special conditions. The results for an impermeable accelerating surface are also discussed. Numerical calculations have been carried out for various values of Prandtl number Pr (0.71 for air), suction or blowing parameter m, temperature parameter r, heat flux parameter s and Schmidt number Sc (for H 2, H 2O, NH 3 and CO 2, which are the most common diffusing species with respect to air).

Thermally developing turbulent flow of pseudoplastic fluids within circular tubes

Heat transfer in turbulent forced convection of pseudoplastic fluids is analytically studied, in thermally developing flow within circular tubes subjected to a prescribed wall heat flux. A splitting-up procedure, in conjunction with the so-called sign-count method for numerical solution of the associated eigenvalue problem, are employed to obtain the temperature distributions and consequently, the local Nusselt numbers along the thermal entry and fully developed regions, for different Reynolds and Prandtl numbers and power-law indices.

INTEGRAL TRANSFORM SOLUTION FOR THE FORCED CONVECTION OF HERSCHEL-BULKLEY FLUIDS IN CIRCULAR TUBES AND PARALLEL-PLATES DUCTS

The thermal entry region in laminar forced convection of Herschel-Bulkley fluids is solved analytically through the integral transform technique, for both circular and parallel-plates ducts, which are maintained at a prescribed wall temperature or at a prescribed wall heat flux. The local Nusselt numbers are obtained with high accuracy in both developing and fully-developed thermal regions, and critical comparisons with previously reported

Magnetohydrodynamic heat transfer over a non-isothermal stretching sheet

This paper presents solutions of the energy equation for the boundary layer flow of an electrically conducting fluid under the influence of a constant transverse magnetic field over a linearly stretching non-isothermal flat sheet. Effects due to dissipation, stress work and heat generation are considered. Analytical solutions of the resulting linear nonhomogeneous boundary value problems, expressed in terms of Kummer's functions, are presented for the case of prescribed surface temperature as well as the case of prescribed wall heat flux, both of which are assumed to be quadratic functions of distance. The boundary value problems are also solved by direct numerical integration yielding results in excellent agreement with the analytical solutions.

Possible transformations for natural convection on a vertical flat plate embedded in porous media with prescribed wall heat flux

This study derived the transformation of boundary layer equations for two-dimensional steady natural convection on a vertical wall embedded in porous media. Three different kinds of thermal boundary conditions are prescribed for wall heat flux: uniform distribution, power law variation, and exponential variation. The flow pattern contains three subregions based on the distance along the flat plate. When inertia resistance is ignored, similarity solution exists in case wall heat flux is in linear distribution. The known relationships of uniform wall temperature relative to wall heat flux variation and uniform wall heat flux relative to wall temperature variation in both cases of the pure fluid flow and the pure porous flow can all be obtained in the present transformation.

Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation

An analysis is carried out to study the heat transfer characteristics in the laminar boundary layer of a viscous fluid over a linearly stretching, continuous surface with variable wall temperature subject to suction or blowing. The study considers the effects of frictional heating (viscous dissipation) and internal heat generation of absorption. Two cases are studied, namely (i) the surface with prescribed surface temperature (PST-Case) and (ii) the surface with prescribed wall heat flux (PHF-Case). The solutions for the temperature and the heat transfer characteristics are obtained in terms of Kummer's functions. For large Prandtl numbers (σ), a boundary layer width of 1/σ is noticed in both PST and PHF cases. Furthermore, it is shown that there is no boundary layer type of solution for small Prandtl number.

Heat transfer in an electrically conducting fluid over a stretching surface

An analysis is carried out to study the heat transfer characteristics in an electrically conducting fluid over a stretching sheet with variable wall temperature and internal heat generation or absorption. Two eases are studied, namely, (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed wall heat flux (PHF case). The solutions for the temperature, the heat transfer characteristics and their asymptotic limits for large Prandtl number (σ) are obtained in terms of Kummer's and parabolic cylinder functions. It is shown that asymptotic limits are not possible for small Prandtl number; this is due to the solution changing by O(1) on length scale of 1/σ. For large Prandtl number, a boundary layer of width 1/σ at η = 0 and an internal layer of width ∝1/σ near the turning point are noticed.

Heat transfer in a viscoelastic fluid over a stretching sheet

An analysis is carried out to study the heat transfer characteristics in a viscoelastic fluid over a stretching sheet with frictional heating and internal heat generation or absorption. Two cases are studied, namely (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed wall heat flux (PHF case). The solutions for the temperature, the heat transfer characteristics and their asymptotic limits for large and small Prandtl numbers are obtained in terms of Kummer's and parabolic cylinder functions. For large Prandtl numbers, a boundary layer width of √ 1 Pr is noticed in both PST and PHF cases. Furthermore, it is shown that there is no boundary layer type of solution for small Prandtl number.

Heat transfer in a second-order fluid over a continuous stretching surface

The heat transfer characteristics of a second-order fluid over a continuous stretching surface with internal heat generation or absorption is analyzed. Two cases are studied, namely (i) the sheet with prescribed surface temperature (PST-case) and (ii) the sheet with prescribed wall heat flux (PHF-case). The solution and heat transfer characteristics are obtained in terms of Kummer's functions. For large values of Prandtl number a uniform approximation is given in terms of parabolic cylinder functions with a boundary layer of width\(\sqrt {{1 \mathord{\left/ {\vphantom {1 {\Pr }}} \right. \kern-\nulldelimiterspace} {\Pr }}} \) in both the PST and PHF cases. It is also shown that no boundary layer type solution exists for small Prandtl number.

Mixed convection boundary layer similarity solutions: prescribed wall heat flux

The similarity solutions for mixed convection boundary-layer flow when the wall heat flux is prescribed are analysed in detail in terms of a buoyancy parameterα andm the exponent of the free stream flow. It is shown that forα〉0 the solution approaches the free convection limit, and forα〈0, there is a range ofα,αs〈α〈0, over which dual solutions exist. The nature of the bifurcation atα=αs, and how the lower branch of solutions behaves asα→0− are also considered. It is established that the solution becomes singular asm→1/5 and the nature of this singularity is also discussed, where it is shown that two separate cases have to be treated, namely whenα is of 0(1) and whenα is small. Finally it is shown that form large the solution approaches that corresponding to exponential forms for the free stream and prescribed wall heat flux. Taken all together this information enables a complete description of how the solution behaves over all possible ranges of the parametersα andm to be deduced.

Solution of low péclet number heat transfer with viscous dissipation in the semi‐infinite axial region of a tube via functional analytic methods

Abstract A solution of the extended Graetz problem with prescribed wall heat flux and viscous dissipation in a semi‐infinite axial region of a tube is obtained by functional analytic methods. The energy equation is split into a set of partial differential equations to obtain a self‐adjoint formulism. Then, an algebraic characteristic equation of the eigenvalue problem for an arbitrary velocity profile is obtained by an approximation method in L 2[0, 1]. In addition, a backward recursive formula for calculating the expansion coefficients of the solution is developed.

Laminar forced convection to non-Newtonian fluids in ducts with prescribed wall heat flux

Heat transfer in laminar forced convection to non-Newtonian fluids in thermally developing flow inside circular tubes and parallel plate ducts with prescribed wall heat flux is solved exactly. The local and average Nusselt numbers are determined and accuracy of the existing approximate solutions is examined.