Heat transfer in a hydromagnetic flow over a stretching sheet

Exact solutions are obtained for the heat transfer in an electrically conducting fluid past a stretching sheet subjected to the thermal boundary with either a prescribed temperature or a prescribed heat flux in the presence of a transverse magnetic field. The solutions for the heat transfer characteristics are evaluated numerically for different parameters, such as the magnetic parameterN, the Prandtl numberPr, the surface temperature indexs, and the surface heat flux indexd. It is observed that for the prescribed surface temperature case the fluid temperature increases due to the existance of the magnetic field, and decreases as the Prandtl number or the surface temperature index increases; for the prescribed surface heat flux case, the surface temperature decreases as the Prandtl number of the surface heat flux index increases, and the magnetic parameter decreases. In addition, varying the prescribed surface temperature indexs affects the mechanism of heat transfer.     

Heat transfer from a stretching sheet in hydromagnetic flow

An exact solution has been found out for the conjugate problem of cooling of a stretching sheet in an electrically conducting fluid in presence of an imposed magnetic field. Temperature distributions in the sheet as well as in the ambient medium have been obtained and the explicit convergence criterion for the solutions has been established.

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Wärmeübergang an einer gedehnten Membran bei hydromagnetischer Strömung

Zusammenfassung Für das Problem der Abkühlung einer gedehnten Membran in einer elektrisch leitenden Flüssigkeit in Gegenwart eines angelegten magnetischen Feldes wurde eine exakte Lösung gefunden. Die Temperaturverteilung wurde sowohl in der Membran als auch im umgebenden Medium erfaßt und ein eindeutiges Konvergenzkriterium für die Lösung festgelegt.

     

Heat transfer on a cylinder in accelerated slip flow

The axisymmetric laminar boundary layer flow along the entire length of a semi-infinite stationary cylinder under an accelerated free-stream is investigated. Considering flow at reduced dimensions, the boundary layer equations are developed with the conventional no-slip boundary condition for tangential velocity and temperature replaced by a linear slip-jump boundary condition. Asymptotic series solutions are obtained for the heat transfer coefficient in terms of the Nusselt number. These solutions correspond to prescribed values of the momentum and temperature slip coefficients and the index of acceleration. Heat transfer at both small and large axial distances is determined in the form of series solutions; whereas at intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the heat transfer along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip.     

Heat transfer in stagnation-point flow towards a stretching sheet

 Steady two-dimensional stagnation-point flow of an incompressible viscous fluid over a flat deformable sheet is investigated when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that for a fluid of small kinematic viscosity, a boundary layer is formed when the stretching velocity is less than the free stream velocity and an inverted boundary layer is formed when the stretching velocity exceeds the free stream velocity. Temperature distribution in the boundary layer is found when the surface is held at constant temperature and surface heat flux is determined. Received on 12 July 2000 / Published online: 29 November 2001     

Heat transfer in unsteady laminar flow through a channel

The temperature distribution in unsteady laminar flow of a viscous incompressible fluid in a flat channel is investigated, when the pressure gradient is an arbitrary function of time. Two techniques are presented (i) explicit finite difference scheme, and (ii) Chebyshev polynomial solution. Using both the techniques, several cases of pressure gradient are considered, with special attention paid to the linearly varying case.     

Heat transfer in magnetohydrodynamic flow near a stagnation point

Summary Steady, axisymmetric, magnetohydrodynamic flow with a stagnation point on an infinite plane wall is considered with a magnetic field applied normal to the wall. Solutions are obtained in the form of series for the velocity, magnetic field and temperature when the magnetic field parameter () and the ratio of viscosity to magnetic diffusivity () are small. The case=O(1) is considered briefly when solutions which Meyer³⁾ obtained by physical order-of-magnitude arguments are derived mathematically as expansions in. Some remarks are made on the consistency of extending the results to flow within the boundary layer near the nose of a bluff body.     

Effect of streamwise structures on heat transfer in a hypersonic flow in a compression corner

Coefficients of heat transfer to the surface in a laminar hypersonic flow (M _∞ = 21) over plane and axisymmetric models with a compression corner are presented. These coefficients are measured by an infrared camera. The parameters varied in the experiments are the angle of the compression corner and the distance to the corner point. Characteristics of the flow with and without separation in the corner configuration are obtained. The measured results are compared with direct numerical simulations performed by solving the full unsteady Navier-Stokes equations. Experiments with controlled streamwise structures inserted into the flow are described. A substantial increase in the maximum values of the heat-transfer coefficient in the region of flow reattachment after developed laminar separation is demonstrated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 112–120, July–August, 2009.     

Heat transfer analysis of a particle-containing channel flow

This paper describes an analytical model of heat transfer in a two-dimensional, steady, nonreacting particle-containing channel flow. An idealized gas flow of specified uniform velocity between insulated parallel plates is assumed and the nonvaporizing particles are conceptualized as contained within an thin sheet injected at the symmetry plane. Two dimensionless parameters that affect the solution are described. These are the effective gas diffusivityK and the dimensionless particle number densityP. The linear, coupled differential equations governing the energy exchange between the gas and liquid phases are solved by means of the Green's function technique. This procedure yields a Volterra integral-series equation as the solution of the gas-phase energy equation. A series solution of this integral equation is obtained by the method of successive substitutions and terms up to second order are calculated.     

Heat transfer of gas-particle flow in a supersonic convergent-divergent nozzle

Summary Heat flux, wall heat transfer coefficients, and wall pressures are determined for high velocity flow of gas-solid mixtures in a converging-diverging nozzle. Flow separation accompanied with oblique shock formation occurs in the diverging section of the nozzle. The shock strength is reduced upon the addition of solid particles. The wall pressure in the convergent section of the nozzle appears unaffected by the presence of solid particles. In the divergent section, however, the wall pressure is slightly lowered. At the maximum ratio of solid to air flow used in the experiments (3.7) increases in the heat transfer rate of up to 20 and 50 percent are obtained in the convergent and separated (divergent) regions of the nozzle, respectively. Slightly larger increases in the wall heat transfer coefficients are also obtained. It is concluded that the wall heat flux and heat transfer coefficients are influenced strongly by the presence of disturbances upstream of the nozzle inlet.Nomenclature W _a air flow rate - W _s solids flow rate - x axial distance from nozzle entrance - L axial length of nozzle - specific heat ratio of fluid - A _e exit cross section of flow - A _* throat cross section of flow - P ₀ inlet pressure - P _s wall separation pressure - P _a ambient exhaust pressure - shock wave angle - shock wave deflection angle - M ₁ Mach number upstream of shock wave - Mach number normal to shock wave - q heat flux - k _f thermal conductivity of fluid - T _wi inside wall temperature - T _wo outside wall temperature - T _ad adiabatic wall temperature - h wall heat transfer coefficient - C nozzle constant - A local cross section of flow - c _p specific heat of fluid - Pr Prandtl number - viscosity of fluid - r _c throat radius of curvature - factor accounting for variation of and Units absolute temperature °R(ankine) °F+459.7 - conductivity 1 BTU (hr ft °F)^–1 4.137×10^–3 cal (s cm °C)^–1 - specific heat 1 BTU (1b °F)^–1 1 cal (g °C)^–1 - absolute pressure 1 psia 0.0680 atm Supported in part by aid provided by the UCLA Space Science Center (Grant NsG 236-62 Libby).Listed for readers not familiar with the units adopted in this paper (editor).     

Heat transfer in supersonic flow over a single spherical cavity

The flow and heat transfer on a plate with a single spherical cavity has been experimentally investigated for M=4 and Re_,L=3.1 · 10⁶. The flow pattern over the cavity has been obtained. Zones of enhanced heat transfer have been detected, and the heat transfer coefficients in and near the cavity have been determined. It has been established that a single spherical cavity has almost no effect on the integral heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 48–52, September–October, 1991.The authors are grateful to V. N. Brazhko for assistance in carrying out the experiments and to T. A. Ershova for assistance in analyzing the results.     

Heat transfer by laminar flow from a rotating sphere

Summary The heat transfer problem for the flow of an incompressible viscous, heat-conducting fluid, due to uniform rotation about a diameter of a sphere, which is kept at a constant temperature, has been solved with viscous dissipation included. Due to inflow at the poles the cooler liquid is drawn from infinity towards the rotating sphere and this causes a lowering of the temperature there. After flowing in the boundary layer of the sphere the liquid gets heated up and causes a rise in temperature near the equator. Numerical results are given in case of water (Prandtl number σ=5), and it is found that the isothermals are surfaces of revolution flattened at the poles and elongated near the equator. The thermal and the velocity boundary layers turn out to be of the same order of magnitude.     

Heat transfer in a flow past a semi-in-finite plate with oscillating temperature

The response of laminar boundary layer flow past a semi-infinite flat plate to harmonic oscillations in the plate temperature in the form of a travelling wave convected in the direction of the free-stream has been studied here. Series solutions in terms of the small amplitude and the small oscillations to the non-linear system have been derived and the resulting nonlinear ordinary equations due to usual similarity transformations are solved numerically. The function affecting the temperature is shown on a graph. Due to greater viscous dissipative heat the function K ₁, increases and it decreases with increasing Prandtl number. Also the time averaged heat flux function K ₁(0) increases with Prandtl number and decreases due to greater viscous dissipative heat.