Im Folgenden wird die analytische Lösung der eindimensionalen, instationären Wärmeleitungsgleichung mit einer Randbedingung 3. Art gegeben. Die Außentemperatur wird dabei als harmonische Schwingung angenommen. Abhängig von den materialspezifischen Eigenschaften des Bauteils (Wärmeleitfähigkeit, Rohdichte, spezifische Wärmekapazität) kommt es zur Dämpfung und zeitlichen Verschiebung der Temperaturwelle im Bauteil. Die analytische Lösung liefert den raum- und zeitaufgelösten Temperaturverlauf innerhalb des Bauteils. Die analytische Lösung ist primär für die Kalibrierung und Validierung numerischer Approximationsverfahren relevant. Die zeitliche Verfügbarkeit von thermischer Speichermasse ist für die thermische Gebäude- und Raumsimulation von besonderer Wichtigkeit. Daher muss ein numerisches Berechnungsverfahren diese Prozesse gut abbilden können. Die hier gezeigte analytische Lösung kann daher zur Bewertung der Güte der gewählten numerischen Approximation verwendet werden. Zu diesem Zweck werden Ergebnisse beispielhaft für zwei getrennte Konstruktionen angegeben.

The field of low-dimensional quantum magnets has received lot of attention owing to the possibility of studying phenomena associated with the quantum nature of matter. Many materials that realize low-dimensional spin arrangements in their structure have been synthesized in the past twenty years due to the emergence and development of crystal growth techniques. These materials have been studied using various experiments in order to explore the wide range of interesting properties predicted theoretically for low-dimensional systems. In this pursuit, novel properties have been observed and many open questions have been raised. One such property that is typically observed in many low-dimensional quantum magnets is heat transport via magnetic excitations. Large magnitudes of magnetic heat conductivity has been found experimentally in materials belonging to this class in addition to the conventionally known phononic heat conduction, and interesting theoretical predictions like the divergence of heat conductivity in certain spin models exist, that have stimulated research in this field. This experimental work mainly deals with the crystal growth and heat transport properties of low-dimensional quantum magnets that include one-dimensional (1D) spin chain systems Sr$_2$CuO$_3$ and SrCuO$_2$, two-dimensional (2D) Heisenberg antiferromagnet La$_2$CuO$_4$, and a five-leg spin ladder La$_8$Cu$_7$O$_{19}$, with a view to understand propagating low-energy magnetic excitations and their interaction amongst themselves, other quasiparticles and impurities present in the systems. These interactions result in scattering processes that govern the magnitude and temperature dependence of heat conductivity. In spite of considerable theoretical and experimental work in the field of heat transport, a complete understanding of the scattering mechanisms is lacking. The work tries to add to the experimental knowledge about magnetic heat transport in such systems and presents cases which motivate the need for theoretical understanding of aspects of heat transport. The focus of this work was twofold. One part focusses on the single crystal growth using the travelling-solvent floating zone (TFSZ) method of materials which realize low-dimensional spin systems in their structure. The TFSZ method is indispensable for growing large single crystals of extraordinary purity, which can be used for investigations using neutrons and other techniques like heat conductivity measurements that probe anisotropic properties. The other part deals with the experimental results on heat transport and other thermodynamic properties of these materials. In order to study the behaviour of the magnetic heat conductivity at high temperatures, and the effect of small amount of magnetic and non-magnetic impurities on the heat transport of 2D Heisenberg antiferromagnet La$_2$CuO$_4$, single crystals of pure La$_2$CuO$_4$, and Ni- and Zn-doped versions, La$_2$Cu$_x$Ni$_{1-x}$O$_4$ and La$_2$Cu$_x$Zn$_{1-x}$O$_4$ for $x$ = 0.001 and 0.003, were grown using the TFSZ method. Heat transport in the pure compound was experimentally investigated for the first time up to very high temperatures of 813 K using two methods, namely the steady state method for low temperatures and the dynamic flash method for measuring high temperature conductivity. Analysis of the magnon mean-free path using empirical models based on semi-classical theories, and qualitative comparison to theoretical calculations seems to suggest that scattering between magnons might play an important role in addition to scattering of magnons with phonons and defects, and that the spin-spin correlation length could be crucial in limiting the mean free path of magnons at high temperatures. These experimental results and indications of probable scattering mechanisms based on non-rigorous analyses and comparisons, strongly motivate the need for theoretical studies. Heat conductivity measurements on the Ni- and Zn- doped versions of La$_2$CuO$_4$ are still incomplete and inconclusive, and hence have not been reported in this work. Heat transport experiments on Ni- and Ca-doped Sr$_2$CuO$_3$ were performed, with a motivation to investigate the role of disorder induced by impurities lying within the spin chains (Ni) and those lying outside the spin chains (Ca), on the heat transport in this system. In both the cases, the magnetic heat transport is observed to be strongly suppressed upon doping. Empirical analysis of the data seems to suggest that in the temperature regime of 100-300 K, the temperature dependence of the mean-free path of magnetic excitations for the Ni- and Ca-doped samples can be described by scattering with defects (Ni and Ca impurities) and phonons alone. However, surprisingly, a strong increase of phononic conductivity is observed perpendicular and parallel to the spin chains of the Ni-doped compounds compared to the pure compounds, whose explanation seems to lie in the existence of an additional dissipative scattering mechanism present in the pure compounds that is lifted upon doping, possibly due to the presence of a spin gap in the doped compounds. The effect of Ni on the Sr$_2$CuO$_3$ and SrCuO$_2$ was also investigated by studying the low energy regime of the spin excitation spectrum using other microscopic probes like nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS). Large single crystals of SrCu$_x$Ni$_{1-x}$O$_2$, with $x$ = 0.01 were grown and used in these experiments that observed the presence of a spin gap in the Ni-doped sample. Further theoretical investigations are however required to understand the possible role of the spin gap in influencing the spin-phonon scattering mechanism, and its relevance to the observed enhancement in phononic conduction. Although we observe that in the case of both 1D and 2D systems, a semi-classical kinetic model for heat transport along with empirical models of scattering processes describe the temperature dependence of the measured heat conductivity surprisingly well in the temperature regime up to 300 K and 800 K respectively, interpretations based on these analyses must be treated as only preliminary, and as a step towards understanding microscopically the scattering mechanisms involved in low-dimensional systems such as the ones discussed in this work. In the direction of exploratory research towards synthesis of novel low-dimensional materials, two cuprate compounds were synthesized in the form of single crystals using the floating zone method for the first time, namely, a five leg $S=tfrac{1}{2}$ antiferromagnetic spin ladder compound La$_8$Cu$_7$O$_{19}$ and an insulating delafossite LaCuO$_{2}$. A bulk 3D antiferromagnetic ordering is observed in La$_8$Cu$_7$O$_{19}$. Heat conductivity of La$_8$Cu$_7$O$_{19}$ is observed to be purely phononic and no contribution from magnetic excitations seem to exist, although the measurements indicates that there is a large anisotropy in heat transport. However, detailed diffraction experiments using x-rays and neutrons indicate that both the crystal and magnetic structures are complicated, and that the details of the structure prevent La$_8$Cu$_7$O$_{19}$ from being a perfect realization of a five-leg spin ladder.