Effect of an Axial Cavity on the Temperature History of a Surface Heated Slab

Abstract

A theoretical study is made of the surface temperature of a front heated slab in the presence of small holes drilled to within a fraction of a centimeter of the heated surface. In addition, equations and calculations are presented which yield an estimate of the error incurred when the surface temperature is measured by a transducer located at the end of such a hole. In the absence of a practical exact solution to the problem, the method of attack chosen here leads to an upper bound on the additional surface temperature or hot spot caused by a cavity. The upper bound is justified because it is a close upper bound and, for cavity dimensions in the range of interest, the resulting hot spot is quite small. It is shown, for instance, that a ½-mm hole drilled to within 1 mm of the exposed surface will cause a time variant surface hot spot that is no more than 1.5% of the surface temperature. If the hole depth is reduced to ½ mm, then the hot spot is less than 5.5% of the surface temperature. An additional finding is that the magnitude of the hot spot is nearly independent of the temporal shape of the surface heat pulse for a large variance in the latter.

A compensation method for the disturbance in the temperature field caused by subsurface thermocouples

“…[2] was then solved by considering boundary conditions [3] through [8] and initial condition [9] using the Crank-Nicholson method with time-steps of 0.01 seconds. For the simulations, a variety of simplified material properties were considered for the domain as well as the thermocouple hole.…”

“…The disturbance of the temperature field by a subsurface thermocouple was first investigated by Masters and Stein [2] by considering a cylindrical cavity beneath the heated surface of a semi-infinite solid. An adiabatic plane was inserted at a depth corresponding to the base of the thermocouple hole, and, using the superposition principle, a heat flux was added in the direction opposite to the original flow of heat, i.e., back toward the heated surface.…”

“…This leads to a significantly greater cooling at the thermocouple tip and hence to a temperature discrepancy compared to the undisturbed case, i.e., the temperature measured at the same location in a sample without a thermocouple. The disturbance created by subsurface thermocouples was observed in the so-called hot spot formed at the surface of aerospatial components exposed to heating during re-entry [2] as well as in instrumented samples used to simulate various metallurgical processes (direct-chill casting of light metals, quenching of steel plates, and tubes). [3] This article investigates the temperature discrepancy caused by the disturbance of the thermal field by subsurface thermocouples.…”

Quantification of the Surface Temperature Discrepancy Caused by Subsurface Thermocouples and Methods for Compensation

“…The Biot number is commonly used to compare the internal thermal resistance to the external thermal resistance, as presented in Eq. [1]:…”

“…These hot spots were first documented and investigated by Masters and Stein. [1] The disturbance in the temperature field was estimated by using the superposition principle, or by reflecting the heat flux flowing onto the TC tip plane back toward the heated surface. The superposition principle assumes that the TC tip resembles an adiabatic plane, and that the disturbance in temperature is a result of the reflected heat flux that would have otherwise flowed through had there been no TC present.…”