Introduction To determine the temperature differences encountered in the flow of heat within electronic systems, it is necessary to recognize the relevant heat transfer mechanisms and their governing relations. In a typical system, heat removal from the active regions of the microcircuit(s) or chip(s) may require the use of several mechanisms, some operating in | CHAPTER 54__ COOLING ELECTRONIC EQUIPMENT Allan Kraus Allan D. Kraus Associates Aurora Ohio THERMAL MODELING 1649 Forced Convection 1662 Introduction 1649 Conduction Heat THERMAL CONTROL Transfer 1649 TECHNIQUES 1667 Convective Heat Extended Surface and Transfer 1652 Heat Sinks 1672 Radiative Heat Transfer 1655 The Cold Plate 1672 Chip Module Thermal Resistances 1656 Thermoelectric Coolers 1674 HEAT-TRANSFER CORRELATIONS FOR ELECTRONIC EQUIPMENT COOLING 1661 Natural Convection in Confined Spaces 1661 THERMAL MODELING Introduction To determine the temperature differences encountered in the flow of heat within electronic systems it is necessary to recognize the relevant heat transfer mechanisms and their governing relations. In a typical system heat removal from the active regions of the microcircuit s or chip s may require the use of several mechanisms some operating in series and others in parallel to transport the generated heat to the coolant or ultimate heat sink. Practitioners of the thermal arts and sciences generally deal with four basic thermal transport modes conduction convection phase change and radiation. Conduction Heat Transfer One-Dimensional Conduction Steady thermal transport through solids is governed by the Fourier equation which in onedimensional form is expressible as q -kA W dx where q is the heat flow k is the thermal conductivity of the medium A is the cross-sectional area for the heat flow and dT dx is the temperature gradient. Here heat flow produced by a negative temperature gradient is considered positive. This convention requires the insertion of the minus sign in Eq. to assure a positive heat flow q. The temperature difference resulting from the steady state diffusion of heat is thus related to the thermal conductivity of the material the cross-sectional area and the path length L. according to Tt T2 cd q K .
