A thermomechanical model of solidification on a plane wall with a single asperity of arbitrary shape

A thermomechanical model of solidification on a plane wall with a single as perity of arbitrary shape f(x), where x is measured along the wall, is pres ented. We shall assume that f(x) --> 0 as x --> +/-infinity. The ratio of t he asperity amplitude to a representative measure of the asperity width is assumed to be much less than one and, hence, is a convenient perturbation p arameter. The molten fluid is assumed to wet the asperity surface perfectly at initial time and to remain quiescent during the process. Solidification begins when the asperity surface temperature is lowered to some value T-0 below the freezing temperature. Deformation of the solidifying shell is ass umed to follow a thermohypoelastic constitutive law that is a rate formulat ion of thermoelasticity. The temperature and stress fields are calculated u sing a stress function approach. The contact pressure profile at the shell/ asperity interface, which is indicative of shell distortion due to the aspe rity geometry, is obtained from the stress field. It is shown that at very early times in the solidification process, the contact pressure is a minimu m at positions of maximum positive curvature and a maximum at positions of minimum positive (i.e., maximum negative) curvature. Idealized asperity geo metries represented by Gaussian, triangular, and trapezoidal profiles are e xamined.