Analyzing the viscoelastic characteristics of materials, especially polymers, is essential for understanding their mechanical properties and their capacity to function in different conditions. This paper presents a novel viscoelastic heat transfer model that integrates a memory-based derivative with the Moore–Gibson–Thomson (MGT) equation. The purpose is to examine the viscoelastic characteristics of materials and assess their response to external stresses and deformations over a certain period of time. In addition to incorporating the third-type thermoelastic model that Green and Naghdi provided, the derivation of this thermo-viscoelastic model included the integration of heat flow and its time derivative into Fourier’s equation. To verify and understand the proposed model, it was applied to consider an unbounded viscoelastic semi-space immersed in a uniform magnetic field and exposed to non-Gaussian laser radiation as a heat source. An analysis of computational results was conducted to evaluate how the behavior of the field variables under consideration is affected by viscoelastic coefficients and memory-based derived factors.

分析材料（尤其是聚合物）的粘弹性特性对于了解其机械性能及其在不同条件下的功能能力至关重要。本文提出了一种新颖的粘弹性传热模型，该模型将基于记忆的导数与 Moore-Gibson-Thomson (MGT) 方程相结合。目的是检查材料的粘弹性特性并评估其在一定时间内对外部应力和变形的响应。除了结合 Green 和 Naghdi 提供的第三种热弹性模型外，该热粘弹性模型的推导还包括将热流及其时间导数积分到傅立叶方程中。为了验证和理解所提出的模型，它被用来考虑浸入均匀磁场中并暴露于非高斯激光辐射作为热源的无界粘弹性半空间。对计算结果进行分析，以评估粘弹性系数和基于记忆的导出因素如何影响所考虑的场变量的行为。